The Role of News Content on Aluminum Price Volatility
A topic modelling approach
Abstract
This thesis examines the long-term relationship between news contents and the volatility of aluminum futures contracts returns. Via Latent Dirichlet Allocation (LDA), a topic model, 20 topics and their proportions over time are extracted from 2147 aluminum-related news articles from the The New York
Times, spanning a 20 year period (31-03-1998 / 30-03-2018). After careful selection, five topics and
their distributions are chosen, and used to model aluminum future price volatility via multiple GARCH and EGARCH models. Most of the topics model the aluminum return volatility quite well, where an EGARCH-X(1,1) model with additional news regressors in the conditional variance seems to model the return volatility better than the benchmark GARCH(1,1) model. Moreover, the topic “market” seems to significantly positively affect the long-term aluminum return volatility even when controlled for macroeconomic and financial events.
Pim Welling
10297529
MSc Economics
Augustus 2018
Verklaring eigen werk
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Table of contents
1 Introduction ...3
2 Literature review………..6
3 Methodology…..……….10
4 Data and preliminary results………...…………....18
5 Results……….26
5 Conclusion………...34
1. Introduction
The correlations between news stories reported by the media and movements in financial markets have been studied extensively in academia. Primary focus seems to lay on the stock market, where stock volatility is assumed to react following relevant news. Indeed, stock market reactions to specific news regarding stocks or the macroeconomic landscape seem logical, yet similar research on commodity markets is seldom observed.
Over the last decades commodity markets have attracted the attention of economists and investors alike, resulting in an increase in operating exchanges and significant growth in both trade volume and variety of commodity futures contracts traded (Borovkova and Geman, 2007). Following Brooks et al. (2013), this increased interest may be partly explained by the historically low correlations commodities seem to have with other asset classes, a feature which attractiveness in the wakes of the “dot-com”-bubble and the “subprime” and sovereign debt crises rose. Furthermore, portfolio hedging and disappointing returns from other asset classes are mentioned as potential drivers of interest (Brooks et al., 2013).
Most commodity markets are volatile, and the volatility itself fluctuates over time; however, throughout the 2000s, commodity prices showed exceptional volatility (Creti et al., 2013; Pindyck, 2004). This “commodity boom” was of concern to policymakers, who not only feared the elevated prices of commodities, but also that these prices had become more volatile and uncertain (Calvo-Gonzalez, 2010). These fears of volatility on a macro level may not be unjustified; Joëts et al. (2017) make mention of theories of investment under
uncertainty, where uncertainty over future returns reduces current investment, hiring, and consumption. They argue that following uncertainty at this micro level starting point, firms may lower investments and consumers their willingness to spend. Hence, uncertainty at micro level may create cyclical fluctuations in aggregate investment at a macro level. Then, in the late 2000s, following the economic downturn of the financial crisis, commodity prices fell abruptly, only to stabilize and show an upward trend with relatively high volatility in recent years (Roache and Rossi, 2010).
Coincidentally, this pattern of increased volatility coincides with a similar pattern of an increased commodity-related news flow. Commodity-related news has been steadily growing between 2003 and 2008, a time when the commodity boom was in full effect. After 2008, when prices seemed to stabilize, news flows seemed to stabilize too (Borovkava, 2015); sparking interest in the role of news on commodity volatility.
The studied connection between news events and markets is nothing new, and neither is the relationship between media and markets. Historically, research in such fields has focused on news as events without quantifying its contents (see Mitchell and Mulherin 1994, for example), or has qualified news data as either “good news” or “bad news” (see Engle and Ng 1993 and Braun et al. 1995), where both were assumed to have different predictability for future market volatility. More recently, Tetlock (2007) used the amount of positive and negative words used in a daily column regarding the stock market to find a correlation between stock prices and news sentiment.
However, recent developments in natural language processing and text mining can bring about large-scale changes in this domain. Latent Dirichlet allocation (LDA), as proposed by Blei, et al. (2003), is a machine learning algorithm for topic modelling that can decompose text into a set of topics, and shows its topic distributions. This way, news articles do not have to be screened manually for its content or its positive or negative sentiment; topics are extracted from the text data and can be used for further analysis.
As for mentioned, commodity markets are of particular interest in this renewed field, where despite growing interest and research little academic literature is found regarding the news effects on commodity markets (Borokova and Mahakena, 2015). Being a part of the commodity market, aluminum specifically has seen a recent surge in prominence; news events such as the United States’ imposed tariffs on steel and aluminum and its sanctions on aluminum company United Company Rusal have both been well-documented by international press. In both instances, aluminum markets responded with increased volatility and
uncertainty (Sanderson, 2018).
In this thesis the long-term relationship between news data and the volatility of aluminum futures contracts returns is studied. In other words: does news and its contents regarding aluminum produce a change in the aluminum futures price volatility?
In order to answer this question, 2147 articles by The New York Times over a 20-year period (31-03-1998 / 30-03-2018) regarding the subject matter “aluminum” or “aluminium” will be used for topic modelling through LDA. Topics extracted from the news data will be weighed for usefulness and relevance regarding the aluminum market, and using standard and modified GARCH and EGARCH models their effects on the volatility of the aluminum returns will be estimated. Moreover, the modified EGARCH model will include
high-frequency macroeconomic and financial control variables, to further isolate the effects of the news content on volatility1.
Ultimately, the obtained results show that certain topics do indeed seem to
significantly affect aluminum future price volatility over the 20-year period. However, only one topic, topic 20 “market”, significantly has a positive effect on return volatility when controlled for macroeconomic and financial variables in a modified EGARCH model.
Adding to a field which as of yet has sparse academic literature, the main contribution of this analysis is that by the employment of LDA, as a different outlook on news data
analysis is combined with volatility modelling. Therefore linking topics in the news, rather than news sentiment to price behavior. Furthermore, a 20-year period is studied, producing news topics which affect commodity price volatility over a long-term horizon.
The rest of this thesis is as follows: first, a review of literature regarding news effects and text analysis in economics is given. Furthermore, earlier literature regarding volatility modelling is presented. What follows in section 3 is the methodology of thesis, where the LDA and GARCH models are introduced. The data, data characteristics, and preliminary results are presented in section 4, where among other things the LDA topic output is
reviewed. Finally, section 5 and 6 contain the estimation result and conclusion of this thesis, respectively.
2. Literature review
As for mentioned, research on news specific effects on commodities is scarce. Although recently new progress in research has been made, most research still focusses on the effects of news on equities. In the following section, existing literature regarding news effects and textual analysis in economics and finance will be given. Subsequently, LDA and its examples of use in economic literature will be reviewed. Finally, earlier literature on volatility modeling and modelling commodity volatility is presented.
1 GARCH models included with additional explanatory variables are often called GARCH-X models. Hereafter, the modified GARCH and EGARCH will be referred to as GARCH-X and EGARCH-X, respectively.
2.1. The role of news on markets
Financial markets are strongly influenced by textual information updates—our so-called “news” (Groß-Klußman and Hautsch, 2011). News is announced in regular and irregular updates, and mass media outlets such as newspapers play an important role in the distribution of news to a broad audience. With new online readership and multiple readings per copy, it is safe to assume that printed press reaches a far broader audience then other sources of financial news, such as analyst reports (Fang and Peress, 2009). As of recent, the study of news
information on financial markets seems to have gained momentum: advances in textual analysis and computational power have made it possible to categorize vast amounts of text data with increasing precision. Topic modeling is one of these new techniques used for text analysis, where semantic structures in bodies of text are discovered and used for further analysis.
Some of the earliest research regarding news effects in finance comes from a study done by Niederhoffer (1971). Niederhoffer let a group of untrained observers classify 20 years of The New York Times headlines into 20 categories of meaning and on a seven-point good-bad scale. He then analyzed how markets reacted to good and bad news, and found that markets do indeed react, even seemingly overreacting to negative news. Given the labor-intensive and error-prone process of data collection and analyzation, Niederhoffer suggested the use of computers for news analysis in future research. In similar fashion, Cutler et al. (1989) also manually analyzed news articles, albeit on a smaller sample. However, with regards to methodology they took a different approach. The authors looked into stock market reactions to specific non-economic events, such as elections and international conflicts. They analyzed large stock market movements in the then past fifty years, and coincident news reports were reviewed for proximate causes of these movements. Interestingly, the authors did not find that the news stories explained changes in variance of market returns without specific macroeconomic events unfolding in the background. The study does, however, conclude with the notion that it was perhaps possible that news of relevance was overlooked. Later research by Engle and Ng (1993) proposed a news impact curve, in a line of studies that focused on proxies for news, such as news volume and arrival. Engle and Ng used unexpected rises or drops in stock returns as a proxy for good and bad news, respectively. Their paper showed that negative news had a greater impact on volatility than positive news, somewhat following Niederhoffer’s earlier results.
Later studies like those of Tetlock (2007) indeed proceeded in the use of computers. Tetlock employed the General Inquirer, a textual-analysis software program, and the Harvard-IV-4 dictionary, which lists words in sentiment categories, to calculate the fraction of
negative words in the daily Wall Street Journal column, “Abreast of the Market”. “Abreast of Market” was fixated on US stock market returns of the most recent day of market activity, where Tetlock’s assumption was that the column influenced investor sentiment. The study found a relationship between news sentiment and price dynamics, where high values of media pessimism led to downward pressure on market prices. Furthermore, unusually high or low pessimism led to temporary high market trading volume. Following Tetlock’s results, numerous papers using similar methodologies were released (see Tetlock et al. 2008 & Loughran and McDonald 2011, for example).
With regards to news effects on commodities, a study by Borovkova (2015) cuts closest to the subject matter of this thesis. In this study, Borovkova examines the main commodity classes and their market responses to news. In her conclusion, the author states that the responses of commodity markets to news sentiment is complex, and varies per commodity class.
Furthermore, she finds that high positive sentiment decreases and high negative sentiment increases commodity return volatility. Another paper by Zheng et al. (2008) use an EGARCH model to study asymmetric news effects on US food prices, finding that price news
destabilizes about a third of the market.
In recent years, alternative approaches towards text analysis have come forward. Advancements in the areas of machine-learning have led to applications that have been used to decipher tone, content and sentiment of news articles (Boudoukh et al, 2012).
2.2. Latent Dirichlet allocation (LDA) in economics and finance
One example of a new and alternative approach to text analysis is the LDA model, proposed by Blei et al. (2003). Through LDA, a certain number of topics can be defined in a corpus of text by the amount and distributions of terms used in the documents.
Employment of LDA has gained popularity in academia in recent years. Using LDA, large corpora of text transcripts from the Federal Open Market Committee (FOMC) have been analyzed by Hansen et al. (2017). The authors looked for changes in transcript subject matter resulting from increasing levels of transparency of the FOMC meetings and transcripts. In similar fashion, a study conducted by Shirota et al. (2015) analyzed monetary policy of the Bank of Japan using text mining technologies such as LDA. Here, transcripts of the Monetary
Policy Meeting held on October 31, 2014, were reviewed per minute for topics and topic distribution. Other research by Feuerrigel et al. (2016) used topic modelling via LDA to look for correlations between topics found in press releases and abnormal returns in the German stock market. Feuerrigel found, as hypothesized, that some topics indeed had resulting effects. Furthermore, in a 2013 paper, Jin et al. detail a “forex-foreteller” system, which with the use of LDA (among other analysis programs) could forecast most of the appreciations and depreciations of currencies studied. Relevant news articles were mined and analyzed for meaning and sentiment, and, together with historical stock indices and currency exchange values, were used successfully in a linear regression model to make forecasts.
However, as the focus of research on news effects shifts to more extensive text mining models, most research seems to be leaning towards sentiment analysis and opinion mining, where the focus lays more on the interpretation of positive versus negative (see Ren et al. 2017, Borkova and Mahakena 2015, Ranco et al. 2015 & Kim et al. 2014, for example).
2.3. Volatility modelling
Financial market volatility has an effect on the economy as a whole. Major world events can cause great turmoil on financial markets; negatively affecting the world economy and showing an important link between financial market uncertainty and public confidence. For this reason, economic policy makers often look at market estimates of volatility as an indicator of the vulnerability of the economy (Poon and Granger, 2003).
Economical and financial time series often exhibit “volatility clustering”: large changes in prices are followed with large changes in prices, whereas small is followed by small; essentially clustering together and creating a persistence of amplitude of price changes (Cont, 2005). This phenomenon was first described by Mandelbrot (1963), and showed empirical regularity in high-frequency speculative prices. However, the explicit modelling of time-varying volatility came later, where the ARCH (autoregressive conditional
heteroskedasticity) model was one of the first and most prominent tools to emerge (Bollerslev et al., 1992).
Introduced in a seminal paper by Engle (1982), the ARCH model assumes that the variance of the return is a function of the previous periods’ squared residuals.
Engle argued that recent events would be more relevant for variance estimation, and opted for higher weights for more recent observations for the squared residuals. His proposed ARCH
model would let the weights be parameters to be estimated, allowing the data to determine the best weights in variance estimation (Engle, 2001).
Later on Bollerslev (1986) introduced a generalized version of the model, the GARCH (generalized ARCH) model. This generalized version also included previous periods’ variance in the conditional variance specification (Engle, 2001). Many ARCH-type volatility models have come forward since. One example is the EGARCH (exponential GARCH) model of Nelson (1991), which allows an asymmetrical effect between positive and negative returns and does not follow the non-negativity constraint of the GARCH model.
Commodity prices are considered to be volatile, and there are numerous studies that focus on the dynamics of its volatility. Creti et al. 2013 examine the links between commodity and stock market volatility, finding evolving correlations and evidence of increased
financialization of commodity markets. Research done by Hayo et al. (2011) shows that US monetary policy events have significant price impact on commodity price volatility;
employing a modified GARCH(1,1) model, they find that there is a “calming effect” of central bank communication on commodity market volatility. A paper by Hammoudeh (2008) makes use of EGARCH and GARCH models, among others, to examine the volatility
behavior of gold, silver, and copper.
3. Methodology
In this section, the methodological framework of this thesis is presented. News articles are preprocessed and ran through a LDA model Python script originally written by Hansen et al. (2017), showing the underlying topics of the text and topic distributions per article. Following this, topics of interest and relevance are selected, and used to model the volatility of
aluminum futures contracts returns using different GARCH and EGARCH models. First, the workings of the LDA model and the specifications of the LDA model used will be given, followed by the detailing of the GARCH and EGARCH models used.
3.1. Latent Dirichlet allocation (LDA) model
LDA, as described by Blei et al. (2003), is a generative probabilistic model for collections of discrete data such as, but not exclusively, text. Suppose that there are M documents which in total combine to a corpus of text with N words, where each word is assumed to be indexed
from a vocabulary of V words. The documents are random mixtures of K latent topics, where each topic is characterized by a distribution over words. LDA then assumes a generative process for how each document in M is created. Following Blei et al. (2003):
1. Choose ! ~ Poisson($)
A number of words N in a document is decided. This follows a Poisson distribution.
2. Choose % ~ Dirichlet(&)
For the document a random mixture of topics is chosen. This follows a Dirichlet distribution over a fixed set of K topics.
3. For each word in !, '(:
(a) Choose topic )( ~ Multinomial(%) (b) Choose a word '( from *('(| )( , .)
Now, for each word in N in each document in M, a topic is selected. This follows from the multinomial distribution which was sampled in (a). Then, according to the multinomial distribution, a word from that topic is generated, where topics and their word probabilities are specified in a K × V matrix . with . = (* = 1|) = 1). Given this generative process, LDA then tries to find a set of topics that are likely to have produced the N words in the M
documents in the text corpus.
Two assumptions are made in this model of LDA. First, as mentioned earlier, the set of topics K following from the Dirichlet distribution is assumed to be fixed. Secondly, the Poisson distribution chosen is somewhat arbitrary and different document length distributions can be employed (Blei et al., 2003).
In this thesis, software originated by Hansen et al. (2017) is used, where a modified version of LDA is written in the programming language Python. In the basic LDA model, the K × V matrix . is viewed as a fixed quantity which is to be estimated. The alternative version used by Hansen et al. is a smoothed version that assumes that . is a random matrix where each row is estimated from a Dirichlet distribution with a single scalar parameter 3. Moreover, the posterior distributions of the latent variables are as follows:
*(%, 4|5, &, .) =*(%, 4, 5|&, .)
*(5|&, .) (1)
Where ' and ) are in bold-font because they are in vector version of the variables. However, according to Blei et al. (2003), this distribution is impossible to compute in general; different approximative inference algorithms for the posterior distribution can be considered. Hansen et al. (2017) make use of a Markov Monte Carlo algorithm called Collapsed Gibbs sampling.
Fig. 1
A graphical illustration of the workings of the modified LDA model are shown in figure 1. Four levels of LDA representation are shown, where parameters & and 3 are
generated once when generating a corpus. The parameter % is sampled per document, and . is sampled for every topic. Finally, ' and ) are sampled per word in N.
3.2. LDA parameterization
In the paper of Hansen et al. (2017), the hyperparameters of the LDA model follow those of Griffiths and Steyvers (2004). Three main parameters have to be set: two hyperparameters for the Dirichlet priors and the amount of topics. Hyperparameter 6 is set on 50/K, and hyperparameter 3 is set on 200/V, in this model leading to 2.5 and ~ 0.0148, respectively. These parameters are also included in the “topicmodels” package for Python.
The setting for the amount of topics K is a common challenge in applying topic modelling, where interpretability and model fitting do not always coincide. Choosing too few will result in broad and extensive topics, and choosing too little produces many small, similar topics (Greene et al., 2014). In this thesis, the number is set at K = 20, which after
3.3. Economic model specification
In financial time series, stylized facts such as little to no return auto-correlation and volatility clustering are commonly observed. Moreover, a “leverage effect” is often encountered, where asset volatility is negatively correlated with asset return. As such, rising asset prices are associated with declining volatility, and declining asset prices with increased volatility. The phrase “leverage” refers to the possible economic interpretation that if a company stock value decreases, it’s debt-to-equity ratio increases, making the stock more volatile (Aït-Sahalia et al., 2013). These phenomena have led to the use of a multitude of variance models for volatility estimation and forecasting.
3.3.1. The GARCH model
The GARCH model was introduced by Bollerslev (1986), which following the ARCH model also employs weighted average for past squared residuals. However, these effects never go to zero as previous volatility forecasts are also included in the variance specification. This model extension is useful when estimating slowly changing variances (Stock and Watson, 2012). The basic structure of the GARCH(1,1) model is given below:
78 = 9 + ;8 (2)
;8 = =8>8 >8 ~ !(0,1) =8@ = &
A+ &B;8CB@ + .B=8CB@
Where 78 is the return, =8@ denotes the conditional variance, with &A > 0, &B > 0, .B > 0, and &B+ .B< 1.
This GARCH(1,1) specification will be used as a baseline model, to which modified versions will be compared for goodness-of-fit.
A GARCH-X model is considered to include the LDA output. The lag lengths are also chosen to be (1,1) for easier comparison and follow the result of Hansen and Lunde (2001), who found that no other lag specifications outperformed the basic (1,1) structure. Secondly, the LDA output variables are included in the conditional variance equation to model the impact of news content on volatility. This also follows from the fact that the LDA model is a
topic model, where the output is given in topics and their distributions and not so much in text sentiment. Therefore, it would also be difficult to estimate their effect directly on the
aluminum futures’ return. For example, a topic regarding mining does not say that it has become more difficult to mine bauxite (the primary source of aluminum), which would possibly increase aluminum futures’ prices. However, one could argue that the broad topic of mining in the news affects the volatility of the returns. The specification for the GARCH-X(1,1) model is as follows:
78 = 9 + ;8 (3)
;8 = =8>8 >8 ~ !(0,1) =8@ = &
A + &B;8CB@ + .B=8CB@ + %B∗ H(IJK8CB+ %@ ∗ LM*NOP,8CB+ %Q ∗ 6RLNOSTU8CB
Where again, 78 is the return, =8@ denotes the conditional variance, with &A > 0, &B > 0, .B > 0, and &B + .B < 1. The included variable “H(IJK 8CB” is a one-period lagged dummy variable which is 1 on days of news regarding “aluminum” or “aluminium”, and 0 otherwise. Variable “LM*NOP,8CB" is a one-period lagged proportion of that particular topic in the news articles sample that day. For example, five percent of all selected news articles that day could be from topic “A”, which would mean 0.05 for the topic “A” variable. No more than one topic is included per model specification. Lastly, the one-period lagged variable “6RLNOSTU8CB” is included, which counts the number of “aluminum news articles” per day. This could be interpreted as a proxy for the amount of news surrounding the subject aluminum.
3.3.2 The EGARCH model
Even though a GARCH(1,1) model can capture the volatility clustering shown in data, it fails to model the “leverage effect”. The EGARCH model introduced by Nelson (1991) meets this objection and allows asymmetrical effects between positive and negative returns. The
specification for the EGARCH-X(1,1) model can be found below:
78 = 9 + ;8 (4)
;8 = =8>8 >8 ~ !(0,1)
SX(=8@) = &
A+ .BSX(=8CB@ ) + YB;8CB+ ZB[|;8CB| − ]2 ^⁄ ` %B∗ H(IJK8CB+ %@∗ LM*NOP,8CB + %Q ∗ 6RLNOSTU8CB
Where 78 is the return and =8@ denotes the conditional variance. However, in this model there are no constraints on the parameters &A, .B, YB, and ZB. Furthermore, the parameter
YBaccounts for an asymmetric effect and ZB for a symmetric effect in the conditional variance. The extra included regressors in the conditional variance are the same as in (3).
When modelling volatility on the basis of news content, certainly on exclusive topics, interest also lies on macroeconomic and financial events unfolding in the background. Earlier mentioned research by Cutler et al. (1989) could not find a causable relationship between stock market volatility and news stories when controlled for macroeconomic events.
Therefore, four high-frequency macroeconomic and financial control variables are added to the conditional variance specification, leading to an EGARCH-X(1,1) model with controls:
78 = 9 + ;8 (5)
;8 = =8>8 >8 ~ !(0,1) SX(=8@) = &
A+ .BSX(=8CB@ ) + YB;8CB+ ZB[|;8CB| − ]2 ^⁄ ` %B∗ H(IJK8CB+ %@∗ LM*NOP,8CB + %Q ∗ 6RLNOSTU8CB+ %bcde8CB+ %fHMSS6R8CB+ %ghijk8CB
+ %lmHkNXnTo8CB
Again 78 is the return and =8@ denotes the conditional variance and there are no constraints on the parameters &A, .B, YB, and ZB; where YB and ZB account for the asymmetric and symmetric effect, respectively. Description and motivation for the inclusion of each control variable can be found below:
VXO – the CBOE S&P 100 Volatility Index
In 1993 the Chicago Board of Options Exchange (CBOE) introduced the CBOE Volatility Index (VXO). Using option data of the S&P 100 index, an average of the Black and Scholes
(1973) option implied volatility is computed. The index has become the de facto benchmark for stock market volatility (Carr and Wu, 2006)2.
A study by Mensi et al. (2013) showed a significant correlation and volatility transmission between commodity and stock markets. Following this result, the one-period lagged daily VXO index is included in the conditional variance as a control variable.
Dollar – trade-weighted US dollar index
The US dollar is the benchmark pricing mechanism for most commodities in international markets, thereby playing a role in commodity price behavior. Their relationship is assumed to be an inverse one, where the prices of commodities tend to rise when the dollar weakens and fall when the dollar strengthens. This follows from the law of one price for tradeable goods; a decline in dollar value must be outweighed by an increase in the dollar price of commodities and/or a fall in foreign currency value to ensure the same price in dollar value. Furthermore, a weaker dollar might raise the purchasing power and commodity demand of foreign consumers (Akram, 2009). These effects may only be larger if the commodity price elasticities are
relatively inelastic, which is the case for aluminum (Stuermer, 2017).
Therefore, the broad trade-weighted US dollar index is included in the model, where it is included as a one-period lagged control variable.
TIPS – Treasury inflation-indexed bond
Frankel (2014) makes the claim that “easy monetary policy” has contributed to higher commodity prices, via either higher demand or lower supply. The author suggests that easy monetary often shows up in the form of low real interest rates, and that real interest rates are an important determinant for commodity prices (Frankel, 2008). This relationship is explained via three mechanisms:
• High interest rates decrease firms’ desire to carry inventories, increasing commodity supply.
• High interest rates encourage speculators to shift into treasury bills, and out of commodity contracts; low interest rates would do the opposite.
2 In 2003 the CBOE altered its calculation of the VXO index and renamed it VIX. However, the old VXO is still
• High interest rates would increase the incentive for commodity extraction (mining bauxite, in the case of aluminum). Non-extracted commodities are non-interest earning, and higher interest rates would encourage firms to liquidate and earn interest on the proceeds of the sales (Economic Outlook, 2012).
Treasury Inflation-Protected Securities, or “TIPS”, are fixed-income securities whose principal payment is tied to the Consumer Price Index (CPI). The principal increases with inflation and decreases with deflation, whereat maturity the US Treasury either pays the original or adjusted principal, whichever is greater. D’Amico et al. (2018) state that TIPS yields can be viewed as a daily proxy for risk-free real interest rates, as such the 30-year 3-7/8% treasury inflation-indexed bond is included as a one-period lagged variable3.
ADSindex – the Aruoba-Diebold-Scotti Business Conditions Index
The Aruoba-Diebold-Scotti Business Conditions Index (ADS index) is a real-time indicator of US business conditions at high frequency, and is maintained by the Federal Reserve Bank of Philadelphia. It consists of six seasonally adjusted economic indicators:
• Weekly initial jobless claims • Monthly payroll employment • Industrial production
• Personal income less transfer payments • Manufacturing and trade sales
• Quarterly real GDP
The ADS index measures real economic activity at a daily level, and makes use of stock and flow data of mixed frequencies. Its average value is zero, which means that any number below zero alludes to a contracting economy, whereas positive values assume positive
growth. In their conclusion, the creators claim to have “proposed a dynamic factor model that permits exactly optimal extraction of the latent state of the macroeconomic activity” (Aruoba et al., 2009, p.24). As such, the ADS index is included in the conditional variance of (5), where it serves as a daily one-period lagged proxy for macroeconomic activity.
4. Data and preliminary results
This section revolves around the gathering and preprocessing of the data used in this thesis. Data characteristics and behavior are displayed and tested, and, moreover, the LDA model’s estimated topics are reviewed and selected for further analysis.
4.1. News data and preprocessing
In order to capture aluminum-related news, a sample of 2147 news articles from The New York Times relevant to the subject matter of aluminum is taken. The New York Times is generally regarded as a thorough and reliable news source, and has a worldwide readership. The sample time frame is from March 31, 1998 up until March 30, 2018, which is motivated by the desire to model long-term volatility. The articles are obtained via the LexisNexis Academic database, where articles are filtered by subject terms “aluminum” and/or “aluminium” and are available for download in text format.
Before the text data of interest can be used in any computer text analysis model, it has to be transformed to raw-text data; white spaces, certain punctuation marks, and different article layouts make it difficult to process well otherwise. A Python script created by Neal Caren4
helps clean up the text data into a CSV file, which along with some manual processing make it ready for further processing. What is left is the date of each article, its text contents, and its headline.
Following Hansen et al. (2017), the raw-text data then needs to be preprocessed further before any LDA modelling can be done. Using the Python package “topicmodels”, the vocabulary of the text corpus will be reduced to a set of words that are more likely to bear meaning for the underlying text content5. Preprocessing goes as follows:
1. Word contractions are written out in their underlying words (words like “don’t become “do not”), and all words will be converted into lower case letters.
4http://www.unc.edu/~ncaren/haphazard/split_ln.py
5 The data pre-processing and following LDA modelling follows the online text mining tutorial of Hansen et al.
(2018), which can be found at https://github.com/sekhansen/text-mining-tutorial/blob/master/tutorial_notebook.ipynb
2. All non-alphanumeric words terms will be removed from the text data, and words containing fewer than two letters are removed as well. This can be useful in the case of symbols and abbreviations, which do not add to the texts contents.
3. Stop words are removed from the text. Stop words are the most common words in a language, and tend to appear in all text. Given their presence in all texts, they are of little help as to describing its contents. In this thesis, a long list of English stop words is used for stop word removal in the text corpus6.
4. Words that are grammatically different, yet bear similar thematic meaning are grouped together. Words such as “praise”, “praising” and “praised” may be spelled differently, but convey similar content. Through “stemming”, words with the same root will be reduced to a common form; “prais” in this particular case. This step works via a deterministic algorithm which strips them of its derivational and inflectional suffixes (Lovins, 1968). Here, the Porter stemmer is used, which is part of Python’s Natural Language Tool Kit (NLTK) (Hansen et al. 2017).
5. Remaining words are ranked by term frequency-inverse document frequency (tf-idf), which measures the informativeness of words. With tf-idf, the number of occurrences of each word in a document is counted. This “term frequency” is then combined with the number of occurrences of those words in all documents, the “inverse document frequency”, to get an informativeness score. Words with high tf-idf scores occur frequently in the document and are more rare in the entire corpus of documents; making them more informative for that document (Blei et al., 2003). In figure 2 the tf-idf scores are plotted against the number of words in the corpus. The tf-tf-idf scores seem to decrease after the 15000th ranked word or so, from where on all remaining words are dropped. This leaves 13538 unique stems in the text corpus, which is less than 15000 because of the shared tf-idf weights between stems. From here on the data is ready for LDA estimation.
Fig. 2
4.2. LDA output and topic selection
The estimated topics and their ten highest probability words found by the LDA model are represented in the appendix (appendix 3). Some topics can be reasonably labeled, for example topic 1 as “mining”, topic 14 as “trade”, and topic 20 as “market”. Other topics seem
somewhat more ambiguous, such as topic 4 “think” and 5 “packaging”. However, this interpretation is subjective, and not part of the LDA model estimation.
Given that the text data consists of news articles surrounding the broad subject of aluminum, it is safe to assume that not all text may appeal specifically to the aluminum market. So, in a theoretical framework, likely not all topics would be of relevance to aluminum futures prices. For example, topic 12, which is labeled “cultural”, is perhaps less likely to causally influence the markets as topic 20 “market”. Secondly, there is not a symmetrical distribution among topics over the entire corpus of text. The earlier mentioned, more ambiguous topic 4 only accounts for around four percent of the content, whereas topic 20, labeled “market” represents roughly nine percent. Thirdly, given that LDA is a so-called “bag-of-words” model where the specific order of the words is not taken into account, it is possible that some topics are predominately centered around a specific time frame. Topic 15, for example, likely features the Reynolds Metal Company. In May 2000 Alcoa Inc, which is the world’s largest aluminum concern, acquired Reynolds Metal Co. for $4.5 billion. In figure 3 it can be seen that indeed most of the topic 15 proportion in the articles can be found around that time, as May 2000 is highlighted by the grey vertical reference line.
tf-id f s co re number of words
Fig. 3
Consequentially, five topics of interest and their proportions are chosen: topic 1 “mining”; topic 7 “politics”; topic 10 “car”; topic 16 “labour”; and topic 20 “market”. In figure 4 the selected topics are illustrated via a “word cloud”, where the size of the words is indicative of their probability in the topic, and via their corresponding proportion in the news sample over time.
However, to make an important note with regards to the topic proportions: The New York Times publishes articles seven days a week, and as such news regarding aluminum is sometimes published in the weekend, when the aluminum futures markets do not trade. Assuming a one-period lag for the news and its contents to take effect on the market, this is solved by treating weekend news as if it was published on the Friday before.
Moreover, on some days no relevant articles are published, and on other days more than one relevant article is published. In such a case, the topic proportions of the articles that day are averaged, where news articles are assumed to be of equal importance for its effects on the aluminum market.
0 .2 .4 .6 .8 to p ic 1 5
01jan2000 01jan2005 01jan2010 01jan2015 01jan2020 time
Fig. 4 0 .1 .2 .3 .4 .5 to p ic 1
01jan2000 01jan2005 01jan2010 01jan2015 01jan2020 time 0 .2 .4 .6 to p ic 7
01jan2000 01jan2005 01jan2010 01jan2015 01jan2020 time
(a) Topic 1 “mining” (b) Topic 7 “politics”
0 .2 .4 .6 .8 to p ic 1 0
01jan2000 01jan2005 01jan2010 01jan2015 01jan2020 time (c) Topic 10 “cars” 0 .1 .2 .3 .4 .5 to p ic 1 6
01jan2000 01jan2005 01jan2010 01jan2015 01jan2020 time
(e) Topic 20 “market”
Fig. 4 (cont.)
First, what strikes is that the topic proportions are somewhat “evened out”, meaning that they will likely affect the aluminum price volatility over the time period studied. This also relates to the content of the topics, where more time-invariant topics are chosen, likely to be of relevance irrespective of the time frame selected. Secondly, a discrepancy with regards to total topic proportions between topics is observed. Indeed, of the selected topics, topic 20 “market” accounts for the largest percentage in the news sample: nine percent. This is
followed by topic 1 “mining” with five percent; while the rest of the selected topics show total news topic percentages between four– and five percent.
4.2. Aluminum futures contracts data
The price data for the aluminum futures contracts is found online via the Trading Economics website (https://tradingeconomics.com/commodity/aluminum). This source contains price data on business calendar dates, meaning effectively that price data is only observed on working days.
In order to estimate return volatility, the price data is transformed into log-return data via the following the formula:
0 .2 .4 .6 to p ic 2 0
01jan2000 01jan2005 01jan2010 01jan2015 01jan2020 time
78 = ln r j8
j8CBs (5)
This also follows from the presence of non-stationarity in the aluminum future price, which was tested with a unit-root test (see appendix 4). After transformation, the data is considered stationary, making it particularly useful for time-series models such as GARCH and
EGARCH. Both the price and log-return of the aluminum futures is plotted in figure 5.
Fig. 5
4.3. Macroeconomic and financial control data
For the macroeconomic and financial control variables, daily data is considered to match the frequency of the aluminum futures returns. Data for the CBOE S&P 100 Volatility Index (VXO), trade-weighted US dollar index (Dollar), and the treasury inflation-indexed bond yields (TIPS) is found on the website of the Federal Reserve Bank of St. Louis7. The data for
the ADS index is retrieved from the website of the Federal Reserve Bank of Philadelphia8, by
which it is also maintained9.
7https://fred.stlouisfed.org/
8https://www.philadelphiafed.org/
9 For the macroeconomic and financial control variables, day-of-the-week effects were considered. However,
these are not included as they provided no significant results. Furthermore, the control variables are included in model (4) at level, following the result of Han and Kristensen (2012) which states that statistical inference for the GARCH-X model is valid even when the covariates are non-stationary.
1000 1500 2000 2500 3000 3500 re tu rn
01jan2000 01jan2005 01jan2010 01jan2015 01jan2020 time -. 1 -. 0 5 0 .05 lo g R e tu rn
01jan2000 01jan2005 01jan2010 01jan2015 01jan2020 time
4.3.1 Macroeconomic and financial control correlation
The macroeconomic and financial variables included in (5) are control variables, and as such any collinearity between them can safely be ignored. Also, the control variables are not collinear with any variables of interest (see appendix 2). However, in order to give additional insight in the underlying control variables’ workings, a correlation matrix computed and shown in table 1.
ADS index VXO Dollar TIPS
ADS index 1
VXO -0.5154 1
Dollar 0.0087 0.2468 1
TIPS -0.0867 0.4754 0.5876 1
Table 1: Correlation coefficients for the macroeconomic and financial variables over the 1998-2018 period
The correlation matrix shows high correlation coefficients with regards to VXO and the ADS index, VXO and TIPS, and TIPS and Dollar. The high correlation between VXO and the ADS index of -0.5154 assumes a negative relationship between real economic activity and stock market volatility, a result which, perhaps, is not surprising. Furthermore, the ADS index measures economic activity and stock market indices are sometimes used as economic activity proxies. Recently Faccini et al. (2017) proposed a predictor for real market activity based on investor’s risk aversion extracted from the S&P 500 option prices. The correlation between the variables Dollar and TIPS is 0.5876, showing that an increase in TIPS yield coincides with an increase in trade-weighted dollar value. One possible explanation could be that when the US real risk-free interest rates rise, foreign investment increases, effectively increasing the trade-weighted dollar value.
4.4. Combining the data for estimation
As mentioned earlier, aluminum only trades on business days, whereas the news variables observations span the entire week. This was solved by treating weekend news as if it was published on the Friday before. However, the ADS index also measures seven days a week. In order to solve for this inequality, the weekend observations for the ADS index were dropped from the data sample. Furthermore, the dates September 25, 2001 and November 15, 2016 are
not present in the aluminum future price data, following this these observations were also dropped for the other variables. Summary statistics for all variables can be found in the appendix (appendix 1).
4.5. Missing data
As often in high-frequency time-series, missing values are observed in the data sample used. For all four control variables in (5) observations are missing. In order to tackle this problem, multiple imputation (MI) is employed. MI is a statistical technique which deals with missing data by using the distribution of the observed data in order to estimate sample set of plausible values for the missing values. This way, the missing values are replaced by the estimated plausible values on order to create a “complete” dataset. This complete dataset will then be used to estimate the EGARCH-X(1,1) model in (5).
5. Results
In this section the results of the different GARCH and EGARCH model estimations are shown and analyzed. Each of the following tables is focused on one topic in specific, where per topic the results of each volatility model specification is displayed and reviewed. The first topic 1 “mining” will be more in depth than the other topics, whereas statistical inference is relatively similar over the different topics volatility models.
To focus first on the standard GARCH(1,1) model (which does not include any additional regressor and can be found in all result tables), it can be seen that the parameters 6Band .Bare both positive and therefore do not violate the non-negativity constraint that is put on them. Furthermore, it can be seen that the value for 6Bis low and significant at the five percent level, which can be interpreted as that the volatility shocks this period hardly feed through the next periods’ volatility. The parameters 6Band .B combined is indicative of the rate at which this effects dies out over time, which in (2) sums up to roughly 1.2, which would indicate volatility persistence.
GARCH(1,1) (2) GARCH-X(1,1) (3) EGARCH-X(1,1) (4) EGARCH-X(1,1) (5) t .0000616 (.0001771) .0000649 (.0001785) .0001461 (.0001781) .0002111 (.0001732) uv -.0000332** (.0000147) -11.27796** (.699279) 1.021202* (.540412) -2.729363** (.5488513) uw .0981928** (.0124462) .1184038** (.0131726) xw 1.098385** (.092834) .8310219** (.0544891) 1.115243** (.0625982) .5098014** (.0795792) yw .0187165* (.0105518) .0532017** (.0164975) zw .2034209** (.0195326) .137036** (.0224706) {w -2.078781 (3.43306) -.1009004** (.0217003) -.095854** (.0344411) {| 6.415506 (10.14252) .6625131** (.2141565) .3599427 (.2883491) {} .0051422** (.0015433) {~ -.0207817** (.0023609) { .0708851** (.0145016) {Ä -.0811674** (.0192806) Obs 5217 5216 5216 5216 (imputed) LL 15276.7 15274.65 15277.19 - AIC -30545.39 -30537.3 -30540.37 - BIC -30519.15 -30497.95 -30494.46 -
Table 2: The GARCH and EGARCH model estimations for news topic 1 “mining”. The coefficients are shown on in the left column and follow from the model specifications of (2), (3), (4), and (5). * is an indication of significance at the 10% level, ** of significance at the 5% level. Notes: The coefficient {Å for the amount of news articles per day is omitted from the table. The variable was dropped from the estimation as it did not show significance in any of the models.
5.1. Topic 1 “mining”
Table 2 summarizes the results for the GARCH and EGARCH models for the topic “mining”. The GARCH-X(1,1) model shows clear significance at the five percent level for the GARCH model parameters. The value for 6B is seen to increase somewhat, which would indicate that a shock today affects volatility tomorrow more than in the benchmark GARCH(1,1) model.
Also, the value for .B decreases slightly, which would mean that this “shock effect” will fade out sooner. This also follows from the combined 6B+ .B, which drops from roughly 1.2 to ~ 0.95, indicating no volatility persistence. The news variables coefficients %B and %@ both show high standard errors and are not significant with high p-values (0.545 for %B and 0.527 for %@), which in combination with a lower maximum log-likelihood (15276.7 versus 15274.65) would not make aluminum return volatility better specified with the inclusion of the news topic “mining” in the GARCH(1,1) model.
The EGARCH-X(1,1) model (4), without the control variables, shows evidence for a leverage effect; albeit weak, as the asymmetric coefficient YB is positive and significant at the ten percent level. The effect is considered weak because of the low value of the coefficient (0.0187165), where a positive value is assumed to indicate that positive news (or price increase) increases volatility more than negative news. Furthermore, the coefficient for the symmetric effect, ZB, is significantly larger, indicating that the symmetric effect dominates the positive leverage effect. The coefficients for the news effects both show significance at the five percent level. The lagged news dummy variable, which is 1 on news days and 0
otherwise, shows a negative relationship with the conditional variance of the aluminum returns. This would indicate that the presence of news itself decreases aluminum market volatility. The topic variable “mining” shows positive relation with regards to volatility, which would mean that specific news with regards to mining would increase aluminum return volatility. Model (4) also beats the GARCH(1,1) and GARCH-X(1,1) with regards to
maximum log-likelihood and AIC and BIC estimates, indicating that aluminum futures return volatility is better specified with the inclusion of the additional news regressors.
The EGARCH-X(1,1) model with included control variables shows more of a positive leverage effect, as the asymmetric coefficient YB is larger and the symmetric coefficient ZB is smaller, indicating that the symmetric effect is less dominating (although bigger than the asymmetric effect). All of the control variables are highly significant, indicating that aluminum return volatility is indeed influenced by these variables. Perhaps surprising is the relatively small effect of the coefficient %b, which indicates the VXO index that models stock market volatility. A stronger positive effect was expected following the results of Mensi et al. (2013). The news dummy variable is still significant and negative, indicating that news lowers aluminum market volatility. The coefficient %@ for the topic “mining” is smaller and not significant, showing it not to be a volatility predictor when controlled for macroeconomic and financial dynamics in the background. Because of the imputed missing values in model (5), a
goodness-of-fit test for this specification cannot be estimated, as this is not supported by statistical software; making a fit comparison between model (4) and (5) not possible.
5.2. Topic 7 “politics”
In table 3 the results of the GARCH and EGARCH models estimations for the topic “politics” is shown. Again, the GARCH-X(1,1) model shows clear significance at the five percent level for the GARCH model parameters. The same dynamics as for topic 1 follow, as 6B increases and .B decreases, indicating that that a shock today affects volatility tomorrow more than in the benchmark GARCH(1,1), but the effects dies out sooner. Moreover, the news variables coefficients %B and %@ again both show high standard errors and are not significant, which in combination with a lower maximum log-likelihood would make this model a worse predictor of aluminum market volatility.
The EGARCH-X(1,1) model without controls again shows evidence for a weak leverage effect, as the asymmetric effect coefficient YB is positive. However, different from the estimations with topic 1, the topic 7 coefficient %@ is not significant, whereas the news dummy coefficient is. The EGARCH-X(1,1) shows a higher log-likelihood and lower AIC and BIC values, assuming it to be a better predictor of volatility than the standard
GARCH(1,1).
The EGARCH-X(1,1) model with included control variables again shows a bigger leverage effect and a significant news dummy coefficient and control variables, whereas the topic variable coefficient is not significant.
GARCH(1,1) (2) GARCH-X(1,1) (3) EGARCH-X(1,1) (4) EGARCH-X(1,1) (5) t .0000616 (.0001771) .0000667 (.0001799) .0001474 (.0001775) .0002097 (.000173) uv -.0000332** (.0000147) -11.37962** (.5710432) 1.022313* (.5522211) -2.66082** (.5478302) uw .0981928** (.0124462) .1180135** (.0124704) xw 1.098385** (.092834) .8384199** (.0391575) 1.11536** (.0639516) .5190072** (.0791871) yw .017814* (.0104308) .0526002** (.0164164) zw .2060494** (.0193) .1370004** (.0223296) {w .025097 (4.327877) -.0542992** (.0192601) -.076305** (.0320914) {| -80.21036 (310.6382) -.298666 (.1844287) -.0442854 (.3429841) {} .0051181** (.0015301) {~ -.0206139** (.0023271) { .0699437** (.0143552) {Ä -.0802641** (.019009) Obs 5217 5216 5216 5216 (imputed) LL 15276.7 15274.42 15274.74 - AIC -30545.39 -30536.84 -30535.47 - BIC -30519.15 -30497.49 -30489.56 -
Table 3: The GARCH and EGARCH model estimations for news topic 7 “politics”. The coefficients are shown on in the left column and follow from the model specifications of (2), (3), (4), and (5). * is an indication of significance at the 10% level, ** of significance at the 5% level. Notes: The coefficient {Å for the amount of news articles per day is omitted from the table. The variable was dropped from the estimation as it did not show significance in any of the models.
5.3. Topic 10 “car”
The model estimation results for the topic 10 “car” can be found in table 4. These results follow almost the exact same dynamics as those of topic 7 “politics”, the only differences being that the asymmetric coefficient YB is significant at the ten percent level instead of the five percent level observed at the estimations for topic 7, and the maximum log-likelihood of (4) is lower than that of (3) and (2).
GARCH(1,1) (2) GARCH-X(1,1) (3) EGARCH-X(1,1) (4) EGARCH-X(1,1) (5) t .0000616 (.0001771) .0000682 (.0001783) .0001514 (.0001777) .0002093 (.000173) uv -.0000332** (.0000147) -11.20817** (.7015288) 1.060629* (.5566829) -2.519709** (.5348228) uw .0981928** (.0124462) .1188048** (.0129043) xw 1.098385** (.092834) .8254854** (.0573778) 1.119729** (.0644716) .538968** (.077282) yw .0180805* (.0103852) .0517532** (.0163243) zw .2061019** (.0192565) .1375695** (.0221733) {w -.1170205 (2.027898) -.069019** (.0193883) -.0988428** (.0336746) {| -43.66058 (122.3372) -.0168439 (.2770586) .4683639 (.5632063) {} .0050217** (.0014854) {~ -.0201772** (.0022644) { .0686576** (.014023) {Ä -.0789712** (.018602) Obs 5217 5216 5216 5216 (imputed) LL 15276.7 15274.52 15274.01 - AIC -30545.39 -30537.03 -30534.03 - BIC -30519.15 -30497.68 -30488.11 -
Table 4: The GARCH and EGARCH model estimations for news topic 10 “car”. The coefficients are shown on in the left column and follow from the model specifications of (2), (3), (4), and (5). * is an indication of significance at the 10% level, ** of significance at the 5% level. Notes: The coefficient {Å for the amount of news articles per day is omitted from the table. The variable was dropped from the estimation as it did not show significance in any of the models.
5.4. Topic 16 “russia”
Results for the model estimations for the topic 16 “russia” are shown in table 5. Interpretation of the results are the same as for topic 1 “mining”, except that the log-likelihood of the EGARCH-X(1,1) model estimation is lower than that of the normal GARCH(1.1) estimation. However, both the AIC and BIC values are lower, indicating a better fit with regards to
GARCH(1,1) (2) GARCH-X(1,1) (3) EGARCH-X(1,1) (4) EGARCH-X(1,1) (5) t .0000616 (.0001771) .0000735 (.0001786) .0001672 (.0001783) .0002106 (.0001731) uv -.0000332** (.0000147) -11.40411** (.547027) 1.129863** (.5542358) -2.636135** (.5468982) uw .0981928** (.0124462) .1181732** (.0121843) xw 1.098385** (.092834) .8386944** (.0357546) 1.127826** (.0641933) .5225941** (.0793281) yw .0189222* (.0103045) .0525385** (.0163936) zw .2047844** (.0192998) .1374314** (.022317) {w -2.631156 (4.077437) -.0919276** (.0200716) -.0825983** (.0336893) {| 9.249335 (11.08385) .5701201** (.2193513) .0982334 (.365689) {} .0051001** (.0015224) {~ -.020523** (.0023461) { .069559** (.0144465) {Ä -.0797609** (.019013) Obs 5217 5216 5216 5216 (imputed) LL 15276.7 15274.89 15276.25 - AIC -30545.39 -30537.78 -30538.51 - BIC -30519.15 -30498.42 -30492.59 -
Table 5: The GARCH and EGARCH model estimations for news topic 16 “russia”. The coefficients are shown on in the left column and follow from the model specifications of (2), (3), (4), and (5). * is an indication of significance at the 10% level, ** of significance at the 5% level. Notes: The coefficient {Å for the amount of news articles per day is omitted from the table. The variable was dropped from the estimation as it did not show significance in any of the models.
5.5. Topic 20 “market”
The model estimations with the inclusion of the topic variable “market” are presented in table 6. The results are quite different than those of the other topics. Although the GARCH-X(1,1) parameter estimations follow a recognizable pattern with regards to 6B and .B, which both show significance at the five percent level, the topic variable coefficient %@ is significant in
contrast with the estimations for the other topic variable coefficients. Moreover, the effect seems unnaturally big with respects to the other coefficient estimations. Comparing AIC and BIC estimates between the GARCH-X(1,1) and GARCH(1,1) gives no further information, making it difficult to determine the fit of this model.
The EGARCH-X(1,1) model estimations also differs from the other topics in that no leverage effect can be detected: the asymmetric coefficient YB is positive, but not significant.
However, the EGARCH-X(1,1) model estimates with control variables paints a different picture. All variables are significant at the five percent level and a positive leverage effect is observed. The topic variable coefficient, %@, also assumes a value more in line with the other variables. Sadly, however, comparison via the goodness-of-fit measurements such as BIC is not possible due the imputed missing variables.
However, which must be noted, is that topic 20 “market” was the most prominent in the news text corpora, furthermore, its standard deviations were larger than those of the other topics studied. GARCH(1,1) (2) GARCH-X(1,1) (3) EGARCH-X(1,1) (4) EGARCH-X(1,1) (5) t .0000616 (.0001771) .0000573 (.0001784) .0001431 (.0001771) .0001992 (.000173) uv -.0000332** (.0000147) -10.72209** (.3928262) .7656729 (.5132936) -2.551838** (.5395511) uw .0981928** (.0124462) .1173516** (.0133172) xw 1.098385** (.092834) .777402** (.0529039) 1.085566** (.0594061) .5388295** (.0779959) yw .0150798 (.0109304) .0517518** (.0163426) zw .2011888** (.0189433) .1331625** (.0225456) {w -1.568824 (1.018638) -.1314216** (.0221423) -.1221587** (.0329763) {| 6.314894** (3.155548) .6283852** (.139752) .4361904** (.2201601) {} .0051372** (.0014786) {~ -.0198371** (.0022788) { .0693362** (.0141706) {Ä -.0745186** (.0187838)
Obs 5217 5216 5216 5216 (imputed)
LL 15276.7 15280.44 15281.99 -
AIC -30545.39 -30548.87 -30549.99 -
BIC -30519.15 -30509.52 -30504.07 -
Table 6: The GARCH and EGARCH model estimations for news topic 20 “market”. The coefficients are shown on in the left column and follow from the model specifications of (2), (3), (4), and (5). * is an indication of significance at the 10% level, ** of significance at the 5% level. Notes: The coefficient {Å for the amount of news articles per day is omitted from the table. The variable was dropped from the estimation as it did not show significance in any of the models.
6. Conclusion
This thesis investigates the long-term relationship between news and its contents and the volatility of aluminum futures contracts returns. Via a LDA model 20 topics and their
proportions over time were extracted from 2147 aluminum-related news articles from the The New York Times, spanning a 20 year period (31-03-1998 / 30-03-2018). After careful
selection, five topics and their distributions are modeled via multiple GARCH and EGARCH model, where a specific EGARCH model included high-frequency macroeconomic and financial control variables.
Firstly, the LDA model captures the topics in the news successfully, finding topics that are easily interpretable and that divide the underlying content well. Secondly, most of the topics seem to positively affect aluminum future volatility, where an EGARCH-X(1,1) model with additional news regressors in the conditional variance seems to model the return
volatility better than the benchmark GARCH(1,1) models. Moreover, the topic “market” seems to significantly positively affect the long-term aluminum return volatility even when controlled for macroeconomic and financial events.
With regards to future work, volatility models which allow for different frequency data could perhaps be utilized, where more low frequency control variables can be added to control for background events such as inflation. The GARCH and EGARCH models used in this thesis only allow for high-frequency data.
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