Industrial energy demand in the Philippines — Assessing model for forecasting: decomposition method vs. error-correction method, and demand elasticity

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Industrial energy demand in the Philippines — Assessing

model for forecasting: decomposition method vs.

error-correction method, and demand elasticity

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Acknowledgment

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Abstract

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1 Introduction

Industry sector is among the major consumer of energy in the Philippines which comprise about one-fourth of the total energy consumption. Its pattern of energy consumption has a great bearing on the energy balance of an economy. See Liu (2005). A large number of arti-cles in energy economics deal with the quantitative assessment of various factors affecting industrial energy consumption. Assessment of these factors is important not only for a bet-ter understanding of past behavior of industrial energy demand but in particular estimating energy requirements of alternative industrialization strategies in developing countries. See Liu (2005).

The variety in which industrial energy is used in production processes, makes it one of the hardest end-uses to analyze, model and forecast. Many studies employ decomposition techniques for the empirical analysis of energy consumption. These empirical analysis has been focused on the changes in the composition of economic activities and its impact on ag-gregate measures of energy intensity. Such studies, includes Myers and Nakamura (1978) and Ang and Zhang (2000), have made connection to the economic theory of index num-bers. Early studies used a fixed base year index that is analogous to Laspeyres index, (for example see Boyd, McDonald, Ross, and Hanson (1987)). See Boyd and Roop (2004). It is also interesting to note that prominent institutions in energy modeling and forecasting such as the National Energy Modeling System (NEMS) of Energy International Agency (EIA), use indexing procedure or decomposition method (DM) (see IAEA (2005)) in the Annual Energy Outlook. This method assumes that energy consumption can be split up to certain com-ponents, for example energy intensity and production (usually denoted by gross domestic product, GDP). Thus, energy consumption movement depends on the unit change of GDP.

Another method surveyed in this paper is the widely used approach in macro-economic forecasting is the Error-correction model (ECM). Early versions of ECM are of Sargan (1964) and Philips (1957) among which were given credits from the works of Davidson, Hendry, Srba, and Yeo (1978), Hendry and Ungern-Sternberg (1981), Currie (1981), Dawson (1981) and Salmon (1982), Hendry, Pagan, and Sargan (1984) and others (see Engle and Granger (1987)). These were even more popularized by Engle and Granger (1987) version of ECM. Recently it has also been used in the analysis of the relationship between energy consump-tion and economic growth (for example, see Hondroyiannis, Lolos, and Papapetrou (2002) and Fatai, Oxley, and Scrimgeour (2004)). The idea is that if the residual of the two variables are non stationary, these series requires a differencing in order to attain a stationary state. Then a long-run relationship is determined to improve forecasting over an unconstrained model.

Since decomposition technique does not require statistical analysis, which could be mis-leading, this paper examines the relationship of industrial energy demand with its corre-sponding economic activity denoted by gross value added (GVA) of the industry sector. Then proceed with forecasting using the decomposition technique and survey its perfor-mance given the outcome of the endogeneity test. Next, we survey ECM method of fore-casting and compare the result with DM approach step-forefore-casting of demand and ten-step ahead forecast. Second major issue evaluated in this paper is the industrial energy demand

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elasticity with respect to income and energy fuel prices evaluating further the estimated result of error-correction models. The empirical analysis distinguishes between the four sub-sectors of industry: manufacturing, mining, construction and electricity, are treated in-dependently.

The empirical result of the endogeneity test show that economic activity is exogenous to industrial energy demand in all the four sub-sectors except mining while industrial energy demand is endogenous to economic activity. This would mean that we cannot use economic activity alone as an explanatory variable in forecasting. Given this result, we find that it has not affected DM’s performance in forecasting. Performing the usual test of regression analysis, we find that DM’s forecasts are significant. On the other hand, in step-forecasting, ECM is better but surprisingly, in a ten-step ahead forecast, its performance is poor. Thus, ECM is capable of a short-run forecast while in the long-run forecast, it is better to use DM approach of forecasting. Furthermore, with the estimated ECM, we find that industrial en-ergy demand as a whole is income and price elastic in the long-run but not in the short-run. The succeeding sections are presented as follows. The statement of the problem is pre-sented in section 2 and section 3 presents the data used and sources. In section 4, we dis-cuss the different methods used in the following order: section 4.1, disdis-cusses the concept of causality tests to determine the interrelationship between industrial energy consump-tion and its corresponding economic activity; in secconsump-tion 4.2, the principle of decomposiconsump-tion technique of forecasting is discussed; and section 4.3 discusses the cointegration and ECM. Empirical results and conclusions are presented in section 5.

2 Thesis statement

In economics, the level of consumption or demand depends on the level of income and price of goods/commodity. Thereby, energy as a commodity of industrial process is consumed as intermediate goods to enable economic activity. So that energy consumption is assumed that it can be split up to certain components, for example energy intensity and production. This technique is called decomposition method. It has been widely used in the analysis and forecasting of industrial energy consumption. This method is adopted from Laspeyres, Paasche and Fisher indexing which are commonly used to measure the inflation rates. In energy economics, it is used to measure the change in energy consumption1 _{(see Boyd and}

Roop (2004)). In this method, economic activity is assumed as the principal component in measuring the change in energy consumption. In this light, we want to examine the rela-tionship between economic activity and energy consumption. Particularly, we want to focus our study on the following questions:

1. Is there a link between economic activity and industrial energy consumption?

2. Whether true or not, how would it affect the industrial energy demand forecasting?

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Moreover, we also want to use the widely used method of forecasting in economics to industrial energy demand. We adopt the error-correction model as this method identifies and corrects the linearity between the variables wherein causality is also considered . We use the usual macro-economic relationship where consumption is described as a function of income and price. So that our study extend to the following arguments:

3. Which method is better for a. short-run forecasting? b. long-run forecasting?

The second part of the part of the analysis in this paper deals on the industrial energy demand price and income elasticities. ECM cointegrating relationship allows us to compare the immediate and overall elasticities of demand, and the model will show the speed of ad-justment. With this study we provide an answer to the next question.

4. Is the industrial energy demand income elastic and price elastic: a. in the short-run?

b. in the long-run?

3 Approach/methods

3.1 Causality test

The empirical analysis tests for the endogeneity of industrial energy consumption E and economic activity (denoted by gross value added, GVA), Y . The relationship between E and Y is determined by causality test introduced by Granger (1969) and Sims (1972). In this test, we say that Y causes E if it satisfies two conditions. First Y as exogenous variable should help estimate E. Second, E should not help in the estimation of Y (see Pindyck and Rubin-field (1998)).

The first condition will be tested as follows. To determine whether Y causes E, we test the null hypothesis Y does not cause E with the unrestricted model (1) and restricted model (2) as unrestricted model: Et = α0+ m X i=1 αiEt−i+ m X i=1 βiYt−i+ εi (1) restricted model: Et = α0+ m X i=1 αiEt−i+ εi (2)

The second condition is to determine whether E causes Y . This test is performed by making Ytthe dependent variable and Etthe independent variable given in the form

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unrestricted model: Yt = δ0+ m X i=1 δiYt−i+ m X i=1 γiEt−i+ εi (3) restricted model: Yt = δ0+ m X i=1 δiYt−i+ εi (4)

where i = 1, ..m stands for the number of lags. The lag length is determined by the Akaike Information Criterion (AIC) and Schwarz Bayesian Criterion (SBC). It is important to set the number lags at its optimal level where it is sufficient to eliminate the serial correlation in the residuals.

Each test is performed by simply running an ordinary least square on each model and compare the group of estimators of the unrestricted and the restricted model using F-test. The sum of squared residuals, RSSur and RSSr for unrestricted and restricted models,

re-spectively are used to calculate F-statistics and test whether the group of estimators, β and γsignificantly differ from zero. F-statistics is calculated as F = (N − k)RSSr−RSSur

q(RSSur) where N

is the number of observations; k is the number of estimated parameters of the unrestricted model; and q is the number of parameter of restrictions; with F (q, N − k) distribution. See Pindyck and Rubinfield (1998).

3.2 Decomposition method

In this section we discuss decomposition technique of forecasting. Energy consumption is decomposed in two ways that is energy consumption approach and energy intensity ap-proach. The first specifies the change in aggregate production level, structural change in production and changes in sectoral energy intensities while the latter involves only the struc-tural change in production and sectoral energy intensity (see Liu (2005)). Since our focus is to forecast on a sector by sector level of industry, we adopt the latter approach. Industrial energy consumption by sector is therefore decomposed as

E = E

Y · Y = I · Y (5)

Sun (2001) introduced forecasting technique employing complete decomposition on the in-dustrial energy consumption using energy consumption approach. The basic idea of this method follows a variation formula of the factorial analysis of the change in an examined index: A − B = C ⇒ B + C = A (see Sun (2001)). Applying this to an intensity approach (5), the index E is decomposed by the factors I and Y . In a complete decomposition method, the change in E is equal to sum of the effects from each factor calculated as

∆Et = Et− Et−1

= ItYt− It−1Yt−1

= (It− It−1)Yt−1+ (Yt− Yt−1)It−1+ (It− It−1)(Yt− Yt−1)

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where the term Yt−1∆Itis the change of I and It−1∆Ytis the change of Y and ∆It∆Ytdenotes

the residual term (see Liu (2005)). Since the change in E is defined as the sum of Ief f ectand

Yef f ectin the form,

∆E = Ief f ect,t+ Yef f ect,t, (7)

we derive Ief f ect,tand Yef f ect,tfrom (6) and (7) and define the effects as follows:

Ief f ect,t = Yt−1∆It+ 1 2∆It∆Yt (8) Yef f ect,t = It−1∆Yt+ 1 2∆It∆Yt. (9)

We measure the economic indices by the change rate of the factors I and Y . The change rate of I, is referred to as α and β as the rate of change of Y from time t = 1, ...T . Thus, we have ∆It = αIt−1and ∆Yt= βYt−1(see Sun (2001)). Inserting αIt−1and βYt−1in (8) and (9), we

have Ief f ect,t = αEt−1+ 1 2αβEt−1 (10) Yef f ect,t = βEt−1+ 1 2αβEt−1 (11)

Then we estimate the I and Y effects using (10) and (11). Finally, sectoral industrial energy demand is forecasted by the sum of (5) and (7) in the form

Et= Et−1+ ∆Et= Et−1+ Ief f ect,t+ Yef f ect,t. (12)

3.3 Cointegration and Error-Correction Method

One of the basic assumption in modeling and forecasting is stationarity. It could be mislead-ing if we assume the mean, variance and covariances of a series to be constant when in fact they’re not. It is in this context that cointegration test is necessary.

Cointegration is a technique for testing the correlation between non-stationary time se-ries variables. A variable is said to be a non-stationary if deviation of the residuals are likely to depart from zero. If the variables are non-stationary, but their linear combination is sta-tionary (integrated of order zero, I(0)) then the series are said to be cointegrated. For exam-ple, if two variables having unit roots (integrated of order one, I(1)) are tested, say, a series of X is equal to 5,6,7, and 8. We get an increments of 1 by getting the first differences. So we get a stationary series by differencing it once, which means our original series was inte-grated of order one, I(1)2. So that a series is said to be of order d if it become stationary after differencing d times.

Engle and Granger (1987) discussed the joint properties of integrated series. For ease of assumption, we consider the series Etand Ythaving an I(1) property could also have an

I(1) linear combination. However, it occurs that the linear combination of two I(1) variables is in fact I(0) if a new variable utcan be defined by

ut= Et− λYt (13)

2_{From Wikipedia, the free encyclopedia}

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where u is an I(0) then Etand Yt are said to be cointegrated and λ is the constant of

coin-tegration or in the case of more than two variables the set of λ values is the coincoin-tegration vector. The variable u is the error term and a constant can be included in (14) to make its mean zero so that it becomes the cointegrating regression equation. Thus, a linear consump-tion funcconsump-tion consisting of I(1) variables may have staconsump-tionary residuals so we can say that they are cointegrated.

Now, let us consider some properties of cointegrated variables (see Holden, Peel, and Thompson (1990)).

• A constant in (14) does not affect the model.

• If two variables are cointegrated then the constant of cointegration are said to be unique. • Cointegration of two variables implies that both will not drift apart, since, u measures

the distance between E and Y , which is regarded as the error, is stationary with zero mean. This can be written as

Et− λYt= 0 (14)

which is interpreted as the long-run or equilibrium relationship between Y and E. • Engle and Granger (1987) proved that two variables with I(1) property have constant

means and are cointegrated then an error-correcting data generating mechanism or error

correction model (ECM) exists which takes the form

∆Et = −ρ1ut−1+ lagged(∆Et,∆Yt) + d(L)ε1t (15)

∆Yt = −ρ2ut−1+ lagged(∆Et,∆Yt) + d(L)ε2t (16)

where utis given by (14), d(L) is a finite polynomial in the lag operator, and ε1and ε2

denote disturbance terms which are possibly contemporaneously correlated. Finally, we define |ρ1| + |ρ2| 6= 0.

3.4 Energy demand ECM specification and estimation

The ECM industrial energy demand model is in the form

  ∆Et ∆Yt ∆Pt  =   A11(L) A12(L) A13(L) ρ1 τ1 A12(L) A22(L) A23(L) ρ2 τ2 A13(L) A32(L) A33(L) ρ3 τ3         ∆E_t−1 ∆Y_t−1 ∆P_t−1 u_t−1 v_t−1       +   C1 C2 C3  +   ε1t ε2t ε3t   (17)

where L is the lag operator , so that Lmεt = εt−m. The parameters Aij(L) on the lagged

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between the equations. The multivariate disturbance εit, i = 1, ...3 could be

contempora-neously correlated. Another condition from the Engle and Granger (1987) Representation theorem is that |ρ1| + |ρ2| + |ρ3| 6= 0 in (17), so that ut−1and must exist in at least one of the

equations. If ρ1 = ρ2 = ρ3 = 0, then error term is omitted. The same holds for the τ s. The

error correction variable in (17) is defined as ut= Et− β1Yt− β2Ptand vt= Et− γ1Yt− γ2Pt.

The ECM estimation is done in the following procedure:

1. To determine the order of integration of the variables, we employ Dickey-Fuller test which is discussed at length by Engle and Granger (1987);

2. Since Engle and Granger (1987) two-step procedure of cointegration is best applied to a univariate case, in this paper we employ the cointegration method proposed by Jo-hansen (1988) and JoJo-hansen and Juselius (1990). This procedure is simply the general-ization of augmented Dickey-Fuller test which takes the form of a likelihood test. See Enders (1995) for a detailed discussion of the method.

3. The forecasting of the energy demand follows Engle and Yoo (1987) method. The infor-mation set for the equilibrium relationship determined by the maximum lilkelihood estimates (MLE) of Johansen-Juselius procedure is tied up in the optimal forecasting. Forecasting with ECM must follow an implication of causality in at least one direction between the variables with the condition that |ρ1|+|ρ2|+|ρ3| 6= 0 and |τ1|+|τ2|+|τ3| 6= 0.

These ensure error-correction term, utand vt−1to enter one of the three equation in (17)

to improve the forecast performance of at least one variable. See LeSage (1990).

4 The data

The panel data examined in this paper consist of manufacturing, mining, construction and electricity of the industry sector for the industrial energy consumption. It covers an annual series from 1981 through 2004. These were provided by the Department of Energy (DOE) of the Philippines. Income or economic activity indicator used is the gross value added (GVA) of the industry sector at 1985 constant prices, broken down into manufacturing, mining, con-struction and electricity sub-sectors from the National Statistical Coordination Board (NSCB) of the Philippines.

Fuel prices compiled by DOE were used to calculate the nominal prices of energy fuels. We use historical pump prices of the petroleum products. For coal prices, import prices from 1988-2004 were used since a bigger portion of coal consumption is imported coal. From 1981 to 1987 coal prices were calculated based on the unit change of the Consumer Price Index (CPI). Similarly, electricity prices from 1981-1987 were calculated based on CPI. The use of natural gas in the industrial process was only made available from 2001 to date through a local production, so prices used for this fuel are from the period 2001-2004. However, there is no available price for the non-conventional fuel such as bagasse3_{, etc. (classified as}

3_{Bagasse is a waste from sugar cane used a energy source in the manufacturing or refining sugar.}

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renewable energy or RE source). But this does not affect our study because the total RE con-sumption comprise an average of 0.01% in the total industrial energy concon-sumption.

Nominal prices of energy fuels were calculated by weighing the consumption of each fuel in the total industrial energy consumption multiplied by its corresponding price and finally get the sum of the products. Thus, we used one series of prices for all the sub-sectors of industry. We aggregated the fuel price of energy since industrial processing plants do not use the same fuels.

Figure 1 shows the graphs of industrial energy consumption by sub-sector. Among the sub-sectors, manufacturing seems to be the most difficult to forecast due to a unsta-ble growth. The effect of the variety of energy use in the production process is obvious in this sector. 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 0 500 1000 1500 2000 2500 3000 3500 4000 4500

Industrial Energy Consumption

tons of oil equivalent, TOE

Figure 1: Industrial Energy Consumption plotted by sector. Dotted line represents manufacturing, dashed line to mining, dash/dot to construction and solid line to electricity.

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it will not affect the performance of our estimation. Scrutinizing further, at a glance, we can see that industrial energy demand is price elastic. In all the sub-sectors, it is clearly seen that demand decreases when price increases. In terms of income, elasticity of demand is not obviously seen in Figure 2.

1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 0 1 2 3 4 5 6 7 8 Manufacturing Sector 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 0 1 2 3 4 5 6 7 8 Mining Sector 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 0 1 2 3 4 5 6 7 8 Construction Sector 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 0 1 2 3 4 5 6 7 8 Electricity Sector

Figure 2: Graphs of energy consumption (dash/dot lines) plotted against GVA (dashed lines)

and nominal prices of energy (solid lines) in their log levels.

5 Empirical results

5.1 Results of Modeling and Forecasting

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the variables (m = 1). Then we proceed with the estimation of models (1), (2), (3) and (4) by an OLS regression.

Table 1: Test for lag lengths

m AIC SBC AIC SBC Manufacturing Construction 1 -78.772 -75.366 -77.525 -74.118 2 -76.292 -70.837 -74.646 -69.191 3 -71.175 -63.863 -67.111 -59.800 4 -68.971 -60.009 -59.738 -50.776 Mining Electricity 1 -56.336 -52.929 -130.421 -127.015 2 -54.679 -49.224 -127.559 -122.104 3 -56.112 -48.801 -120.113 -112.801 4 -53.738 -44.777 -111.818 -102.856

Table 2 presents the results for the endogeneity test between energy consumption and GVA per sub-sector of the industry, Y . In section 4.1, we noted two conditions that must be satisfied in order to allow us to use Y as a function of energy consumption. These conditions are: 1) Y must help predict energy consumption (Y → E); and 2) energy consumption must not help predict Y (E not→ Y ). The empirical result in all the sectors except mining subsector (Table 2) suggests that industrial economic activity Y does not help predict industrial energy consumption E but E → Y . Thus, we cannot use Y in the forecasting of energy consumption alone.

Table 2: Granger Causality Test

Null Hypotheses F(1,23) Probability F(1,23) Probability

Manufacturing Construction H0,1: Y not→ E 1.251 0.276 2.833 0.107 H0,2: E not→ Y 198.188 0.000 21.591 0.000 Mining Electricity H0,1: Y not→ E 7.884 0.010 2.111 0.161 H0,2: E not→ Y 24.630 0.000 12.219 0.002

Decomposition Method of Forecasting

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β in (10) and (11), respectively, are calculated on a year by year basis. It follows that Ief f ect

and Yef f ect factors are estimated annually. Then we estimated annual effects and use it to

calculate the historical step by step forecasting.

The result of the forecasts are presented Figure 3 and the diagnostic test of the forecast is presented in Table 3. In Figure 3, we find that the forecasted values lies within the confi-dence bounds at 95% significant level. Notice in Figure 3 that the forecast errors seemingly follows the trend of the predicted values. In this case, it would imply that the forecast errors contains information of the prediction which is a violation of an independence of the errors. Hence, we investigate the residuals for the presence of serial correlations employing sample autocorrelation function (SACF). The test results suggest no serial correlation (Figure 4) as the sample autocorrelations do not exceed the critical value of ±0.4170 at 95% significance level and die out as the number of lags increases.

Since the forecast is not obtained from a linear regression, the diagnostic test is only per-formed on the residuals of the forecast. The sum of squared residuals³R2 = 1 −(P E− ˆE)2

P ( ˆE− ¯E)2

´

are impressive. In Table 2 that the decomposition model explains about 43% to 87% of the estimates. Hence, we can say that consumption is correlated with the change in intensity and sectoral GVA Y . Moreover, the standard errors ³σˆ2_f = P ˆε2i

N −2, where ˆεi = E − ˆE

´ of the forecasts on each sector are significantly close to zero, thus, we conclude that the model fits the data well.

Table 3: Simulation Statistics of Decomposition Forecasts Manufacturing Mining Construction Electricity

R2 0.427 0.863 0.865 0.8707

¯

R 0.393 0.855 0.857 0.8631

σ_f2 0.031 0.064 0.046 0.0060

RMSE 0.167 0.239 0.204 0.0734

Error-Correction Model Forecasting

As we have pointed out in section 4.4, forecasting with ECM must follow an implication of causality in at least one direction between the variables (see Engle and Yoo (1987)). There-fore, we must verify first the order of integration of the variables since the causality test is valid if the variables are in the same order. The AIC and SBC statistics (see Table 9 of the Appendices for the result of the test) suggests that we used length of lags for the following sectors: manufacturing, m = 4; mining, m = 3; m = 1; and electricity, m = 4. In construc-tion, we find a conflicting result: AIC suggests m = 4 and SBC suggests m = 1. Thus, we perform ADF unit root test from m = 1, .., 4 and decide which lag length is better in the construction sub-sector as we go along with ECM procedure. Other implication will be dis-cussed in the latter part of this section. The result of the test is presented in Table 4. ADF test suggests that the variables of manufacturing, mining and electricity are integrated of order one I(1) with the specific lag lengths suggested by AIC and SBC significant at 5% level. In

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1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 5 6 7 8 9 10 11

1a. Actual vs. Predicted Manufacturing Consumption

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 −0.4 −0.2 0 0.2 0.4 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 0 2 4 6 8 10

1b. Actual vs. Predicted Mining Consumption

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 −0.4 −0.2 0 0.2 0.4 0.6 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 1 2 3 4 5 6 7 8

1c. Actual vs. Predicted Construction Consumption

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 −0.2 0 0.2 0.4 0.6 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 5.5 6 6.5 7 7.5 8

1d. Actual vs. Predicted Electricity Consumption

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 −0.1 −0.05 0 0.05 0.1 0.15

Figure 3: Decomposition Method: Time Series forecast plotted against the actual series. There are four sets of graphs which corresponds to the four sub-sectors. The upper graphs of each set correspond to predicted and actual series plotted against the their confidence intervals and the lower graphs to forecast error. The solid lines correspond to predicted series, dashed lines to actual series and dash/dot lines to the upper and lower confidence bounds at 95% significance level.

the construction sub-sector, we find the same order of integration in all its variables at lag length m = 1 at 5% significant level, hence, we choose SBC’s suggestion in favor of m = 1. Since we find the same order of integration on all the variables in all the sub-sectors, this lead us to perform Johansen and Juselius (1988) generalized cointegration procedure.

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0 2 4 6 8 10 12 14 16 18 20 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4

Sample Autocorrelation Function

Lags

Sample Autocorrelation

Figure 4: Sample autocorrelation function of the residuals for decomposition method.Critical value for all the sectors is equal to ±0.4170. Dotted represents manufacturing, dashed to line, dash/dot line to construction and solid line to electricity.

Table 4: Unit root test (Augmented Dickey Fuller Test) m Manufacturing Mining Construction Electricity E 1 -1.647 -3.348 -1.651 -2.558 2 -1.294 -2.545 -1.563 -2.805 3 -1.127 -1.950 -1.614 -2.655 4 -1.747 -3.094 -1.211 -2.982 Y 1 -1.113 -0.914 -1.990 -4.907 2 -3.957 -1.020 -3.119 -3.492 3 -3.861 -1.006 -4.626 -3.544 4 -2.216 -0.873 -4.445 -3.219 P 1 -2.982 -2.982 -2.982 -2.982 2 -1.331 -1.331 -1.331 -1.330 3 -0.799 -0.799 -0.799 -0.799 4 -0.890 -0.890 -0.890 -0.890 Critical 1% 5% 10% Value -4.200 -3.545 -3.215

The cointegration test is summarized in Table 6. This is performed on three variables involving industrial energy consumption by sector, E, the corresponding GVA on each sub-sector, Y and the nominal prices of energy fuels, P . We find that trace statistics and maximal

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Table 5: Granger Causality Test

Dependent Ei Yi P

Variable F-stat Prob F-stat Prob F-stat Prob

Manufacturing, m = 4, F(19,15) E1 4.962 0.074 7.614 0.037 3.101 0.149 Y₁ 0.474 0.756 4.397 0.090 2.059 0.250 P 0.648 0.657 0.038 0.995 0.704 0.628 Mining, m = 3, F(20, 12) E2 3.884 0.055 22.364 0.000 20.992 0.000 Y₂ 0.627 0.617 0.914 0.475 1.210 0.366 P 2.266 0.157 0.884 0.488 0.978 0.449 Construction, m = 1, F(22, 4) E3 1.816 0.194 0.042 0.839 4.287 0.053 Y3 0.724 0.405 0.032 0.859 6.357 0.021 P 0.018 0.894 5.716 0.027 1.753 0.202 Electricity, m = 4, F(19, 15) E4 16.958 0.008 12.921 0.014 12.136 0.016 Y4 2.008 0.257 1.782 0.294 0.809 0.578 P 3.162 0.145 4.488 0.087 8.732 0.029

eigenvalue in manufacturing, mining and electricity sectors do not exceed the critical value at 95% level. Hence, we cannot reject the null hypothesis of two cointegrating relationship, (r = 2). However, we cannot reject null hypothesis with r ≤ 0 and r = 0 for the trace statistic and maximal eigenvalue, respectively in contruction sector. Therefore, we conclude that the cointegrating relationship for this sector is zero (r = 0). This result coincides with the above result where we find three causality direction in the construction sector. This would imply that error-correction term (ECT) is not necessary in its estimation. Hence, the estimation is simply a vector autoregressive (VAR) in difference level. Recall that the number of cointe-grating relationship suggests the inclusion of ECT equal to the number of r, thus, we include two ECTs for all the sectors where we find two causality direction and with cointegrating re-lationship r = 2.

Table 6: Test for Cointegration, MLE estimates

Manufacturing Mining Construction Electricity 90% 95%

H0 H1 m= 4 m= 3 m= 1 m= 4 CV CV

λtrace λtrace λtrace λtrace

r≤ 0 r >0 170.746 71.004 20.774 112.589 27.067 29.796

r≤ 1 r >1 38.128 17.873 9.816 52.347 13.429 15.494

r≤ 2 r >2 1.924 0.076 3.482 0.408 2.705 3.841

λmax λmax λmax λmax

r= 0 r = 1 132.618 53.131 10.957 60.242 18.893 21.131

r= 1 r = 2 36.204 17.797 6.334 51.938 12.297 14.264

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We now proceed with ECM forecasting using the causality and cointegration informa-tions. The result of the forecast versus the actual values and forecast residuals are shown in Figure 5. Each sector is plotted against its actual values along with its confidence bounds (95% significance level); and the corresponding forecast residuals are shown on the adjacent lower plot. We can clearly see from the graphs that all the forecast values lie within their confidence intervals. And we also find that forecast errors are significantly different from zero. 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 7 7.5 8 8.5 9

2a. Actual vs. Predicted Manufacturing Consumption

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 −0.4 −0.2 0 0.2 0.4 0.6 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 3.5 4 4.5 5 5.5 6 6.5

2b. Actual vs. Predicted Mining Consumption

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 −0.4 −0.2 0 0.2 0.4 0.6 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 1 2 3 4 5 6 7

2c. Actual vs. Predicted Construction Consumption

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 −0.4 −0.2 0 0.2 0.4 0.6 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 6.4 6.6 6.8 7 7.2 7.4

2d. Actual vs. Predicted Electricity Consumption

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 −0.4 −0.2 0 0.2 0.4 0.6

Figure 5: Error-Correction Method: Forecast plotted against the actual series. There are four sets of graphs which corresponds to the four sectors. The upper graphs of each set correspond to predicted and actual series plotted against the their confidence intervals and the lower graphs to forecast error. The solid lines correspond to actual series, dashed lines to predicted series and dash/dot lines to the upper and lower confidence bounds at 95% significance level.

In Figure 5, seemingly, the forecast errors are independent from the predicted values. To determine if this observation is satisfied statistically, we perform a test for sample autocor-relation on the residuals. The empirical results are shown in Figure 6. The figure depicts that the sample autocorrelations of the residuals in all the sectors die out as the number of

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lags increases at 95% significant level. The lags (5, 2, and 1 for manufacturing, mining and electricity, respectively) which shows seeming autocorrelation in the residuals are further tested by Lagrange Multiplier (LM). The tests do not reject the null of no autocorrelation in the residuals.4 Hence, the assumption of no serial correlation in the forecast residuals is satisfied. 0 2 4 6 8 10 12 14 16 18 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3

Sample Autocorrelation Function

Lags

Sample Autocorrelation

Figure 6: Sample Autocorrelation Function of the Residuals. Critical value of manufacturing (dotted line) is equal to ±0.458, mining (dashed line) to ±0.447, construction (dash/dot line) to ±0.426 and electricity (solid line) to ±0.458.

Now let us examine if the residuals significantly differ from zero. The results are sum-marized in Table 7. The mean of the residuals in all sectors are almost zero. Skewness of the manufacturing, mining and construction are skewed to the left, implying that the data series carry an information from the past, while residuals of electricity is skewed to the right. We can also see that the kurtosis of construction and electricity sectors are close to 3 which sig-nifies normality while manufacturing and mining exceeds the the value of 3 which suggest a departure from normality. Finally, we perform a test for normality of the residuals. The Jarque-Bera statistics (Table 7) do not exceed the critical value of 5.991 (5% level) in all sec-tors. This suggests that the residuals are significantly different from zero, thus we conclude that the residuals are normally distributed.

We have tested for the long-run equilibrium relationship between the variables. The results show that all the equations in each sector excluding construction, exhibit two cointe-grating relationships (r = 2). In this sense, the model include 2 error-correction term (ECT) (corresponding to the cointegration rank r) to improve the forecastability in at least one of

4_{For manufacturing, lags 1 up to 5 is futher tested by LM test, results suggest no autocorrelation in the}

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Table 7: Jarque-Bera test for normality of the residuals Manufacturing Mining Construction Electricity

Mean -0.000 0.000 0.000 -0.000 Std dev. 0.024 0.043 0.166 0.008 Skewness -0.754 -0.005 -0.022 0.006 Kurtosis 4.334 2.538 2.076 2.623 JB-stat 2.158 0.419 1.127 0.330 Probability 0.339 0.810 0.569 0.847 Crit. Val. 5.991 5.991 5.991 5.991

the variables. Construction sector on the other hand, exhibit no cointegrating relationships but the variables have three causality direction. Therefore, we assume that the model exhibit linear relationship between the dependent and the independent variables. The assumption of no serial correlation in the residual is also satisfied in the SACF test. Figure 6 shows that the confidence bounds (at 95% significant level) do not increase or decrease over time and over the prediction, hence, we assume that the residuals are homoschedasctic or have a con-stant variance. Moreover, Jarque-Bera test suggest that the residuals exhibit normality. Thus, ECM satisfies all the four principal assumption of a linear regression. Therefore, we can use the model to a ten-step ahead forecast.

Decomposition model versus ECM

In this section, we compare the result of the historical forecast of DM and ECM. The graph of decomposition model forecast are presented in Figure 3 with the corresponding error fore-casts while Figure 4 presents the ECM forefore-casts. The empirical result show that in both figures the predicted values lie within the confidence interval at a significant level of 95%. The graphs also show that the confidence bounds of decomposition models are relatively wider which would imply that the ECM forecast performance is better. Moreover, the mean absolute error and forecast error of ECM are relatively lesser as evidently seen in the Figure 5. These results suggest choosing ECM to model the three sectors of industrial energy de-mand (manufacturing, mining and electricity) and a VAR model in difference level for the construction sector.

Ten-step Ahead Forecast

Let us investigate further the ability of the two methods for a ten-step ahead forecast since forecasting is commonly known as predicting the future. Figure 7, exhibits the result of the simulation of a 10-step ahead forecast of DM and ECM. Again, to get a comparable estimate of the two methods, we performed the ten-step ahead forecast on the logarithms of the se-ries on both methods and then transformed it to their levels. In this case, we find that DM’s performance has improved. In all the sectors ECM’s future forecast is explosive. Thus, we conclude that for the manufacturing, mining and electricity sectors DM outperforms ECM in ten-step ahead forecast

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20050 2006 2007 2008 2009 2010 2011 2012 2013 2014 500 1000 1500 2000 2500 3000 3500 4000

Manufacturing Demand Forecast, in TOE

20050 2006 2007 2008 2009 2010 2011 2012 2013 2014 0.5 1 1.5 2 2.5 3x 10

6 Mining Demand Forecast, in TOE

20050 2006 2007 2008 2009 2010 2011 2012 2013 2014 20 40 60 80 100 120 140

Construction Demand Forecast, in TOE

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 1100 1200 1300 1400 1500 1600 1700

Mining Demand Forecast, in TOE

Figure 7: 10-step ahead forecast: DM vs. ECM. The solid lines correspond to the DM forecast, the dashed lines to ECM.

Moreover, Figure 7 shows that from 2005 through 2006, ECM’s performance is quite im-pressive, since the predicted values are not far the the 2004 actual energy consumption. Hence, we conclude than ECM is capable of a short-run forecast while DM to a long-run forecast.

5.2 Conclusion to Modeling and Forecasting

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which are evidently shown by the low root mean square error, R2, uncorrelated residuals and confidence test of 95% interval. On the other hand, error-correction model shows a more promising performance. The principal assumptions of a regression model such as linearity of the variables, independency of the residuals (tested by SACF), residuals having constant variance, hence are homoschedastic and that the residuals are normally distributed, are all satisfied. Thus, we assume that the model fits the data well. Comparing the two methods: 1) we find that ECM has relatively lower residuals or errors as evidently shown by Figure 3 and Figure 5; 2) and we also find more confident forecast with ECM as depicted by a narrower confidence intervals; 3) interestingly, we have seen that the industrial energy sub-sectors cannot be modeled by one method wherein the construction sector a VAR model in differ-ence level is better. As a whole, the findings lead us to conclude that ECM outperforms DM in a step forecasting.

However, as the statistical tests suggest that DM and ECM methods are acceptable, we find it necessary to use them in a ten-step ahead forecast. Because one of the purpose of forecasting future demand is to provide a helpful information in the policy making and strategies for industrialization particularly in a developing country as the Philippines. Sur-prisingly, we find that ECM is only capable of short-run forecasts while in long-run forecast, it’s performance is poor. Thus, it is better to use DM for a long-run forecast.

Further research is needed to find a better approach and model in forecasting. More so, a larger sample or observation may improve the forecast performance of error-correction model.

5.3 Results of Industrial Energy Demand Elasticity Analysis

In this section we evaluate the full dynamic behavior of the ECM models to determine the short-run and long-run elasticities of the four sub-sectors of the industrial energy demand with respect to income and prices denoted by the variables GVA and nominal prices of en-ergy fuels. We examine the estimated ECM representation result in forecasting for man-ufacturing, mining and electricity. For the construction sector, it is outright that there is no long-run elasticity as there are no cointegrating relationship as resulted in the Johansen coin-tegration test, hence, only the short-run elasticity has to be determined. The coefficients of the ECM model are presented in Table 14 to Table 17 of the appendix. The insignificance of the estimators as denoted by test statistics, indicates non-causality between the independent and dependent variables. The non-significance of the ECT term indicates the absence of a long-run causality . The absence of short-run causality is denoted by the non-significance of the lagged explanatory variables. Thus, short-run elasticities of industrial energy demand function are determined by the significant coefficients of the lagged explanatory variables and the long-run elasticity is determined by the coefficients in the estimation of cointegra-tion. Hence, if all the variables including ECT term, will indicate non-causality then the dependent variable is strongly exogenous, which shows an evidence of inelasticity of en-ergy demand with respect to income and prices of enen-ergy fuels.

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manufacturing, mining and electricity sub-sectors, respectively are: u_1,t−1 = E_t−1− 281.927Y_t−1+ 103.183P_t−1 (18) v_1,t−1 = E_t−1− 5.161Y_t−1− 3.555P_t−1 (19) u_2,t−1 = E_t−1+ 33.363Y_t−1− 18.137P_t−1 (20) v_2,t−1 = E_t−1− 5.846Y_t−1− 0.469P_t−1 (21) u_3,t−1 = E_t−1− 155.686Y_t−1− 30.577P_t−1 (22) v_3,t−1 = E_t−1− 10.147Y_t−1+ 5.516P_t−1 (23)

A 1% increase in income correspond to 14.874% increase in energy consumption and a 1% increase in the energy price of fuels is equivalent to 5.444% decrease in energy consumption in the long-run. For mining sub-sector, the long-run elasticity is -6.709% (wrong sign) with respect to income and -3.647% with respect to energy price of fuels. Electricity sub-sector on the other hand, has an elasticity of 17.938% percent with respect to income and 3.523% with respect to energy price of fuels, is actually a wrong sign. As expected, the income elasticities of energy demand are high which is in accordance with the study where Asia records higher elasticity than the industrialized countries and regions. This means that in order to achieve a high economic growth, developing countries consume more energy, which is natural for an emerging economy as the Philippines. But as the result suggests, only the manufacturing sub-sector can be judged elastic in terms price and income because its coefficents has the correct signs.

The short-run elasticity is determined by the estimated ECM. We use two linear com-bination of the integrated variables as given in (18) to (23). The estimated ECM in (17) is simplified as ∆Zt= α + m X i=1 βi∆Zt−1+ λut−1+ vt−1+ εt (24)

The Ztvector consist of industrial energy demand, income and nominal prices of fuels,

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Table 9 reports the results of simplified ECM where the short-run elasticity is determined. Only in the energy demand equations we find significant coefficients. Energy consumption equation of the electricity sub-sector is the most robust equations since it comprise the most number of significant coefficients. The signs of the coefficients of the manufacturing, mining and electricity sub-sectors are unacceptable in the economical theory. Hence, construction is the only sub-sector that is adversely affected by a unit increase in price which correspond to approximately 43% increase in energy demand. We find this result reasonable as the prod-ucts produced by this industry are not the necesities of life and therefore substitutable.

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Table 8: Simplified ECM Representation Dependent Variables

Independent ∆Et, Manufacturing ∆Et, Mining ∆Et, Construction ∆Et, Electricity

∆E_t−1 7.503∗ (5.846) ∆E_t−2 0.257∗ _5.595∗ (3.569) (5.105) ∆E_t−3 −0.663∗∗ _3.176∗ (-3.083) (5.241) ∆E_t−4 1.953∗ (3.962) ∆Y_t−1 −3.664∗∗ _−3.729∗ _−4.810∗ (-2.496) (-11.609) (-5.780) ∆Y_t−2 −2.549∗ _−3.512∗ (-8.377) (5.347) ∆Y_t−3 −1.901∗ (4.914) ∆Y_t−4 −2.149∗∗ (-2.065) ∆P_t−1 0.657∗ _−0.429∗∗∗ _−0.454∗ (4.634) (1.638) (-4.147) ∆P_t−2 −0.840∗ (-2.942) ∆P_t−3 ∆P_t−4 −0.184∗ (-2.942) u_t−1 0.0158∗ _−0.118∗ _0.031∗ (3.225) (-12.251) (6.563) v_t−1 −0.002 −0.032∗ _0.010∗∗ (-0.089) (-4.086) (2.683) C −12.506 0.945 0.100 46.526 (-2.961) (9.621) (2.288) (6.420) ¯ R2 0.4468 0.9344 0.0742 0.9066 σ_ε2 0.0160 0.0037 0.0321 0.0005 DW 2.3487 1.9500 2.5946 2.8969

∗,∗∗,∗∗∗_{indicate significance at the 1%, 5% and 10% levels (one-tailed t-test, normal distribution), respecively}

and values in parenthesis are the t-statistics. SACF results suggest no serial correlations in the residuals.

5.4 Conclusion to Industrial Energy Demand Elasticity

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electricity sub-sectors are inelastic with respect to income and energy price of fuels in both the short-run and long-run. This result is reasonable given that energy as a commodity is unsubstitutable and therefore its importance in the industrial energy process is high. Since construction consumption comprise an average of 2% in the total industrial energy demand of the Philippines, we can say that industrial energy demand as a whole does not respond immediately to a unit increase of income and energy price of fuels, thus, it is inelastic with respect to income and energy price in the short-run. Moreover, with a 68% average share of manufacturing sector in the total industrial energy demand of the Philippines, we conclude that industrial energy demand is adversely affected by a unit increase of income and energy price of fuels in the long-run.

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A

Appendices

Table 9: Test for lag lengths for ECM estimation

AIC SBC AIC SBC m Manufacturing Construction 1 -86.375 -80.920 -70.853 -66.489 2 -83.861 -75.505 -64.171 -53.726 3 -107.716 -96.763 -66.236 -54.288 4 -112.089 -97.923 -75.610 -60.499 Mining Electricity 1 -59.691 -55.327 -130.053 -123.507 2 -57.039 -49.727 -112.999 -105.687 3 -101.722 -89.773 -122.546 -110.597 4 -93.602 -79.436 -151.388 -137.222

Table 10: Manufacturing Granger Causality Test

Dependent E1 Y1 P

m= 1, No. of Observations = 22, No. of Variables = 5

E₁ 0.523 0.479 0.603 0.447 19.758 0.000

Y1 3.379 0.083 10.874 0.004 4.295 0.004

P 0.406 0.532 1.934 0.182 1.349 0.261

E₁ 2.035 0.170 0.622 0.551 8.684 0.004

Y1 1.170 0.340 10.214 0.002 8.237 0.004

P 3.493 0.061 1.338 0.296 4.358 0.035

E1 6.219 0.014 16.351 0.000 8.414 0.005

Y1 1.033 0.423 3.286 0.0722 2.691 0.109

P 2.052 0.177 1.544 0.269 2.727 0.106

E1 4.962 0.074 7.614 0.037 3.101 0.149

Y₁ 0.474 0.756 4.397 0.090 2.059 0.250

P 0.648 0.657 0.038 0.995 0.704 0.628

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Table 11: Mining Granger Causality Test

Dependent E2 Y2 P

E2 2.565 0.126 0.133 0.718 4.007 0.060

Y2 0.718 0.407 0.066 0.799 1.991 0.175

P 0.508 0.485 1.260 0.276 0.924 0.349

E2 1.698 0.218 0.687 0.518 1.938 0.180

Y2 0.503 0.614 0.278 0.761 1.245 0.317

P 0.262 0.773 0.270 0.767 0.676 0.524

E2 3.884 0.055 22.364 0.000 20.992 0.000

Y2 0.627 0.617 0.914 0.475 1.210 0.366

P 2.266 0.157 0.884 0.488 0.978 0.449

E₂ 1.664 0.316 8.864 0.028 8.645 0.030

Y2 4.752 0.080 3.893 0.108 5.406 0.065

P 0.483 0.750 0.784 0.589 1.080 0.471

Table 12: Construction Granger Causality Test

Dependent E3 Y3 P

Variable F-stat Prob F-stat Prob F-stat Prob m= 1, No. of Observations = 22, No. of Variables = 4

E₃ 1.816 0.194 0.042 0.839 4.287 0.053

Y3 0.724 0.405 0.032 0.859 6.357 0.021

P 0.018 0.894 5.716 0.027 1.753 0.202

E3 2.143 0.163 0.380 0.692 0.039 0.961

Y3 0.325 0.729 0.391 0.685 0.460 0.642

P 0.605 0.563 0.065 0.936 0.566 0.583

E3 4.158 0.047 0.659 0.599 0.985 0.446

Y3 0.561 0.655 2.025 0.188 2.111 0.177

P 0.805 0.525 0.924 0.471 0.623 0.619

E3 4.751 0.115 1.793 0.329 1.334 0.422

Y₃ 0.704 0.639 0.474 0.757 1.026 0.511

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Table 13: Electricity Granger Causality Test

Dependent E4 Y4 P

E4 11.385 0.003 3.466 0.081 1.539 0.232

Y4 3.672 0.073 8.219 0.011 0.701 0.414

P 0.054 0.818 3.292 0.088 1.256 0.278

E₄ 1.514 0.253 0.581 0.571 3.926 0.044

Y4 1.901 0.185 2.308 0.136 0.483 0.626

P 0.931 0.417 3.217 0.070 1.603 0.236

E₄ 3.173 0.085 3.268 0.080 2.202 0.165

Y4 4.099 0.049 5.795 0.020 4.249 0.045

P 2.869 0.103 2.598 0.124 5.382 0.025

E4 16.958 0.008 12.921 0.014 12.136 0.016

Y4 2.008 0.257 1.782 0.294 0.809 0.578

P 3.162 0.145 4.488 0.087 8.732 0.029

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2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2500 3000 3500 4000 4500 5000 5500

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2000 3000 4000 5000 6000 7000 8000 9000 10000

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2400 2600 2800 3000 3200 3400 3600 3800 4000 4200 4400

20050 2006 2007 2008 2009 2010 2011 2012 2013 2014 500 1000 1500 2000 2500 3000 3500 4000

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2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 25 30 35 40 45 50 55 60

20050 2006 2007 2008 2009 2010 2011 2012 2013 2014 0.5 1 1.5 2 2.5 3x 10

20050 2006 2007 2008 2009 2010 2011 2012 2013 2014 1 2 3 4 5 6 7 8 9x 10

Figure 9: 10-step ahead forecast: DM vs. ECM. The solid lines correspond to the DM forecast, the dashed lines to ECM (upper graphs correspond to m = 1 and m = 2 from the left to the right, respectively and the lower graphs to m = 3 and m = 4).

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20050 2006 2007 2008 2009 2010 2011 2012 2013 2014 20 40 60 80 100 120 140

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 100 105 110 115 120 125 130 135 140 145

20050 2006 2007 2008 2009 2010 2011 2012 2013 2014 20 40 60 80 100 120 140

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2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 1100 1200 1300 1400 1500 1600 1700 1800

Electricity Demand Forecast, in TOE

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 1100 1200 1300 1400 1500 1600 1700

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 1100 1200 1300 1400 1500 1600 1700

Figure 11: 10-step ahead forecast: DM vs. ECM.The solid lines correspond to the DM forecast, the dashed lines to ECM (upper graphs correspond to m = 1 and m = 2 from the left to the right, respectively and the lower graphs to m = 3 and m = 4).

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Table 14: Manufacturing ECM Representation Dependent Variable

Independent (19,15) ∆Et Probability ∆Yt Probability ∆Pt Probability

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Table 15: Mining ECM Representation Dependent Variable

∆E_t−1 0.069 0.412 0.301 (0.424) 0.682 (1.280) 0.236 (1.002) 0.345 ∆E_t−2 0.341 0.264 0.149 (2.458) 0.039 (0.966) 0.362 (0.584) 0.575 ∆E_t−3 0.033 0.127 0.347 (0.356 ) 0.731 (0.693) 0.507 (2.024) 0.077 ∆Y_t−1 -3.813 -1.808 -0.613 (-6.772) 0.000 (-1.627) 0.142 (-0.592) 0.570 ∆Y_t−2 -2.574 -1.371 -0.439 (-5.167) 0.000 (-1.395) 0.200 (-0.480) 0.644 ∆Y_t−3 0.154 -0.338 -0.802 (0.525) 0.613 (-0.583) 0.575 (-1.483) 0.176 ∆P_t−1 0.655 0.617 0.138 (3.025) 0.016 (1.446) 0.186 (0.346) 0.737 ∆P_t−2 1.654 0.771 -0.406 (7.189) 0.000 (1.700) 0.127 (-0.961) 0.364 ∆P_t−3 1.096 0.529 0.198 (6.001) 0.000 (1.469) 0.179 (0.590) 0.571 u_t−1 -0.117 -0.032 0.002 (-7.868) 0.000 (-1.107) 0.300 (0.078) 0.939 v_t−1 -0.004 0.045 0.057 (-0.371) 0.729 (1.556) 0.158 (2.096) 0.069 C 0.975 0.574 0.392 (5.521) 0.000 (1.646) 0.138 (1.207) 0.261 R2 0.966 0.538 0.653 ¯ R2 0.921 -0.096 0.177 σε 0.0044 0.0172 0.0150

Table 16: Construction ECM Representation Dependent Variable

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Table 17: Electricity ECM Representation Dependent Variable

Industrial energy demand in the Philippines — Assessing model for forecasting: decomposition method vs. error-correction method, and demand elasticity