Exchange rate forecasting based on oil price fluctuations

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Exchange rate forecasting based on oil price

fluctuations

Bachelor’s thesis in Finance and Organization University of Amsterdam

Faculty of Economics and Business Author: Bart Jägers

Student number: 10624341 Date: June 2016

Field: Finance

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Abstract

This paper investigates whether oil price fluctuations are able to provide reasonable out-of-sample forecasts of the subsequent change in the exchange rate. This will be established according to a simple and a lagged oil-pricing model. The simple model uses the contemporaneous oil-prices for prediction whereas the lagged model uses lagged oil prices. The oil-pricing models are measured for three different frequencies of data, for daily, monthly and quarterly data. In order to assess the quality of the forecasts provided by the oil-pricing models, the forecasts will be compared against forecasts made by two distinctive random-walk benchmarks, one consisting of a drift and one without a drift included. This analysis is performed for four different oil-exporters’ currencies and for four different oil-importers’ currencies with a varying degree of dependence on oil. This is done in order to evaluate the forecasting ability of the oil-pricing models. The general null-hypothesis which is tested is that of equal forecasting ability between the oil-pricing models and the separate RW-benchmarks. The main empirical evidence is that the oil-pricing models are able to outperform the RW-benchmarks, especially for the daily frequency of data. The results for the monthly data frequency were also significant although to a lesser extent. The results for the quarterly data were often insignificant. Furthermore, an additional series of hypotheses is considered in order to optimally allocate the different resulting effects provided by each model and to distribute the different effects for the oil-exporting and oil-importing currencies. Overall, we learn that oil-price fluctuations are able to provide reasonable predictions for the change in the exchange rate and thus that the efficient market hypothesis does not apply to the exchange rate market.

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Statement of originality

This document is written by Bart Jägers who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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1 Introduction

1.1 Oil-price and exchange rates

Oil represents the world’s most important fuel and is also the most widely traded commodity. It is responsible for our modern way of living as it underpins many of today’s products and is crucial to transport systems (UKOG (2015). On the 20th_of

January this year, Besteman (2016) posted an article in the Dutch Financiële Telegraaf regarding the recent oil-price shock and its consequences. The price per barrel of crude oil dropped severely from about $110 to under $30 today due to a large supply shift that began in June in the second quarter of 2014. This is of great importance to many economic agents and the economy as a whole, because of its immediate as well as long-term consequences. For example, this directly affected the consumers’ real income via the lower prices at the gas station, but also affected the costs of many end products of firms in different industries within the manufacturing and transporting sector (Besteman, 2016). This is due to lower costs of production. But the impact goes deeper and beyond the consumers’ wallets. The oil-price shock also affected the balance of payments and the fiscal balance of countries related to oil-export/oil-import (Arezki and Blanchard, 2014). For instance, many oil-exporting countries immediately lost a substantial amount of revenues due to this large price drop, while the opposite occurred for oil-importing countries whose value of oil-imports decreased due to the lower prices, assuming they maintain the same volume of import. This implies that wealth is transferred from oil-exporters to oil-importers which will cause shifts in the balances of the current account of these countries and a subsequent portfolio reallocation in order to recover the net external financial sustainability of oil-exporters (oil-importers) (Arezki and Blanchard, 2014). This reallocation can take place by an appreciation (depreciation) of the real exchange rate in order to improve the trade balance. Thus, there is an economic relationship between the price and the exchange rates of exporting and oil-importing countries.

This paper investigates whether oil-price fluctuations are able to forecast exchange rates. Predictability of exchange rates goes against the efficient market hypothesis. This the concept that at any moment all available information and news is priced in perfectly into the exchange rate (Timmermann and Granger, 2004). However, the market is often not perfectly efficient, meaning that there could be a certain time difference in which economic effects are displayed into the exchange. This provides the opportunity to investigate whether changes in the price of oil are able to forecast the exchange rate and to what extent this occurs. Also important is how fast this effect is incorporated.

1.2 Research and objectives

The research is conducted as follows. First, the predictive ability of changes in oil-prices on several exchange rates with respect to the U.S. Dollar is measured in a simulative out-of-sample analysis. This is done according to two different oil-pricing models. The first model represents a simple linear oil-oil-pricing model and the second model is a lagged oil-pricing model. These models use the change in

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the oil-prices to forecast the change in the exchange rate. Subsequently, for assessing the forecasting quality of these oil-pricing models, the predictions are compared against predictions made by two distinctive random-walk benchmarks, namely a RW-benchmark consisting of a drift-term and a RW-benchmark without the drift term included. This research takes place for three different frequencies of data, namely at the daily, monthly and quarterly frequency. This is done in order to find out if the data frequency is of importance for the forecasting ability of the oil-pricing models. The forecasts provided by the separate oil-pricing models is considered to be of quality if they are able to outperform those provided by the random-walk benchmark models.

The main objective of this research is thus to test whether the exchange rate forecasting ability of the simple and the lagged oil-pricing models are able to outperform that of the two RW-benchmarks. This will be tested according to the following null-hypothesis: there is equal forecasting ability of the exchange rate between the individual oil-pricing models vis-à-vis the random-walk benchmarks. In addition, the second objective is to evaluate the forecasting ability. This involves checking whether the quality of the forecasts provided by the two oil-pricing models is dependent upon the frequency of data and whether the exchange rate is of an oil-exporters’ or an oil-importers’ currency. Also whether this is dependent upon the degree of dependence on oil-trade. Therefore, in this investigation there are 8 countries considered which have different sizes of oil-export/oil-import over total export/import per country. Also, the different countries considered vary in terms of scale of economy for the purpose of measuring a few extremities. These differences between countries are important to take into consideration in the process of evaluating the results why an oil-pricing model is able to outperform the RW-benchmark(s) and also to be able to make a generalizing conclusion. The oil-exporting currencies considered are: the Russian Ruble, the Canadian Dollar, the Norwegian Krone and the Mexican Peso. The oil-importing currencies included are: the Japanese Yen, the Indian Rupee, the South-Korean Kwon and the Singapore Dollar.

1.3 Contribution vis-à-vis the existing literature and main findings

Regarding the existing literature, the vast-majority of empirical research establishes evidence for in-sample forecasting ability of the exchange rate at a long-term horizon. A long-term horizon is considered to be on monthly or quarterly frequency of data. Moreover, a lot of investigations use a different explanatory variable for forecasting the exchange rate instead of the oil-price which is used in this thesis. This paper relates best to the research provided by Ferraro et al. (2015). They use oil-price fluctuations as the explanatory variable for the Canadian- U.S. Dollar exchange rate. They establish evidence for out-of-sample predictability at the short-horizon. The short-horizon is considered to be the daily frequency of data. This thesis provides an additional insight by extending the research provided by Ferraro et al. (2015) by considering a variety of oil-exporting and also oil-importing countries in order to find out if the same conclusion can be derived and possibly generate an explanation for this based on the country-specific differences.

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ability of oil-price fluctuations on the exchange rate vis-à-vis the two random-walk benchmarks. This is mainly found at the daily frequency of data, thus at the short-horizon. But also for the monthly data frequency, although to quite a lesser extent than the daily data frequency. The results break down at the quarterly data frequency. This is by and large in line with the empirical evidence found by Ferraro et al.(2015). However they find that the predictability breaks down for the monthly and quarterly frequency. When evaluating the results in this thesis, it can be concluded that the forecasting ability of the oil-pricing models is dependent upon the frequency of data used. Moreover, it does not seem to be the case that the forecasting ability provided by the oil-pricing models is better for oil-exporters’ currencies. Also, the results were too controversial in order to conclude that the forecasting ability of the oil-pricing models is dependent upon the degree of oil-dependence of the currencies considered. At last it is concluded that the effect of a change in the oil-price is short-lived and has a transitory effect on the exchange rate

1.4 Thesis organization

The remaining part of this paper is organized as follows. Section 2 describes a selection of the existing literature regarding exchange rate forecasting and empirical evidence in detail. Section 3 sets out the different countries in the data set which is used for the investigation and its rationale. Section 4 explains the research method, describes the different oil-pricing models, describes the random-walk benchmarks used for comparison and explains the final test which is used for assessing the forecasting quality for comparison purposes. Section 5 presents the results and inferences reached by the analysis and comparison of the models. Section 6 enumerates a conclusion. Lastly, section 7 presents an appendix containing different graphs and tables containing all the results of the research in this paper.

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2 Literature review

Please recall that the focus of the analysis in this paper lies on determining the forecasting ability of changes in the oil-price for the exchange rates. The quality of the predictability is measured by comparing the forecasts of the oil-pricing models to those provided by two distinctive RW-benchmarks.

This chapter sets forward a selection of the existing literature which can be divided into categories related to the relationship between the oil-price and exchange rates, exchange rate forecasting and forecasting based on oil-price. Subsequently, on the basis of this overview, the research in this paper is optimally positioned in the framework of related literature as a whole.

2.1 Relationship between the oil-prices and exchange rates

Theoretically, the exchange rate of an oil-exporting (oil-importing) country may experience an appreciation (depreciation) when the oil prices go up and a depreciation when the oil prices go down, suggesting that there is a negative relationship between the oil-prices and exchange rates (Akram, 2004). This relationship is also discussed in the following researches.

A research conducted by Armano and Van Norden (1998a,b), revealed a robust and interesting negative in-sample relationship between the contemporaneous real domestic price of oil and the real exchange of Germany, Japan and the U.S. Such a negative relationship would imply that a depreciation in the real exchange rate was caused by higher real energy prices. Obstfeld (2002) also discusses the correlation between the relative export price and the nominal exchange rate for the Canadian – U.S. Dollar. For mineral fuel price indices, Obstfeld finds a positive correlation which implies that the price of U.S. exports relatively to the Canadian exports tends to rise when the Canadian currency depreciates with respect to the U.S. dollar. The research by Armano and Van Norden (1998a,b) and Obstfeld (2002) was revisited by Issa et al. (2008). They investigated and confirmed the negative relationship, by using the same equation used by Armano and Van Norden (1998a,b,), between the real Canadian-U.S. dollar exchange rate and real energy prices. Opposed to the research done by Armano and Van Norden (1998a,b), and by Issa et al. (2008), this thesis focusses on the out-of-sample relationship instead of the in-sample relationship of oil-price fluctuations on the nominal exchange rate of multiple currencies with respect to the U.S. Dollar.

Another study regarding international macroeconomic foundations, performed by Obstfeld and Rogoff (1996), concluded that the effect of a change in the oil price is rather short-lived, because this effect is almost immediately translated and reflected into the exchange rate. They find that this is the case for small and open oil-exporting economies. Furthermore, Faust et al. (2003) find that models which are using real-time data have larger forecasting ability. They also find that sometimes it is better to use real-time forecasts of future fundamentals instead of actual future fundamentals. In this thesis, also real-time data is considered for all data frequencies of the oil-price fluctuations and the exchange rates in order to evaluate the forecasting ability. Moreover, it is interesting to investigate whether the conclusions regarding the presumed

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ephermal effect of a change in the oil-price on the exchange rate found by Obstfeld and Rogoff can be confirmed by also considering a second and a third lag in the lagged oil-pricing model.

Another research performed by Chen and Rogoff (2003) studies the empirical link between exchange rate responses to world commodity price shocks, as this could provide new insights regarding monetary policy. They do this by investigating the real exchange rate behavior of three countries, namely Canada, Australia and New Zealand, where primary commodities form a significant share of the total exports. They find in-sample evidence that dynamic commodity price indices have explanatory power for real exchange rates in the long-run. This thesis extends this research from Chen and Rogoff (2003) to more recent data, because in this thesis also the latest oil-price shock is taken into consideration. Also, the focus of this thesis lies instead on the out-of-sample predictive ability of a single commodity, namely the oil price, rather than the in-sample predictive ability of commodity price indices.

2.2 Macroeconomic variables for forecasting

In a study provided by Chen et al. (2010) the forecasting ability is investigated with the same underlying fundamentals, namely the oil price and the exchange rate. However, this research studies the reverse causality with respect to this thesis, namely the dynamic relationship between exchange rate fluctuations and world commodity price movements at the quarterly frequency. For the commodity price movements an average price indices is taken which averages across several commodities. In their research they find robust evidence for both in-sample as well as out-of-sample that exchange rates predict world commodity price movements. However, this is in the reverse direction. It is interesting to check whether there is also a dynamic forecasting relationship in the reverse direction, namely between fluctuations in the oil-price and the change in the exchange. This is considered in this thesis.

There is also more specific literature available on using macroeconomic fundamentals to predict nominal exchange rates. Research provided by Meese and Rogoff (1983a, b, 1988) emphasizes on the explicability and validity of various models for exchange rates. Apart from that, they also discuss the out-of-sample predictability of these various models. The key insight provided by Meese and Rogoff (1983a, b, 1988) for this thesis is related to their methodology of predicting and consecutively measuring predictability of exchange rates. They compared the out-of-sample-fit forecasting accuracy of various structural models with a set of random-walk benchmarks in order to measure the forecasting ability of the exchange rate of their models. The structural models they considered were the Dornbusch-Frankel and the Frenkel-Bilson model, which are commonly referred to as the sticky-price monetary model and the flexible-price monetary model respectively. For the random-walk benchmarks, they considered two possibilities, a random walk model consisting of a drift and one without a drift. Subsequently, they made a comparison between the predictions provided by structural models and those of the random-walk benchmarks. The same method of assessing the quality of the forecasts by comparing against the random-walk benchmarks is used for the forecasting

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exercise in this thesis. In order to produce the forecasts, Meese and Rogoff (1983a, b, 1988) estimated their predictions by structural models in a rolling regression format at a one-to-twelve month horizon. They did this for the exchange rates of three different currencies with respect to the U.S. Dollar. However, important to notice is that they measured their predictions of the structural models in an out-of-sample-fit setting. This is the most relevant key insight for this thesis. This means that the forecasting model uses forecasts of the main explanatory variable in order to forecast the exchange rate. In other words, this means that the future or realized contemporaneous value of the explanatory variable is used to predict the future exchange rate. Thus, this forecasting method is not an actual out-of-sample forecasting exercise, this will be done according to the lagged oil-pricing model. However, measuring out-of-sample-fit is still relevant to do because if the lagged values of explanatory variable, which in this thesis is the change in the oil-price, were to provide inaccurate predictions of the exchange rate, then I would end up concluding that the changes in the oil-prices do not serve as a good explanatory variable. This, while the actual reason for the lack of forecasting ability might not be due to the absence of a relationship between the changes in the oil-prices and the change in the exchange rate, but rather due to the poor forecasts generated by the lagged oil-pricing model. In the investigation in this thesis, the simple oil-pricing model uses the actual realized oil-prices for the out-of-sample-fit forecasting exercise. This is possible due to the fact that a simulative forecasting exercise is performed, this means that forecasts are made for a period for which the actual values of the change in the exchange for comparison purposes are already known. The main findings from the research by Meese and Rogoff (1983a,b, 1988) are that, despite the fact that they base their forecasts on the actual realized values of macroeconomic explanatory variables, such as interest rates and output-gaps, the structural models were not able to improve on the random walk model on the relatively short term horizon. However, from a methodological standpoint, the research by Meese and Rogoff (1983a,b) is supportive of the view that out-of-sample fit is an important criterion for evaluating the predictive ability of empirical exchange rate models and this will also be used in the investigation in this thesis. The differences opposed the research by Meese and Rogoff (1983a,b,1988) are the different forecasting models and the different explanatory variable.

In a later research regarding in-sample forecasting conducted by Chinn and Meese (1995), the result obtained by Meese and Rogoff (1983a,b) was confirmed as their findings conclude that for predictions on short-term horizons, the random walk model is not outperformed by fundamental exchange rate models. However, they do find that error correction terms provide significantly better predictive ability at the long-term horizon than a no change forecast for a subset of currencies. Mark (1995) also revisited the research by Meese and Rogoff (1983a, b, 1988) and Chinn and Meese (1995) and also found evidence for an in-sample outperforming predictability on the long-horizon for changes in the logarithm of spot exchange rates with respect to a random-walk benchmark by including a drift factor in the benchmark.

Furthermore, Cheung et al. (2005) addresses the controversy surrounding the choice of the underlying fundamental used for forecasting. They find that that monetary fundamentals, such as interest rates or output, do not improve the

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out-of-sample exchange rate predictability in the relatively longer horizon, namely monthly and quarterly. They conclude that this is not even the case for out-of-sample fit forecasting. This in line with the conclusion derived from the research done by Meese and Rogoff (1983a,b) which shows that other macroeconomic fundamentals, such as interest rates, output gaps and inflation differentials have little to no forecasting power for exchange rates. Cayen et al. (2010) did research on identifying economic developments that drive exchange rates in the long-run. The research was performed over the 1980-2007 period and they found highly significant coefficients in a dynamic two-factor model of which one of those factors is driven by commodity prices. Based on this finding by Cayen et al. (2010), it would make sense to use oil-price fluctuations as an explanatory variable for predicting the exchange rate as oil is the world’s most widely traded commodity.

This specifically is investigated in a research performed by Ferraro et al. (2015). In their research, they use fluctuations in the price of oil in order to forecast the change in the Canadian– U.S. Dollar exchange rate. They also consider data at three different frequencies: daily, monthly and quarterly. In order to predict the exchange rates they perform out-of-sample fit analysis and also truly out-of- sample analysis. The former was introduced in the seminal paper by Meese and Rogoff (1983a) as was mentioned earlier and this is measured by conducting a simple linear regression. The latter is measured with a lagged- commodity pricing model. The same models used for prediction of the exchange rates are used in this thesis. Ferraro et al. (2015) also test the forecasting ability of their models by comparing their forecasts vis-à-vis to those provided by the two random-walk benchmarks. However, for this final comparison, they use a different test compared to this thesis. Ferraro et al. (2015) use the DM-test developed by Diebold and Mariano (1995) whereas this thesis uses the ENC-t test which is also a test on equal forecasting ability (Clark and McCracken, 2001). The simple and the lagged oil-pricing models used by both Ferraro et al. (2015) and this thesis, are nested models. In their paper, Ferraro et al. (2015) argue that the results of the DM-test statistic breakdown for nested models. However, they refer to a paper published by Giacomini and White (2006) which states that the under certain assumptions the DM-test is applicable to nested models. In this paper there is made use of the ENC-t test which is also a test on equal forecasting ability (Clark and McCracken, 2001). In contrast to the DM-test, the ENC-t test is developed and able to test the hypothesis of equal forecasting accuracy for nested models. This is also the rationale for considering this test.

In contrast to the conclusion derived by the vast majority in previous research, Ferraro et al. (2015) do find evidence for a systematic short-term relationship regarding outperformance of the random-walk benchmarks at the daily frequency between changes in the price of oil and the nominal exchange rate. However, they find that these results break down at the monthly and quarterly frequency. They explain that this is possibly due to the fact that their forecasting experiment is performed in an out-of-sample setting while the vast majority of previous research perform an in-sample forecasting exercise. Also they strengthen the result obtained by Obstfeld and Rogoff (1996) that high frequency data, such as daily data is needed in order to capture the short-lived

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effect of a change in the price of oil on the exchange rate, as they found insignificant results at the monthly and quarterly data frequency. However they do find that this effect is transitory. This thesis wants to investigate whether the results which are found by Ferraro et al. (2015) can be strengthened and are not the result of selective reasoning for the choice of emphasizing on the Canadian – U.S Dollar exchange rate or the choice of test of equal predictive ability.

This thesis relates best to the existing literature on out-of-sample (fit) forecasting of the exchange rates.

2.3 Hypotheses

The general null-hypothesis which will be tested for each currency considered is: H0: Equal exchange rate forecasting ability of the oil-pricing model vis-à-vis the two different random-walk benchmarks

H1: Outperforming forecasting ability of the oil-pricing model vis-à-vis the two different random-walk benchmarks

Under H0, the oil-pricing model represents the simple oil-pricing model or the lagged oil-price model measured separately versus the two different random-walk benchmarks.

Due to the presumption that the effect of a change in the oil-price on the exchange rate is short-lived (Obstfeld and Rogoff ,1996), the expectation is that data at the daily frequency would be better able to capture such a short-lived effect with respect to data at the monthly or quarterly frequency. Thus, it is expected that the oil-pricing models provide stronger forecasting ability at the short-horizon opposed to the long-horizon

Moreover, due to the choice of including multiple currencies in this investigation in order to be able to further explain the results, it is expected that two different countries experience the drop in a different way. For instance, Russia is very dependent upon the revenues of the export of oil and it is plausible to suspect that the oil price plummet will affect this exchange rate more than Mexico which has a much lesser degree of dependence on oil revenues. However, if this also has an effect on the forecasting ability of the Ruble opposed to the RW-benchmarks versus the Mexican Peso versus the RW-benchmarks, is interesting to find out. The same applies to the importers, for example, Japan and India are much more dependent on the import of oil than Singapore as their share of oil-import over total import is larger in comparison. Again, the way in which the exchange rate of a currency moves due to a change in oil-prices is presumed to be dependent on the degree of dependence of oil-export or oil-import. Thus, it is expected that more significant results are found for Russia and Norway opposed to Mexico and Canada for the oil-exporters. And that more significant results are found for Japan, India and South-Korea opposed to Singapore1_.

Moreover, exporters in general depend much more on oil than oil-importers due to the fact that oil-exports are much more concentrated across countries than oil-imports and therefore a more significant effect caused by the oil-price change is expected to be found in the case for oil-exporting currencies

1

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(Arezki and Blanchard, (2014). This is also the rationale for considering both oil-exporters and oil-importers with a varying degree of oil-dependence and economic size. A few of the currencies considered could be viewed as commodity currencies as their external value mainly reflects global movements of country specific commodity exports, such as for example the significant oil exports of Russia and Norway. There is also a distinction between net exporting and net importing countries for both exporting and importing currencies.

Taking this into consideration, more explicit set of additional hypotheses can also be derived.

1) The oil-pricing models provide stronger forecasting ability at the short-horizon opposed to the long-short-horizon.

2) The oil-pricing models provide stronger forecasting ability as the degree of dependence upon the oil trade is higher.

3) The oil-pricing models provide stronger forecasting ability for oil-exporting countries opposed to oil-importing countries.

4) The simple oil-pricing model provides stronger forecasting ability opposed to the lagged oil-pricing model.

5) The effect of a change in the price of oil on the exchange rate is rather short-lived (but market is not perfectly efficient) and thus has a transitory effect.

6) As the window width becomes smaller, the stronger forecasting ability is provided by the oil-pricing models.

In the process of evaluating the results provided by the test for the general hypothesis, these additional hypotheses will be answered in order to fulfill the second objective of this investigation.

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3 Data description

3.1 Oil-exporting and Oil-importing countries

The figures 1 – 5D in the appendix provide additional information regarding the oil-price and the exchange rate developments and the differences between the countries considered (International Trade Centre statistics, 2001 – 2015) In figure 1 in the appendix, the monthly oil price developments are graphically displayed. In the last decade, the oil price had predominant upward trend with some minor adjustments up and down along the way. However, there were two major oil price shocks of which the first was caused by the financial crisis in the course of 2008 and the second was due to a supply shift during 2014. As a consequence, the oil price was affected extensively as the price of a barrel dropped from approximately $140 to $40 per barrel during the financial crisis and from approximately $110 also to $40 per barrel within the time-frame 2014-2015. Today, the oil price per barrel has even dropped under $30. This probably has had and still has a large effect on the exchange rates of the currencies which are set to be investigated. The following oil-exporting countries are set to be investigated: Canada, Russia, Mexico and Norway. The oil-importing currencies considered are: Japan, India, South-Korea and Singapore. All of these currencies have a floating-peg exchange rate regime as it would not be relevant to include currencies with a fixed exchange rate regime.

In the figures 2A-D and 3A-D, the simultaneous changes in the exchange rates for the exporters’ currencies considered and importers’ currencies considered is graphically presented respectively. As is evident from the graphs, all of the exchange rates of the oil-exporting countries increased with respect to the U.S. Dollar during the oil-price shocks in the course of 2008 and recently in 2014. An increase in the exchange rate implicates a depreciation opposed to the U.S. Dollar. However, it is important to be aware of the fact that during 2008, there was a financial credit crisis which probably also affected the exchange rates. This increased the market inefficiency and it is likely that the oil-price is to a lesser extent able to provide good forecast in the change in the exchange rates due to other influences. Although, by taking this into consideration, it can still be ascertained that the oil-price and the exchange rates are related.

Also the exchange rates of the oil-importing currencies increased initially against the U.S. Dollar during the oil-price shocks. This indicates a depreciation while an appreciation would be expected in case of a drop in value of important commodity import. However, this depreciation could be explained by the change in volume imported. As is evident from figure 4B, the value of oil-import over total import initially increased during the course of 2008 when the oil-price started to fall. This lower price could have initiated an immediate boost in the volume imported which possibly could have decreased the importers’ currencies. But as the oil-price continued to drop, the value of oil-import over total import becomes lesser and lesser and thus, the total value of oil-import would decrease. This is clearly visible in figure 4B in the course of 2014, when the oil-import value over total import value reduces.

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3.2 Differences between countries

The important differences between the oil-exporting and the oil-importing countries are provided in table 1. These differences are provided in order to answer the additional hypotheses (2) and (3) in the evaluation of the results.

Amongst the four oil-exporting countries, Russia and Canada represent the relatively larger economies while Mexico and Norway form smaller open-economies. Important to notice are the differences between the countries. These are also displayed in figures 4A-B and 5A-B.

For example, notice that Russia’s share of oil-export over total export is much larger than that of Canada. Also although Mexico has a larger economy, Norway has a significant larger export of oil. Moreover, Mexico is consistent the only significant overall net importer amongst Russia and Norway, while Canada is neither a significant net-exporter or net-importer as their external balance is almost in equilibrium the oil-exporters. This is evident from figures 5A and 4A respectively.

Then, amongst the four importers, Japan and South-Korea form the larger economies opposed to the relatively smaller economies of India and Singapore. Notice that even tough Japan has the largest economy, the share of oil-imports over total imports is higher for South-Korea and India. Furthermore, Japan switches from being a significant overall net exporter to being a significant overall net importer. South-Korea and Singapore are net exporters opposed to India which is a significant net importer. This is visible in figures 5B and 4B respectively.

Thus, varying countries are taken into consideration in the sample of this research in order to possibly be able to explain and distribute the results for oil-exporting and oil-importing countries.

3.3 Data collection

The forecasting ability of the oil-price fluctuations is measured at three different frequencies of data, namely at a short-horizon represented by daily data and at a long-horizon frequency which is represented by monthly and quarterly data. The data which is collected for the three different frequencies for both the nominal exchange rates and the oil-prices, is end-of-sample. This means that data is gathered up till the latest present observations. All the data is gathered by accessing the WM/Reuters database through DataStream. For the exchange rates, the data observations at the daily frequency are measured on the working days from Monday to Friday. The monthly data observations are measured on the last day working day of the month. The quarterly data observations are measured at the last working of the third month of the quarter. The same measurements hold for the oil-price observations at the three different frequencies.

3.4 Research period

All of the information regarding the research period, the data collection, the total sample size, the in-sample data windows and the number of forecasts made are

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provided in table 2 in the appendix.

The data sample which is set to be investigated for all the currencies involved is from the first of January 1997 until April first of 2016. The daily data sample for all currencies contains 5022 observations. The monthly data sample for all currencies contains 230 observations and the quarterly data sample contains 76 observations from Q1 of 1997 to Q1 of 2016 for all currencies considered. The data sample for the crude oil-prices contain the same amount of observations for each frequency.

The rationale regarding the choice for the specific time-frame, thus from January 1997 until April 2016, is as follows. This research period is chosen with regard to the fact that some of the countries included in this research conducted a fixed-peg exchange rate regime prior to 1997 before implementing a floating-peg regime. Also, data is not available for all of the three frequencies considered for all the currencies prior to 1997. Therefore, the data sample which is set to be investigated is restricted to start from 1997 for the sake of performing a sound comparison across the different countries and data frequencies. The data sample ends in 2016 in order to optimally capture the on-going effect oil the oil-price plummet of 2014.

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4 Research method

4.1 Test outline

Recall the first objective which is to check whether the changes of oil-prices as the underlying explanatory fundamental have outperforming predictive ability against the RW-benchmarks for estimating exchange rates of different currencies. First, the forecasting ability of the two different oil-price models is separately measured in a simulative out-of-sample context. This paper distinguishes between two different methods in order to measure a simulative out-of-sample context, namely via an “out-of-sample-fit” measure and via a “ truly out-of-sample” measurement. Both methods were introduced by Meese and Rogoff (1983a,b, 1988) of which the former method is later revisited by West (1996), Cheung et al. (2005) and Ferraro et al. (2015). Both “out-of-sample-fit” and “out-of-sample” are estimated by two different theoretical models, namely the simple linear oil-pricing model and the lagged oil-price model respectively. Subsequently, the RW-benchmarks are described. Finally, the null-hypothesis of equal predictive ability between the oil-pricing models and the RW-benchmarks is tested in order to determine the performance of the models. This is mainly done on the basis of the ENC-t test and a comparison of the mean squared errors of the forecasts.

4.2 Models

4.2.1 Simple Linear oil-price model

The first model is represented by the simple oil-pricing model. This model measures the out-of-sample-fit forecasting ability. This involves the following population regression model:

𝐿𝑛(𝑆_𝑡) − 𝐿𝑛(𝑆_𝑡−1) = 𝛼 + 𝛽 ∗ (𝐿𝑛(𝑃_𝑡) − 𝐿𝑛(𝑃_𝑡−1)) + 𝜀_𝑡, 𝑡 = 1, … , 𝑇, (𝟏. 𝟏)

This is the population parameter model of the simple oil-pricing model in which

𝐿𝑛(𝑆_𝑡) − 𝐿𝑛(𝑆𝑡−1) represents the first difference of the logarithm of the exchange rates which are considered with respect to the U.S. Dollar, 𝐿𝑛(𝑃_𝑡) − 𝐿𝑛(𝑃_𝑡−1) represents the first difference of the logarithm of the oil prices, 𝜀_𝑡

represents the unforecastable error-term and 𝑇 refers to the total sample size. This model is estimated for three different data frequencies.

In order to explain the term: out-of-sample-fit, it is important to note that the realized values of the log first difference change of the oil prices at time t are used for forecasting the exchange rate in model (1.1) at time t. In other words, the contemporaneous log first difference change in the oil-price of tomorrow at time t is used for predicting the log first difference change in the exchange rate of tomorrow at time t. This implicates that this forecast is not a true out-of-sample estimation, but rather an out-of-sample-fit estimation because in-sample data of

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tomorrow at time t is used of the log first difference change in the oil-prices for forecasting out-of-sample predictions of the log first difference of the exchange rate. Also, the simple oil-pricing model is used in a simulative forecasting exercise because in order to assess the quality of the predictions made by this model, it is necessary to have the actual log first difference change in the exchange rates considered and the actual realized contemporaneous oil-prices at that same time. This method was introduced by Meese and Rogoff (1983a,b). In essence, this is an ex-post forecast according to West (1996) because of the use of the actual oil-price of tomorrow in order to predict the exchange rate of tomorrow. This method is useful for evaluating the forecasting ability of a model, rather than actually making an ex-ante prediction. Because when making an a real (not simulative) ex-ante prediction, it is not possible to use the contemporaneous realized oil-prices of tomorrow to predict the exchange rate of tomorrow.

4.2.2 The Shapiro-Wilk test for normality

The reasoning behind the use for the logarithm of the first differences of the exchange rate and the oil-price is due to normality. Prior to the research, the conventional Shapiro-Wilk test was performed in order to test the null-hypothesis of normal distributed data of the exchange rates and the oil-prices. The results of this test for data at the daily frequency for both the exporting and oil-importing currencies are listed in table 3 in the appendix and support the rationale behind the use of the logarithm of the first difference version of the variables. The results for the test at the monthly and quarterly frequency are also significant but these results are not presented in the table because the point is made clear. Also, if for the daily frequency the logarithmic version of the variables is used, then for the sake of comparison this also has to be done for the other frequencies. The reason why it is important to check for normality of the variables is also explained in the appendix.

4.2.3 Rolling-Regression and varying in-sample windows

The parameters of alpha and beta in population model in (1.1) are estimated on the basis of the most up-to-date information with respect to the given time of the forecast. This is achieved by implementing the conventional rolling-regressions which were established by Meese and Rogoff (1983a,b) and were also used by Cheung et al. (2005) and Ferraro et al. (2015). This means that for every forecast period, the sample is rolled forward one-step-ahead in order to continuously re-estimate the parameters of the oil-pricing model over a fixed window through the entire sample until the sample is exhausted. This is performed for the three different frequencies of data considered. The number of in-sample observations which are being rolled-over in order to re-estimate the parameters before the process is repeated, is called the window, or the window width and is represented by: R. There is also a distinction made between the in-sample estimation window sizes in order to optimally capture the effects of a certain data frequency. This basically means that different fractions of in-sample data of the total sample size are used in the rolling estimation exercise of the out-of-sample forecasts. The

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different fractions are: 1/4 (25%), 1/10 (10%) and 1/15 (6 2

3%). See column 6 in

table 2 in the appendix for a clear overview on the number of in-sample observations within each window which is used to re-estimate the parameters. There is also an example provided in the caption of table 2 how to interpret this. By considering multiple windows, it is also possible to test the additional hypothesis (6). This means that when the window becomes smaller, which implies that the ratio increases in which the parameters: alpha and beta are re-estimated, the performance by the oil-pricing models regarding predictability, increases. This could also support the use of the rolling-regression method instead of the ordinary regression.

Zivot and Wang (2006) argue that the choice for rolling regression instead of a normal regression is due to stability inferences and is also conducted in order to evaluate the predictive accuracy. When financial time series data is analyzed according to a statistical model, the key assumption is that the parameters of the model investigated are constant over time. However, this assumption may not be reasonable as the economic environment often changes considerably. A common technique which is used in order to assess the constancy of the parameters of a model is via rolling regression. Because, a rolling regression opposed to an ordinary regression is able to capture instability arising from a change in the parameters at some point during the sample. This leads to better estimations of the parameters. The rolling-regression is a dynamic regression instead of the ordinary regression model which is a static regression. Thus, the rolling technique is useful in order to adjust the parameters for crises periods such as the recent oil price crisis which otherwise would affect the constancy of the parameters used for the forecasts. If the static, ordinary regression is applied to generate the estimations of the parameters, then this would probably result less accurate predictions. All things considered, it is presumed that the rolling regression method will generate more accurate predictions by continuously updating the parameters used for forecasting.

The rolling method of regression with varying in-sample windows is applied to model (1.1) for the three different data frequencies. This results in series of continuously updated estimates of the alpha and beta parameters. Subsequently, these parameters will be fitted into the simple oil-pricing model. This will yield in the corresponding one-step-ahead simulative out-of-sample-fit forecasts of the logarithm of the first difference change in the exchange provided by the simple oil-pricing model. This is displayed in equation (1.2).

∆𝑆_𝑡+1𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑠 𝑠𝑖𝑚𝑝𝑙𝑒 𝑜𝑖𝑙−𝑝𝑟𝑖𝑐𝑒 𝑚𝑜𝑑𝑒𝑙 = 𝛼̂_𝑡 + 𝛽̂_𝑡 ∗ ∆𝑃_𝑡+1+ 𝜀_𝑡, 𝑡 = 𝑅, 𝑅 + 1, … , 𝑇 − 1 (𝟏. 𝟐)

In which 𝛼̂_𝑡 and 𝛽̂_𝑡 represent the parameter estimates of 𝛼 and 𝛽 respectively

provided by the rolling-regressions. 𝑅 represents the in-sample window estimation size and the rolling in-sample window is presented by {𝑇 − 𝑅 + 1, 𝑇 + 𝑅 + 2, … , 𝑡}. The different window sizes considered are equal across the

competing models and are represented in table 2.

Subsequently, the quality of the forecasts provided by (1.2) is checked by regressing the actual values of the logarithm of the first difference change in the exchange rate on the forecasted values of the logarithm of the first difference

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change in the exchange rate. This regression is represented in equation (1.3) below:

∆𝑆_𝑡+1𝑎𝑐𝑡𝑢𝑎𝑙 = ∆𝑆_𝑡+1𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑠 𝑠𝑖𝑚𝑝𝑙𝑒 𝑜𝑖𝑙−𝑝𝑟𝑖𝑐𝑒 𝑚𝑜𝑑𝑒𝑙 + 𝜀_𝑡 (𝟏. 𝟑)

The quality of the forecasts and thus the quality of the simple oil-price forecasting model can be derived from a test on 𝛽̂ = 1. In this test it is checked

whether the coefficient of the explanatory variable significantly differs from 1. This is not preferable, because the forecasts made by the simple oil-pricing model in (1.2) will only valuable if the beta is approximately one and thus do not significantly differ from one. The results of this test for the simple oil-pricing model are represented in table 4 for the exporting currencies and in table 5 for the importing currencies.

4.3 Lagged oil-pricing model

The second model is represented by the lagged oil-pricing model. This model measures the truly out-of-sample forecasting ability. Recall that the simple oil-pricing model measures the out-of-sample-fit forecasting ability in which the realized contemporaneous log first difference change in the oil-price of tomorrow at time t is used for estimating the parameters at time t in a rolling-regression format. Also recall that this method is useful for evaluating the forecasting ability of a model, rather than actually making an ex-ante prediction due to the fact that in a real ex-ante prediction, the realized contemporaneous oil-prices of the future (tomorrow at time t) are not available. Therefore, the lagged oil-pricing model is also considered, which does not use the realized oil-prices but rather the oil-prices of the previous observation. For instance, this is the oil-price of the previous day for the daily data frequency and for the monthly data frequency, the oil-price observation of the previous month. This involves the following population regression model:

𝐿𝑛(𝑆_𝑡) − 𝐿𝑛(𝑆𝑡−1) = 𝛼 + 𝛽 ∗ (𝐿𝑛(𝑃𝑡−1) − 𝐿𝑛(𝑃𝑡−2)) + 𝜀𝑡, 𝑡 = 1, … , 𝑇, (𝟐. 𝟏) This is the population parameter model of the Lagged oil-pricing model. Notice that the only difference with respect to (1.1) is: 𝐿𝑛(𝑃_𝑡−1) − 𝐿𝑛(𝑃_𝑡−2) instead of

𝐿𝑛(𝑃_𝑡) − 𝐿𝑛(𝑃𝑡−1). This means that the logarithm of the first difference change of the oil-price of the previous observation at time t-1 is used instead of the contemporaneous one at time t as explanatory variable. This model is also estimated for the three different data frequencies, daily, monthly and quarterly.

Moreover, the number of lags considered in 2.1 is only one due to the presumption that the effect of a change in the oil-price on the exchange rate is rather ephermal and perhaps even less than a single day. Therefore, this presumption also explains the expectation to find more significant results for the daily frequency of data at the short-horizon. Thus, the emphasis in this research lies on the minimum number of lags possible to consider, namely one. However, in order to strengthen the presumption above, also a second and a third lag of the

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oil-price are included for the lagged oil-price model.

The same method of fitting the out-of-sample forecasts with varying in-sample data windows which is used for the simple oil-price model is also used for the lagged-oil price model. This implies, fitting the series of estimations of the parameters: alpha and beta provided by the rolling regression into the lagged oil-pricing model for the three different frequencies of data, namely daily, monthly and quarterly. This will yield in the corresponding one-step-ahead simulative out-of-sample forecasts of the logarithm of the first difference change in the exchange provided by the lagged oil-pricing model. This is displayed in equation (2.2) below.

∆𝑆_𝑡+1𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑠 𝑙𝑎𝑔𝑔𝑒𝑑 𝑜𝑖𝑙−𝑝𝑟𝑖𝑐𝑒 𝑚𝑜𝑑𝑒𝑙 = 𝛼̂_𝑡+ 𝛽̂_𝑡∗ ∆𝑃_𝑡+ 𝜀_𝑡, 𝑡 = 𝑅, 𝑅 + 1, … , 𝑇 − 1 (𝟐. 𝟐)

In which 𝛼̂_𝑡 and 𝛽̂_𝑡 again represent the parameter estimates of 𝛼 and 𝛽

respectively by the rolling-regressions. 𝑅 represents the in-sample window estimation size and the rolling in-sample window is presented by {𝑇 − 𝑅 + 1, 𝑇 + 𝑅 + 2, … , 𝑡}. The different in-sample windows are 1/4, 1/10 and 1/15 of the total sample size and are stated in table 2.

Subsequently, again the quality of the forecasts provided by (2.2) is checked by regressing the actual values of the logarithm of the first difference change in the exchange rate on the forecasted change by equation 2.3. This is represented by the regression in the equation (2.3) below:

∆𝑆_𝑡+1𝑎𝑐𝑡𝑢𝑎𝑙 _{= ∆𝑆} 𝑡+1

𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑠 𝑙𝑎𝑔𝑔𝑒𝑑 𝑜𝑖𝑙−𝑝𝑟𝑖𝑐𝑒 𝑚𝑜𝑑𝑒𝑙_{+ 𝜀}

𝑡 (𝟐. 𝟑) Then the quality of the forecasts and thereby the quality of the lagged oil-price forecasting model is derived from a test on 𝛽̂ = 1. These results are listed in table 6 for the exporters’ currencies and in table 7 for the importers’ currencies.

After explaining the methodology for both the simple and the lagged oil-pricing model, the reason for considering the additional hypothesis (4) regarding the presumption that the simple model provides stronger forecasting ability than the lagged model can be derived. Because the simple oil-pricing model uses the contemporaneous realized value rather than the lagged-value of the oil-price as the explanatory underlying fundamental. This should make it relatively easier to capture the real relationship between the oil-price and the exchange rate and therefore it expected that stronger significance in the results will be found for the forecasts provided by the simple oil-pricing model.

4.4 Random-Walk Benchmarks

The RW-benchmarks which were developed in the seminal paper by Meese and Rogoff (1983a,b) have been the most popular benchmark models in the field of exchange rate forecasting. Due to alleged inference problems there is also a distinction considered in this thesis between a RW-benchmark consisting a drift and a RW-benchmark without a drift. This was also considered by Meese and Rogoff (1983a,b) and Ferraro et al. (2015). These inference problems stem from a

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series of critical papers by Kilian (1999) among others such as Berkowitz and Giorgianni (2001) and Rossi (2005,2007). Kilian (1999) argued that the results which were found in the research by Mark (1995), regarding the evidence for outperforming predictive ability of empirical exchange rate models on the long-horizon, were due to the fact that Mark (1995) included a drift-term in the RW-benchmark. By taking into account both types of RW-benchmarks, this thesis is robust to the criticism provided by Kilian (1999).

The two types of RW-benchmarks represent the following equations: RW-benchmark model without a drift:

𝐿𝑛(𝑆_𝑡) = 𝐿𝑛(𝑆𝑡−1) + 𝜀𝑡, 𝑡 = 1,2, … , 𝑇 (𝟑. 𝟏) RW-benchmark model consisting of a drift:

𝐿𝑛(𝑆_𝑡) = 𝜕 + 𝐿𝑛 (𝑆_𝑡−1) + 𝜀_𝑡, 𝑡 = 1,2, … , 𝑇 (𝟑. 𝟐)

In these models, 𝐿𝑛(𝑆_𝑡) represents the logarithm of the exchange rate at time t. This is explained by: 𝐿𝑛(𝑆_𝑡−1) which is the logarithm of the exchange rate from the previous observation. Notice that in order to get the RW-benchmark, the drift parameter: 𝜕 is added which is a constant. The: 𝜕 used in (3.2) is measured in the same way as Meese and Rogoff (1983a) initially estimated it, namely by taking the mean of the logarithm of the exchange rate change. However, in the investigation in this thesis, there is made use of the rolling regression and thus this constant term is continuously re-estimated. This estimation of the parameter: 𝜕 is repeated for each frequency of data with the varying in-sample

windows.

Then, in the RW-benchmark without the drift-term included, the forecasted values of the log first difference change in the exchange rate are straightforward as these are determined by the log first difference change in the exchange rate of the previous observation at t-1. This is presented in (3.3) below:

𝐿𝑛(𝑆_𝑡+1𝑓𝑜𝑟𝑒𝑎𝑠𝑡𝑠 𝑅𝑊 𝐵𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘) = 𝐿𝑛(𝑆_𝑡−1) + 𝜀_𝑡, 𝑡 = 1,2, … , 𝑇 (𝟑. 𝟑) In the RW-benchmark consisting of a drift, the rolling estimations of the constant term are fitted in order to make the forecasted values of the logarithm of the exchange rate for the RW-benchmark with drift model. This is presented in (3.4) below:

𝐿𝑛(𝑆_𝑡+1𝑓𝑜𝑟𝑒𝑎𝑠𝑡𝑠 𝑅𝑊 𝐵𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝑐𝑜𝑛𝑠𝑖𝑠𝑡𝑖𝑛𝑔 𝑜𝑓 𝑎 𝑑𝑟𝑖𝑓𝑡) = 𝜕̂ + 𝐿𝑛(𝑆_𝑡−1) + 𝜀𝑡, 𝑡 = 1,2, … , 𝑇 (𝟑. 𝟒)

Whereas for the two different oil-pricing models the quality of these estimations would be checked by regressing the actual changes in the log exchange rate on the fitted forecasted values and subsequently testing for 𝛽 = 1. This will not be

done for the forecasts produced by the RW-benchmarks due to the presumption that these benchmarks are valuable predictors anyway as these are widely used in the widespread forecasting literature.

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4.5 Comparing forecasting ability

In this paragraph, the forecasting ability of the two oil-pricing models, the simple-oil price model and the lagged-oil price model, will be compared against that of the two separate RW-benchmarks introduced by Meese and Rogoff (1983a,b). This comparison is principally established according to the ENC-t test provided by Clark and McCracken (2001). On the basis of the results of this test, the general hypothesis of equal forecasting ability between the competing models will be answered. Also, the mean squared errors (MSE’s) of the forecasts of each model will be used as a measure of comparison in order to see whether these results support the outcome of the ENC-t test. The latter is also checked with the results of the test on 𝛽 = 1 for separate oil-pricing models from regressions in (1.3) and (2.3) in paragraphs 4.2.3 and 4.3. The additional value from the ENC-t test is that this specifically tests which model has better forecasting ability vis-à-vis the random-walk benchmarks. The MSE comparison also provides some insight regarding which model has better forecasting ability by checking for which model the errors are the smallest. However this test is not able to check if this difference in the mean squared errors is sufficient to be significant in order to say something about outperforming forecasting ability. The same is true for the results from the regressions in (1.3) and (2.3). These measure the quality of the forecasts provided by the separate individual oil-pricing models and purely on the basis of these results, it will not be able to tell if the oil-pricing models outperform the predictions made by the random-walk benchmarks. When considering all these results together, this should provide an good estimation of the forecasting ability and thus whether the acceptation or rejection of general hypothesis is a righteous decision. This final result will be discussed in the results section in chapter 5.

4.5.1 ENC-t test

In order to conduct the ENC-t test, there are some preliminary stages which clarify the test and are also conducted in this paper. These are by and large provided in the appendix beneath table 9 and for the full explanation of the statistical properties and assumptions, see the paper provided by Clark and McCracken (2001).

The ENC-t test is a test provided for making a comparison of out-of-sample forecasting errors between an unrestricted model and an restricted version of the unrestricted model and consecutively measures if the unrestricted model is able to outperform the restricted model in a one-sided test. The derivations of the restricted models in terms of the models considered in the research in this paper are presented below:

Unrestricted model: Simple oil-pricing model:

𝐿𝑛(𝑆_𝑡) − 𝐿𝑛(𝑆_𝑡−1) = 𝛼 + 𝛽 ∗ (𝐿𝑛(𝑃_𝑡) − 𝐿𝑛(𝑃_𝑡−1)) + 𝜀_𝑡 (1.1) Restricted model: RW-benchmark without a drift:

𝐿𝑛(𝑆_𝑡) = 𝐿𝑛(𝑆_𝑡−1) + 𝜀_𝑡 (3.1)

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The 𝛼 and 𝛽 term in the unrestricted model are set equal to zero within the restricted model.

And for Restricted model: RW-benchmark consisting of a drift:

𝐿𝑛(𝑆_𝑡) = 𝜕 + 𝐿𝑛 (𝑆_𝑡−1) + 𝜀_𝑡 (3.2)

this is rewritten into → 𝐿𝑛(𝑆_𝑡) − 𝐿𝑛(𝑆𝑡−1) = 𝜕 + 𝜀𝑡

Now, the 𝛽-term in the unrestricted model is set equal to zero within the restricted model.

The same transformation or derivation holds for the lagged oil-pricing model as the unrestricted model:

𝐿𝑛(𝑆_𝑡) − 𝐿𝑛(𝑆_𝑡−1) = 𝛼 + 𝛽 ∗ (𝐿𝑛(𝑃_𝑡−1) − 𝐿𝑛(𝑃_𝑡−2)) + 𝜀_𝑡

Thus, both of the unrestricted models can be transformed in both of the restricted models which implicates that these models are nested.

Under the general null-hypothesis of equal exchange rate forecasting ability of the competing model considered, the unrestricted model nests the restricted model and thereby would include 𝑘2 excess parameters. 𝑘2 is defined as

the number of variables present in the unrestricted model but not in the restricted model.

Under the alternative hypothesis, the number of restrictions represented by 𝑘2 are invalid and the unrestricted model is true.

The restrictions 𝑘₂ in this investigation are the for the comparison of the oil-pricing models with the RW-benchmark without a drift as the restricted model: 𝛼 and 𝛽 equal to zero.

And the restriction 𝑘2 for the comparison of the oil-pricing models with

RW-benchmark consisting of a drift as the restricted model is: 𝛽 equal to zero.

The results of the ENC-t test are provided in tables 11-14. The results which are insignificant with a certainty level of 99%, 95% and 90% are indicated with *,**,*** respectively. Also, The critical values of the ENC-t test deviate slightly from those of the standard normal distribution. See table 10 for these

adjusted critical values.

4.5.2 Mean squared errors (MSE’s)

Another measure of predictive accuracy is provided by comparing the MSE’s of the competing models. This is a conventional straightforward measure which represents the average of the squared errors.

The lower the MSE’s, the more accurate are the forecasts of the exchange rate change due to lower errors with respect to the actual values of the exchange rate change. Thus, this gives an indication which model produces better forecasts and presumably has better forecasting ability. The results of the MSE’s of the predictions made by the oil-pricing models and the random-walk benchmarks are provided in tables 8 and 9 for the oil-exporting and the oil-importing countries respectively. These results will be used in order to see if these strengthen the final decision based on the ENC-t test.

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5 Results

This chapter is divided into four subsections. In the first two subsections, the results are discussed for the simple pricing model and for the lagged oil-pricing model. This includes the results of the tests on 𝛽 = 1 of the forecasts provided by the regressions (1.3) and (2.3) in paragraphs 4.2.3 and 4.3. These results are presented in tables 4-7 and are discussed for the different currencies considered.

Subsequently, in 5.3 the results of the ENC-t test are described which indicate the performance regarding the forecasting ability of the oil-pricing models vis-à-vis to both of the RW-benchmarks for the different exporting and importing currencies considered.

Then, in the last subsection, an overall discussion of the results will be given in which the general null-hypothesis for both the oil-pricing models vis-à-vis the separate random-walk benchmarks is answered according to tables 15-18. Included in this discussion, regarding the decision of acceptation or rejection of the general null-hypothesis, are the results of the comparison of MSE’s provided by tables 8-9 and the results of the tests on 𝛽 = 1 provided by the regressions (1.3) and (2.3) in tables 4-7 for the separate oil-pricing models. Subsequently, an overall comparison is made in which the differences between the countries involved in the research are put under scrutiny in order to allocate or distribute results associated with a certain characteristic, such as the degree of oil-dependence, whether the country is an oil-exporter or an oil-importer and or whether the country is an overall net exporter or net importer.

All things considered, this enables me to provide a righteous and clearly defined answer regarding the forecasting performance of the two oil-pricing models and to provide an answer on the additional hypotheses as well.

Important to notice is that the results are interpreted by and largely due to the fact there are too many result to comment on individually. This is primarily intended for the results in 5.1 – 5.3 of the research in preparation for the final comparison. Also, in the results section, there is often referred to the hypotheses. Recall that these are stated in chapter 2, paragraph 3.

5.1 Simple oil-pricing model results

First is commented on the results provided by the regressions (1.3) and (2.3) on the test on 𝛽 =1. Table 4 lists these results for the oil-exporting countries which will be discussed first. Recall that it is good if the estimated beta’s are close to 1 in order to conclude that the oil-price as the underlying fundamental would serve as a good predictor. However, the beta’s are never exactly equal to 1, so if there is a significant deviation found from 𝛽 =1 then it is also good to look at the standard errors (S.E’s).

By looking at the overall results presented in table 4, it can be concluded that the estimates of the beta’s are significantly indifferent from 1 for almost all of the data frequencies. Except for some currencies’ estimates of the beta’s on the daily frequency with the largest window width: R = 1/4 (window width is 25% of total sample size, see table 2 for the exact number of observations in each

Exchange rate forecasting based on oil price fluctuations