Forecast of electricity consumption and economic growth in Taiwan by state space modeling

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Forecast of electricity consumption and economic growth in Taiwan

by state space modeling

Hsiao-Tien Pao

*

Department of Management Science, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan, ROC

a r t i c l e

i n f o

Article history:

Received 13 November 2008 Received in revised form 16 June 2009

Accepted 22 July 2009

Available online 10 September 2009

Keywords:

Error-correction model State space model SARIMA model Electricity consumption Economic growth

a b s t r a c t

This paper investigates the Granger causality between electricity consumption (EL) and economic growth for Taiwan during 1980–2007 using the cointegration and error-correction models. The results indicate that EL and real GDP are cointegrated, and that there is unidirectional short and long run Granger causality from economic growth to EL but not vice versa. Considering cointegrated property, this study proposes a new error-correction state space model (ECSTSP) with the error-correction term (ECT) in its state vector to forecast both EL and real GDP simultaneously, whereas the ECM is not in the state vector of classical state space model (STSP). The out-of-sample forecasting ability of the ECSTSP is compared with STSP and SARIMA models using six forecasting horizons from 1-year to 6-year. The results suggest that all of the models have strong forecasting performance with MAPE less than 5.4%, but the ECSTSPs have the smallest average values of MAPEs for both EL and GDP, which are 2.50% and 1.74%, respectively. For short-term predictions, SARIMA models are as good as STSP or ECSTSP ones. For long-term predic-tion, ECSTSP is the best model, because the cointegration relationship between real GDP and EL is taken into account in this model.

1. Introduction

Energy is the foundation of economic development. Electricity is the most flexible form of energy and constitutes one of the vital infra-structural inputs in socioeconomic development. Both economy and energy consumption in Taiwan have been growing rapidly. In the 1990s, energy consumption increased about 5% per year, with real GDP growing at an average annual rate of about 5.4%. Among the categories of energy consumed, electricity took up 52%, petroleum 38%, and the rest 10%. Total electricity consumption (EC) rises sharply from 82.60 billion (kwh) in 1990 to 229.20 billion (kwh) in 2007, implying an annual growth rate of 6.19%. Official energy projections for Taiwan indicate a continuing increase in demand for energy, especially for electricity, in the next two decades (Bureau of Energy, Ministry of Economic Affairs in Taiwan). There are numerous studies that deal with the causality rela-tionship between EC and economic growth. This study tried to focus on studies conducted in the recent five years, i.e., 2004 and afterwards, especially regarding countries with developing econo-mies, such as Taiwan. These studies are summarized inTable 1. The findings from the studies vary not only across countries but also across methodologies for the same country. In a summary of the

literature on the causal relationship between EC and economic growth, there is evidence to support bidirectional or unidirectional causality, or no causality, between EC and economic growth.

Evidence in either direction will have a signiﬁcant bearing on policy. If, for example, there is unidirectional causality running from economic growth to EC, it could imply that electricity conservation policies may be implemented with little or no adverse effect on economic growth. Unidirectional causality running from economic growth to EC was revealed by Ghosh [1]for India, by Mozumder and Marathe[2]for Bangladesh, by Narayan and Smyth

[3]for Australia, by Yoo[4]for Indonesia and Thailand, and by Chen et al.[5]for Korea, Singapore, India, Malaysia and the Philippines.

In contrast, if a unidirectional causality runs from EC to economic growth, reducing EC could lead to a fall in economic growth while increasing it may contribute towards a country’s economic growth. Unidirectional causality running from EC to economic growth was revealed by Shiu and Lam[6]and Yuan et al.

[7]for China, by Wolde-Rufael[8]for Shanghai, China, by Ho and Siu[9]for Hong Kung, by Altinay and Karagol[10]for Turkey, by Lee and Chang[11]for Taiwan, and by Chen et al.[5]for Indonesia.

On the other hand, if bidirectional causality is found, economic growth may demand more electricity whereas more EC may induce economic growth. EC and economic growth may complement each other and energy conservation measures may negatively affect economic growth. For example, Jumbe[12]for Malawi, Tang[13] *Tel.: þ886 3 5131578; fax: þ886 3 5710102.

E-mail address:htpao@mail.nctu.edu.tw

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j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e n e r g y

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and Yoo[4]for Malaysia, Yoo[4]for Singapore, Morimoto and Hope

[14]for Sri_Lanka, Zachariadis and Pashourtidou[15] for Cyprus, Yoo[16]for Korea, Yang[17]for Taiwan, and Chen et al.[5]for Hong Kong found bidirectional causality between EC and economic growth. In addition, Chen et al.[5]found bidirectional causality for 10 Asian countries using panel data.

Finally, no causality in either direction would indicate that energy conservation policies may not affect economic growth, and rise in real income may not affect EC. Chen et al.[5]found that there was no causality between economic growth and EC in China, Taiwan and Thailand.

Recently, various studies have been conducted to explore the causality relationship between total energy consumption and economic growth in Taiwan ([11]and[17–20]). Although the EC is an important category constituting 52% of the total energy consumption in 2007, there are very few studies concerning the relationship between electricity use and GDP for Taiwan. In articles[5,11,17], different results were provided by using annual data sets from 1971 to 2001, 1954 to 2003 and 1954 to 1997, respectively. Furthermore, to the best of our knowledge, there is no study to jointly forecast both EC and real GDP dynamically, using the results of causality relationship studies and quarterly data sets.

The two purposes of this study are as follows. The first one is to investigate the causality relationship between EC and economic growth, and to obtain policy implications from the results. This purpose is accomplished by the following steps: First, stationarity and cointegration are tested; second, error-correction models are estimated to test for the Granger causality; finally, the F-tests are performed to determine the joint significance levels of causality between the two variables.

The second purpose is to construct a new error-correction state space model (ECSTSP hereafter) for forecasting of both EC and real GDP simultaneously, taking the cointegration property into account. For modeling and forecasting time series, univariate Box– Jenkins ARIMA [21] linear models are used. Recently, some

univariate nonlinear models have been proposed. Pappas et al.

[22,23]proposed an adaptive method based on the multi-model partitioning ﬁlter for short-term electricity load forecasting. Aza-deh[24]presented an integrated algorithm based on ANN, simu-lated-based ANN, time series and DOE (ANOVA and DMLT) to forecast monthly electricity in Iran. Lauret[25]proposed the use of Bayesian regularization as a technique to estimate the parameters of a neural network in order to forecast load. For long-term fore-casting, Pao[26]proposed an ANN to forecast electricity market pricing. Articles [27] and [28] presented a trigonometric grey prediction approach and a grey prediction with rolling mechanism approach to forecast electricity demand in China and Turkey, respectively. On the other hand, the multivariate models of neural network techniques[29,30], regression and econometric approach

[31–33] have been also applied in predicting EC. Karanﬁl and Ozkaya [34] utilized the Kalman Filter technique for GDP fore-casting in Turkey. Furthermore, Jebaraj and Iniyan [35] made a literature survey in order to give a brief overview of different types of energy modeling and forecasting.

This paper is organized as follows. The next section outlines the econometric methodology and models. Section3presents the data source, shows the empirical results and makes model comparisons. Section4provides the discussion and policy implications. The ﬁnal section summarizes this work and concludes.

2. Methodology

According to Engle and Granger[36], a linear combination of two or more nonstationary series (with the same order of inte-gration) may be stationary. If such a stationary linear combination exists, the series are considered to be cointegrated and long run equilibrium relationship exists. Incorporating these cointegrated properties, the error-correction model (ECM) is speciﬁcally adopted to examine the Granger causality among variables. Taking the cointegration property into account, this study proposes a new ECSTSP to forecast both EC and real GDP simultaneously. The out-Table 1

Empirical results from causality tests between electricity consumption and economic growth for developing countries.

Author Country Method Period Finding

Mozumder and Marathe[2] Bangladesh VECM 1971–1999 GDP / EL

Narayan and Smyth[3] Australia VECM 1966–1999 GDP / EL

Yoo[4] Thailand Indonesia Malaysia Singapore Hsiao’s version of GC 1971–2002 GDP / EL GDP / EL GDP 4 EL GDP 4 EL Chen et al.[5] Korea

Singapore India Malaysia Philippines Indonesia China Taiwan Thailand Hong Kong 10 Asian countries VECM Panel VECM 1971–2001 GDP / EL GDP / EL GDP / EL GDP / EL GDP / EL GDP ) EL GDP o EL GDP o EL GDP o EL GDP 4 EL GDP 4 EL

Shiu and Lam[6] China VECM 1971–2000 GDP ) EL

Yuan et al.[7] China VECM 1978–2004 GDP ) EL

Wolde-Rufael[8] Shanghai, China TY version of Granger non-causality 1952–1999 GDP ) EL

Ho & Siu[9] Hong Kong VECM 1966–2002 GDP ) EL

Altinay and Karagol[10] Turkey GC and VAR 1950–2005 GDP ) EL

Lee and Chang[11] Taiwan Weak exogeneity 1954–2003 GDP ) EL

Jumbe[12] Malawi GC & VECM 1970–1999 GDP 4 EL

Tang[13] Malaysia GC 1972–2003 GDP 4 EL

Morimoto and Hope[14] Sri Lanka Regression 1960–1998 GDP 4 EL

Zachariadis & Pashourtidou[15] Cyprus VECM 1960–2004 GDP 4 EL

Yoo[16] Korea VECM 1970–2002 GDP 4 EL

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of-sample forecasting ability of ECSTSP is compared with both the state space model (STSP) and SARIMA, where STSP and SARIMA are the multivariate and univariate benchmark models, respectively. 2.1. Granger causality, stationarity and cointegration

Since the use of the ECM requires the series to be cointegrated with the same order, it is essential to ﬁrst test the series for sta-tionarity and cointegration. The Augmented Dickey-Fuller [37]

(ADF) and the Phillips-Perron[38](PP) unit root tests are used to investigate the stationarity and the order of integration of the variables. If a nonstationary series has to be differenced d times to become stationary, then it is said to be integrated of order d: i.e., I(d). The differenced data is to be applied for the causality test.

Yt) are the differences in these

variables that capture their short run disturbances. The

m

t,

n

tare the

serially uncorrelated error terms. The ECTt1 is derived from

the long run cointegration relationship. This speciﬁcation can test the short and long run causality among co-integrated variables. The optimum lag lengths m, n, q and r are determined bases on Akaike’s

₁BS

Q

₂B2S /

Q

_QBQS (3)

In this expression, the time series is yt; S is the seasonal periodicity;

B is the backward shift operator; d is the order of regular differ-ences; D is the order of seasonal differences, and at, at1,. are

independent random shocks. The series atis assumed to be a white

noise process, and

f

pðBÞ and

q

qðBÞ are polynomials in B of order p

and q respectively. The roots of

f

pðBÞ ¼ 0 and

q

qðBÞ ¼ 0 should lie

outside the unit circle. 2.3. STSP model

STSP modeling was introduced by Kalman[43]and is known as Kalman ﬁltering. It is appropriate for jointly forecasting several related time series that are dynamically interacting. Taking the autocorrelations among the whole set of variables into account, the SAS STATESPACE may give better forecasts than methods that model each series separately [44]. The methods used in the STATESPACE procedure are described in Akaike [42]. These methods assume that the time series are jointly stationary. Nonstationary series must be made stationary by some preliminary transformation, usually by differencing. If the stationary multivar-iate time series, xt, of dimension r is taken into account, where

xt¼ (x1,t, x2,t,.,xr,t), a STSP model for this multivariate time series

could be written as:

zt ¼ Fzt1þ Get (4)

where ztis a state vector of dimension s, whose ﬁrst r components

compose xtand whose last s r elements are conditional

predic-tions of future xt, for example, zt¼ (x1,t, x2,t, x3,t, x1,tþ1jt, x3,tþ1jt,

x1,tþ2jt)0. F is an s-by-s transition matrix. G is an s-by-r input matrix,

with the identity matrix Irforming the ﬁrst r rows and columns. etis

a sequence of independent normally distributed random vectors of dimension r with mean 0 and covariance matrix

S

ee. Even though

the variables have been differenced for stationarity, STATESPACE procedure forecasts them in their non-differenced levels.

In this study, the STSP model would be employed for fore-casting of both EL and real GDP interrelated time series with a feedback relationship, if a cointegration relationship exists between the two variables. The proposed new ECSTSP model includes ECT in its state vector, where ECT is derived from the cointegrating vector. However, the state vector of classical STSP model does not include ECT. The state vector zt of ECSTSP has

dimension s, whose ﬁrst 3 elements are xt, xt¼ (

D

ELt,

D

GDPt,

D

ECTt), whose last s-3 elements are conditional predictions of

ELtþ2jt)0. The transition matrix F has dimension sxs. The input

matrix G has dimension sx3, with the identity matrix I3 forming

the ﬁrst 3 rows and columns. 3. Data and experimental results 3.1. Data analysis

The data provided cover the period from 1980 to 2007 (sample period 1) with each data point representing EL (Fig. 1) and real GDP (Fig. 2) for each quarter. All data are taken from the AREMOS economic-statistic data banks, created by the Ministry of Education in Taiwan. The sub-period from 1990 to 2007 (sample period 2) is employed to conﬁrm the parameter stability in estimating the ECM. Both series EL and GDP appear to be nonstationary in level. As shown inFig. 1, the EL data show strong seasonality and growth trends. The electricity peak season for each year generally occurs in July to September, because electricity use is greatest in the summer. The troughs of these two series fall in the fourth season of each year, which contains many Chinese holidays and vacations.

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All of the empirical analysis on the relationship between vari-ables has only studies the relationship of the trend[7], seasonal factors can cause a biased estimator. Thus, this study uses the X-12-ARIMA Seasonal Adjustment Program [45] to remove seasonal effects from both EC and real GDP quarterly data sets. The resulting seasonally adjusted ELSA and GDPSA time series are also shown in

Figs. 1 and 2, respectively. The descriptive statistics of EL, ELSA, GDP, and GDPSA variables are reported in Table 2 for both sample periods 1 and 2.

3.2. Results of unit roots, cointegration and Granger causality tests In this analysis, the order of integration of data is investigated. In order to avoid the biased estimator caused by seasonal factors, seasonally adjusted variables are used in the models. They are LELSA and LGDPSA, the natural logarithms of ELSA and GDPSA. The logarithm variables have economic meaning because they are regarded as the growth of the respective differenced variables. For sample period 1, panel A ofTable 3presents the results of the ADF and PP unit root tests on the levels and the ﬁrst differences of both LELSA and LGDPSA variables. In addition to LELSA and LGDPSA variables, the unit root tests of both EL and GDP variables are shown in panel B of Table 3, for the STSP forecasting model to use in sample period 2. Results of both the ADF and the PP tests indicate that all of the series are nonstationary. However, ﬁrst differences of

these four series lead to stationarity. This result indicates that all of the variables inTable 3are of order one, i.e., I(1).

Given that the employed series are of the same order of inte-gration, the next step is to test whether the two series LELSA and LGDPSA are cointegrated over the two sample periods. Table 4

shows the results of the Johansen test. The trace and eigenvalue tests reject both the hypotheses of no cointegrating equation and of at most one cointegrating equation at 5% level of significance over the sample period 1. This implies that there are two cointegrating equations at 5% level of significance. However, only one cointe-grating equation of the two is consistent [46]. The trace and eigenvalue tests also reject the hypothesis of no cointegrating equation at 5% level of significance over the sample period 2.Table 4shows that the estimated cointegrating vectors normalized with respect to LELSA are (1.00, 1.163) and (1.00, 1.220) for both sample periods. The results shown in panel B ofTable 4also indicate that the two series EL and GDP have one cointegration equation with the optimal lag length 4 over the sample period 2 (the hypothesis of no cointegration equation is rejected at 5% level). The estimated cointegrating vectors normalized with respect to EL are (1.00, 23.492). The positive signs of the variables conform to the theory in literature[7], i.e., there is a long-term positive relationship between real GDP and EC for Taiwan. The existence of a cointegrating 0

20 40 60

Mar-80 Mar-82 Mar-84 Mar-86 Mar-88 Mar-90 Mar-92 Mar-94 Mar-96 Mar-98 Mar-00 Mar-02 Mar-04 Mar-06

Billion

EL ELSA

Fig. 1. Electricity consumption from 1980 to 2007 in Taiwan.

0 1 2 3 4

Mar-80 Mar-82 Mar-84 Mar-86 Mar-88 Mar-90 Mar-92 Mar-94 Mar-96 Mar-98 Mar-00 Mar-02 Mar-04 Mar-06

Million

GDP GDPSA

Fig. 2. Real GDP from 1980 to 2007 in Taiwan.

Table 2

Descriptive statistics of included variables.

Variables Usable obs. Mean S.D. Min. Max. Panel A: sample period 1980–2007

EL 116 26,014,980 12,776,311 8,332,261 52,985,000 ELSA 116 25,998,693 12,489,520 9,244,621 48,998,635 GDP 116 1,828,285 848,978.2 593,538 3,440,210 GDPSA 116 1,827,890 847,309.6 613,714 3,377,318 Panel B: sample period 1990–2007

EL 72 38,589,517 12,173,618 17,515,317 64,305,493 ELSA 72 38,563,734 11,631,932 20,051,444 57,815,522 GDP 72 2,270,806 571,398.5 1,291,437 3,446,720 GDPSA 72 2,270,195 567,335.8 1,312,886 3,345,857

Table 3

Results of ADF and PP unit root tests.

Variables ADF statistics PP statistics

Levels First differences Levels First differences Panel A: sample period 1980–2007

LELSA 1.118 [1] 11.592 [0]a _{1.025 [3]} _{11.592 [0]}a

LGDPSA 2.324 [1] 6.778 [0]a 2.472 [2] 6.478 [2]a Panel B: sample period 1990–2007

LELSA 2.810 [1] 12.588 [0]a _{2.362 [1]} _{12.588 [0]}a

LGDPSA 2.021 [1] 6.016 [0]a 2.300 [0] 6.026 [1]a EL 0.402 [3] 17.182 [2]a 1.354 [14] 15.916 [12]a GDP 0.586 [4] 4.107 [4]a _{1.109 [15]} _{9.611 [15]}a

Note: Each ADF and PP tests uses an intercept and no trend and leg length has been chosen based on minimum AIC. Fingers in brackets are the lag lengths.

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relation indicates that the real GDP and EC have an inherent co-movement tendency over the long run.

Cointegration implies the existence of causality, at least in one direction. However, it does not indicate the direction of the causal relationship. Hence, to shed light on the direction of causality, the ECM based causality tests are performed. The short run F-statistics, long run t-statistics and joint F-statistics for Eq. (1) and (2)are reported in Table 5. The results show that only the electricity equation (Eq.(1)) contains the significant variables. However, no significant variable is contained in the GDP equation (Eq.(2)). Thus, the robustness of electricity equation is checked for two sample periods. Generally speaking, the equation appears to be robust to various departures from standard regression assumptions in terms of residual correlation by Lagrange multiplier (LM) test, hetero-scedasticity by BPG test[47,48], autoregressive conditional heter-oscedasticity by ARCH test[49], misspecification of functional form by RESET test[50], or non-normality of residuals by Jarque–Bera test. Panel A ofTable 6displays the results from these tests. For sample period 2, the Jarque–Bera test is performed by smoothing the outlier residual in 1998q3, which corresponds to the 921 earthquake (dated on September 21) in Taiwan.

Table 5shows that short run causality is found only from real GDP to EL, but not the reverse, i.e., there is unidirectional Granger causality. The coefﬁcients of ECT are found to be signiﬁcant in the EC equation, which indicates that given any deviation in the ECT, both variables in the ECM would interact in a dynamic fashion to restore long run equilibrium. Moreover, the interactive term of

change in GDP (

D

GDP), along with the ECT in the electricity equation, is signiﬁcant at 1% level. These indicate that GDP is strongly exogenous and whenever a shock occurs in the system, EC would make short run adjustments to restore long run equilibrium. Hence, bringing domestic electricity prices in line with interna-tional market prices or any well-designed conservation policy can play an effective role in managing the electricity sector.

3.3. Constancy of cointegration space

One important problem with ECMs is that the estimated parameters may change over time. Unstable parameters can result in model misspecification and, if any structural break exists, necessary adjustment of the ECM parameters and variables to reflect the structure break should be made[3]. Once the ECM has been estimated, the author assesses the parameter constancy by using the cumulative sum of recursive residuals (CUSUM) and the CUSUM of square (CUSUMSQ) tests, which were proposed by Brown et al.[51]. In this study, only the electricity equation contains a significant ECT, which can be derived from the long run cointe-grating vector. Thus, the CUSUM and CUSUMSQ tests are needed Table 4

Results of Johansen cointegration test. Eigenvalue Trace Stat. 5% critical value Max Eigen. Stat. 5% critical value Number of cointegration Panel A: sample period 1980–2007

Variable: LELSA and LGDPSA; Lags interval: 1–2

0.207 31.677a _12.321 _25.289a _11.225 _None

0.057 6.388a _4.130 _6.388a _4.130 _{At most 1}

Normalized cointegration equation: LELSA ¼ 1.163 LGDPSA Panel B: sample period 1990–2007

Variables: LELSA and LGDPSA; Lags interval: 1–2

0.222 18.543a _12.321 _17.321a _11.225 _None

0.018 1.221 4.130 1.221 4.130 At most 1 Normalized cointegration equation: LELSA ¼ 1.220 LGDPSA

Variables: EL and GDP; Lags interval: 1–4

0.306 25.295a _12.321 _24.437a _11.225 _None

0.013 0.858 4.130 0.858 4.130 At most 1 Normalized cointegration equation: EL ¼ 23.492 GDP

Notes: Trace and maximal eigenvalue tests indicate the existence of one cointe-gration equation at 5% level.

a_{Denotes rejection of the hypothesis at 5% level. The lag length has been chosen}

based on minimum AIC.

Table 5

Results of causality tests based on the ECM. Dependent

variables

Source of causation (independent variable) Short run Long run Joint (short-run/ECT)

DLGDPSA DLELSA ECTt1 DLELSA, ECTt1 DLGDPSA, ECTt1

F-statistics t-statistics F-statistics Panel A: sample period 1980–2007

DLGDPSA 1.046 0.720 0.831

DLELSA 3.489a _3.606a _7.845a

Panel B: sample period 1990–2007

DLGDPSA 0.092 1.812 1.177

DLELSA 4.299a _2.448a _6.529a

The lag lengths are selected using Akaike’s information criterion.

a_{Implies signiﬁcance at the 5% level.}

Table 6

Results of robustness tests and stability tests for electricity equation in the ECM. 1980–2007 1990–2007 Value Prob. Value Prob. Panel A: Robustness tests

LM(4) [c2_(4)] _3.8384 _0.4283 _1.3165 _0.8586

RESET [F(m,n)] 0.0456 0.8253 0.4129 0.5229 BPG [c2_(5)] _6.5542 _0.2560 _5.9345 _0.3126

ARCH [c2_(4)] _0.2924 _0.5887 _0.2549 _0.6136

Jarque–Bera 1.2597 0.5327 0.8463 0.6550 Panel B: Stability tests

Maximum LR F-statistic (1989q1) 3.3399 1.0000

Maximum LR F-statistic (1998q4) 2.4912 1.000 Maximum Wald F-statistic 3.3399 1.0000 2.4912 1.000 Exp LR F-statistic 0.9567 1.0000 0.5052 1.000 Exp Wald F-statistic 0.9567 1.0000 0.5052 1.000 Ave LR F-statistic 1.6927 1.0000 0.9041 1.000 Ave Wald F-statistic 1.6927 1.0000 0.9041 1.000 Panel C: Chow forecast tests

Forecast from 1989q1 to 2007q4 1.2888 0.2329 Forecast from 1998q4 to 2007q4 0.9306 0.5865 -30 -20 -10 0 10 20 30 82 84 86 88 90 92 94 96 98 00 02 04 06 CUSUM 5% Significance

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only for the electricity equation[3]. The equation is estimated by OLS first and the residual is subjected to the CUSUM and CUSUMSQ tests.Figs. 3,4plot the CUSUM and CUSUMSQ statistics when EC is the dependent variable. The results indicate no instability in the coefficients as the plots of the CUSUM and CUSUMSQ statistics are confined within the 5% critical bounds of parameter stability.

In addition, the plot of the recursive estimates of each coefficient from electricity equation is shown inFig. 5for sample period 1. If the coefficient estimation displays significant variation, as more data are added to estimate the electricity equation, it is a strong indication of instability of coefficient estimation. In Fig. 5, the estimated coefficients rise steadily as more data are added to the electricity equation.

Furthermore, the Quandt-Andrews unknown breakpoint tests

[52]are also employed to test for unknown structural breakpoint amongst all the regressors from the electricity equation for two sample periods. The tests are performed with 10% of trimming on the data set. The results shown in panel B ofTable 6fail to reject the null hypothesis of no structure break. Since Eq.(1) is linear, the results of LR F-statistic are identical to the results of Wald F-statistic as shown in panel B ofTable 6. The maximum F-statistics are in 1989q1 and 1998q4 for sample 1 and 2, respectively, and that are the most likely breakpoint locations. Therefore, the Chow’s forecast tests are performed and specify 1989q1 and 1998q4 as the ﬁrst observations in the forecast period for two sample periods, respectively. The tests reestimate the electricity equation for the periods 1980q1 to 1988q4 and 1990q1 to 1998q3 for two sample period, and use the result to compute the prediction errors for the remaining quarters. The results shown in panel C ofTable 6fail to reject the null hypothesis of no structure change in the electricity equation before and after 1989q1 for sample 1 and 1998q4 for sample 2, respectively.

Overall, the structure of the parameters has not diverged abnormally over the period from 1980 to 2007. It appears that applying Granger causality tests based on the ECM does not suffer from any problem caused by a structure change during the 1980– 2007 period, and the coefﬁcient estimates of ECM are stable. Thus,

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 82 84 86 88 90 92 94 96 98 00 02 04 06

CUSUM of Squares 5% Significance

Fig. 4. Plot of the CUSUMSQ for dependent variable LELSA, 1980–2007.

-.8 -.6 -.4 -.2 .0 1985 1990 1995 2000 2005 1985 1990 1995 2000 2005 1985 1990 1995 2000 2005 1985 1990 1995 2000 2005 1985 1990 1995 2000 2005

Recursive ECT Estimates ± 2 S.E. -.6 -.4 -.2 .0 .2 .4 .6

Recursive LELSA(-1) Estimates ± 2 S.E. -0.4 0.0 0.4 0.8 1.2

Recursive LELSA(-2) Estimates ± 2 S.E. -0.8 -0.4 0.0 0.4 0.8 1.2 1.6 2.0 2.4

Recursive LGDPSA(-1) Estimates ± 2 S.E. -3 -2 -1 0 1

Recursive LGDPSA(-2) Estimates ± 2 S.E.

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panel B in Tables 3–5 indicate that the results of stationarity, cointegration and causality relationship during 1990–2007 are similar to the results during 1980–2007. That is, there is unidirec-tional Granger causality running from GDP to EC in the long and short run, while electricity has a neutral effect on GDP in both the short and long run.

3.4. Building SARIMA models

The EC series given inFig. 1assumes that the seasonality and the trend exist in the historical data and extend to the future with the same pattern, thus the univariate SARIMA models are employed using sample period 2. According to the autocorrela-tion funcautocorrela-tion (acf) and partial autocorrelaautocorrela-tion funcautocorrela-tion (pacf) of EL, the first regular and first seasonal differences are employed to remove the growth trend and the seasonality characteristics. During this process, the first five observations are lost. The acquired stationary time series can be used to identify the SAR-IMA model. AIC is used to determine the best model. At the seasonal level, the acf has a spike at lag 4 and cuts off after lag 4 and the pacf dies down. At the nonseasonal level, the acf has a spike at lag 1 and cuts off after lag 1, and the pacf dies down. As we can see here, the best available model generated from the estimation data set is SARIMA (0,1,1)5(0,1,1)4. The residual

analysis indicates that the model is adequate. The estimated model equation is as follows.

1 B1 B4ðELtor GDPÞ ¼

m

þ ð1

q

1BÞ

1

q

₂B4at (5) In accordance with the process of building the EL model, the best available model for real GDP is obtained. It is the SARIMA (0,1,1)5(0,1,1)4with no intercept model, as shown in Eq.(5). The

residual analysis indicates that the GDP model is adequate. For both EL and real GDP variables, using 12-year, 13-year,.,17-year quarterly data sets and full data sets from 1990 to 2001, 1990 to 2002,., 1990 to 2006 and 1990 to 2007 as estimation periods, the estimated coefﬁcients on SARIMA models are shown inTable 6. The forecast values are shown inFigs. 6(a–c) and 7(a–c)for EL and GDP, respectively. The out-of-sample forecasting abilities of the SARIMA models are evaluated and compared with STSP and ECSTSP models by using testing data during the following periods: 2002–2007, 2003–2007,., and 2007. Three statistics, root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE), are used as performance criteria. Results are shown inTables 7 and 8. The MAPE results are a means to judge the accuracy of the forecast, in which MAPE less than 10% is a highly accurate forecast[53]. For both EL and real GDP, the estimated SARIMA models using full data sets are employed to forecast over the period 2008–2015. Results are shown inTable A1,Figs. 6(d) and 7(d).

3.5. Building STSP and ECSTSP multivariate models

The SAS STATESPACE procedure is appropriate for jointly forecasting several related time series that are dynamically inter-acting. The procedure selects the STSP model automatically and assumes that the input series are stationary. If the series are nonstationary, then the process may fail. Based on the ADF and PP statistics, panel B ofTable 3shows that the integrations of EL and real GDP are I(1), respectively. The result of the Johansen test in panel B ofTable 4indicates that both EL and GDP are cointegrated. Thus, the ECT derived from the long run cointegration relationship is stationary. Taking the cointegration relationship into account,

the proposed ECSTSP model with vector xt¼ (

D

GDPt,

D

ELt, ECTt) is

constructed. The classical STSP model with vector xt¼ (

D

GDPt,

D

ELt) is also constructed, where the xtvector is deﬁned in Eq.(4).

Even though the variables have been differenced for stationarity, STATESPACE procedure forecasts them in their non-differenced level. For both EL and GDP variables, using 12- ,13-,., 17-year data sets and the full data sets in period 2, the seven state vectors: z1t,

ELtþ2jt 0 (7)

The out-of-sample forecasting performances are shown inTable 7

by using testing data. The forecast values are shown inFigs. 5 (a–c) and 6 (a–c)for two variables.

Both ECSTSPFulland STSPFull models with zFull and yFull state

vectors are used to predict EC and real GDP simultaneously over the period 2008–2015. Results are shown inTable A1,Figs. 5(d) and 6(d). The zFulland yFullstate vectors corresponding to transition

and input matrices FFulland GFull; speciﬁed in Eq.(4), are presented

b

c

d

Billion Billion Actual ECSTSP STSP SARIMA 40 50 60 70 45 55 65 75 Billion 40 60 80

Mar-02 Mar-03 Mar-04 Mar-05 Mar-06 Mar-07

Mar-03 Mar-04 Mar-05 Mar-06 Mar-07

Mar-05 Mar-06 Mar-07

Mar-07 Mar-08 Mar-09 Mar-10 Mar-11 Mar-12 Mar-13

Billion Actual ECSTSP STSP SARIMA Actual ECSTSP STSP SARIMA Actual ECSTSP STSP SARIMA

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2.5 3 3.5

a

b

c

d

2.5 3 3.5 2.5 3 3.5

Million Million Million Million Actual ECSTSP STSP SARIMA 3 4 5

Mar-03 Mar-04 Mar-05 Mar-06 Mar-07

Mar-07 Mar-08 Mar-09 Mar-10 Mar-11 Mar-12 Mar-13

Actual ECSTSP STSP SARIMA Actual ECSTSP STSP SARIMA Actual ECSTSP STSP SARIMA

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EL_tþ1jt1 3 7 7 7 7 5þ 2 6 6 6 6 4 1 0 0 1 0:12 0:00 4:21 0:55* 10:73* _0:77* 3 7 7 7 7 5 e1;t e2;t (9)

The*_and#_{on the coefﬁcients of the transition and input matrices F}

and G indicate that they are signiﬁcant at the 5% and 10% level, respectively.

3.6. Out-of-sample forecasting performance comparisons

The forecasting ability of the new multivariate ECSTSP model is compared with the multivariate ECSTSP and univariate SARIMA

models. In general, the forecasting performance of the multivariate models is highly dependent on the availability and reliability of data on independent variables over the forecasting period, which requires further efforts in data collection and estimation. On the other hand, univariate time series analysis provides another modeling approach, which only requires the historical data of the variable of interest to forecast its future evolution behavior. Therefore, the prediction error of univariate model can be less than the prediction error of multi-variate model. However, if the multimulti-variate model has stronger modeling power than the associated univariate model, the multi-variate model is likely to achieve better prediction performance. For the performance evaluation, the predictive accuracies of the three models for both EC and real GDP are compared over the six different forecast horizons, 6-year, 5-year,., 1-year, using sample period 2. Four observations can be made. First, all of the models have strong forecasting performance, because all of the MAPEs are less than 5.4%. Second, the ECSTSPs have the smallest average values of MAPEs over six forecasting horizons for both EL and GDP, which are 2.50% and 1.74%, respectively. For two variables, the average values of MAPEs are MAPEECSTSP<MAPESTSP<MAPESARIMA(shown inTable 7). Third, the

forecasting accuracies of both ECSTSP and STSP are not sensitive to the length of forecast horizon, but the forecasting accuracies of SARIMA models are. For two variables, the variances of MAPEs (VMAPE) over six forecasting horizons are VMAPESTSP<VMAPEECSTSP<VMAPE SAR-IMA(shown inTable 7). For short-term prediction (1 and 2 year), the

univariate SARIMA models are as good as ECSTSP ones for both series. These results may be expected since the SARIMA model is available for short prediction periods. For long-term prediction periods (3-year to 6-year), both STSP and ECSTSP models are better than SARIMA models, because the STSP model is appropriate for jointly forecasting several related time series that dynamically interact. Finally, for long-term prediction, the best models are ECSTSP for two variables, because the cointegration relationship between real GDP and EC is taken into account in the ECSTSP model.

This study concludes by using three models to forecast both EC and real GDP for Taiwan up to year 2013. The forecasts of two variables over the 2008–2013 period, together with the actual data Table 7

SARIMA coefﬁcients for electricity consumption and real GDP in Taiwan. Estimation period Electricity consumption Real GDP

q0 q1 q2 q1 q2 1990–2001 28,201.0a _0.8854a _0.6769a _0.2709b _0.7991a 1990–2002 23,850.4a _0.8814a _0.5896a 0.3189a 0.7036a 1990–2003 21,674.0a _0.9030a _0.4911a 0.3381a 0.4697a 1990–2004 19,755.2a _0.8889a _0.5127a 0.3400a 0.5192a 1990–2005 15,887.4 0.8476a _0.5169a _0.3468a _0.5098a 1990–2006 8562.3 0.7616a _0.5093a _0.3088a _0.5168a 1990–2007 7458.6 0.7584a _0.5196a _0.3296a _0.4734a

a_{Denote signiﬁcance at the 5% level.} b_{Denote signiﬁcance at the 10% level.}

Table 8

Out-of-sample comparisons between ECSTSP, STSP and SARIMA models.

ECSTSP STSP SARIMA

Electricity GDP Electricity GDP Electricity GDP

Forecasting period 2002–2007 RMSE 2,580,842.88 106,427.89 2,601,980.83 110,754.40 3,311,868.93 172,511.25 MAE 2,080,817.21 77,478.10 2,100,604.05 82,061.58 2,754,532.04 137,231.42 MAPE 3.90% 2.53% 4.04% 2.69% 5.32% 4.47% Forecasting period 2003–2007 RMSE 1,596,771.96 76,284.54 1,693,889.88 96,808.67 2,384,135.37 130,307.88 MAE 1,373,947.66 56,878.51 1,393,269.02 72,323.68 2,022,144.92 102,174.30 MAPE 2.57% 1.90% 2.62% 2.36% 3.79% 3.31% Forecasting period 2004–2007 RMSE 1,645,895.44 41,111.90 1,684,145.67 68,269.16 2,053,217.94 66,971.61 MAE 1,278,933.98 33,567.65 1,300,411.04 51,318.58 1,660,985.40 49,728.90 MAPE 2.38% 1.10% 2.43% 1.65% 3.01% 1.60% Forecasting period 2005–2007 RMSE 1,136,792.72 72,618.97 1,159,622.34 95,316.45 1,855,532.67 140,591.78 MAE 842,647.20 52,837.55 957,385.07 72,117.83 1,594,815.12 121,331.24 MAPE 1.52% 1.64% 1.75% 2.23% 2.87% 3.80% Forecasting period 2006–2007 RMSE 1,561,909.54 64,567.62 1,423,396.02 62,189.97 1,404,183.40 50,346.40 MAE 1,419,260.35 47,838.60 1,291,615.37 47,653.14 1,229,182.90 45,842.32 MAPE 2.57% 1.46% 2.34% 1.46% 2.18% 1.46% Forecasting period 2007 RMSE 1,329,412.62 71,722.45 1,525,655.64 70,404.47 731,592.56 58,937.36 MAE 1,148,128.67 59,992.16 1,347,123.71 61,411.96 694,850.52 48,567.61 MAPE 2.04% 1.79% 2.39% 1.84% 1.20% 1.45% Mean (MAPE) 2.50% 1.74% 2.60% 2.04% 3.06% 2.68% Var (MAPE) 0.53 0.19 0.50 0.18 1.65 1.50

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in 2007, are illustrated inFigs. 6(d) and 7(d)and presented in detail inAppendix A.Table A1,Figs. 6(d) and 7(d)show that the fore-casted values of ECSTSP are less than SARIMA and greater than STSP, especially in the second half of the forecasting period. Thus, the ECSTST model tends to give values that are neither too large nor too small for long-term forecast among the three different models. 4. Discussion and policy implications

The ﬁnding of unilateral short and long run causality from real GDP to EC without any feedback effects can be explained from a perspective of economic structure and electricity usage structure. In many Asian developing countries, economic growth is causing the industrial and commercial sectors, where electricity has been used as a basic energy input, to expand[5]. In Taiwan, the annual average growth rates of EC of the industrial, commercial and household sectors are 6.05% 7.52% and 5.85% respectively, with the annual average growth rate of real GDP about 5.4% from 1990 to 2007. Hence, the expansion in GDP also increases the need for electricity. Economic growth results in a higher proportion of national income to spend on highly electricity-consuming goods and/or services such as plasma display panel televisions and high-speed wired or wireless Internet connections, and thereby stimu-lates further EC. Intuitively, increased real income requires enor-mous EC.

Moreover, the empirical results indicate that there is no causality running from EC to economic growth. In Taiwan, the energy intensity (defined as the amount of energy consumed per GDP) is 8532 Btu/USD in 2007, which is more than the average energy intensity in Asia and Oceania (6706 Btu/USD), and is also more than the average energy intensity in the world (8035 Btu/ USD) (Energy Information Administrator (EIA), 2007). The higher energy intensity in Taiwan reflects inefficient energy usage in industry, as well as in the commercial and household sectors. This indicates that much improvement needs to be made in EC effi-ciency. Hence, electricity efficiency and conservation will not hurt economic growth and development.

The results of this paper suggest that electricity conservation policies such as rationalizing the tariff structure, improving efﬁ-ciency and managing demand, which aim at curtailing waste of electricity and reducing EC without affecting the end-use beneﬁts, can be adopted because they bring no harm to Taiwan’s economic growth. Moreover, around 57% of electricity was consumed for industrial production in 2007. Therefore, the government of Taiwan should also encourage domestic industries to adopt new technol-ogies to minimize CO2 emissions in order to respond to the

recommendations of the Kyoto protocol. 5. Conclusions

This paper examines the causality between EC and real GDP in Taiwan during 1980–2007 using the ECM model for seasonally adjusted quarterly data. The sub-period from 1990 to 2007 is employed to conﬁrm parameter stability in estimating the ECM. The results indicate the following: (1) both series appear to be nonstationary in levels, but stationary in the ﬁrst differences for actual value and logarithmic form; (2) a stationary linear cointe-gration relationship between two variables exists; (3) there is unidirectional short and long run strong Granger causality from economic growth to EC, while electricity has a neutral effect on GDP in both the short and long run; and (4) no structure change exists during 1980–2007 and the estimated parameters of ECM are stable. Therefore, energy conservation is a feasible policy with no damaging repercussions on economic growth for Taiwan.

The ﬁnding of this paper is compared with three of the leading research results[5,11,17]. In[5], Chen et al. found that electricity and GDP are neutral with respect to each other in 31 annual observations over the period 1971 to 2001. Lee and Chang [11]

found that a unidirectional causality runs from EC to economic growth based on the 50 annual observations during 1954–2003. Yang[17]found that a bidirectional causal linkages between GDP and EC from the 44 annual observations during 1954–1997. The difference in the ﬁndings or the results of this study and that of

[5,11,17] may largely be attributed to the choice of the sample periods and the sampling data sets. The sample periods used in this paper are 1980–2007 and 1990–2007. And, the sampling data used in articles [5,11,17] are 31, 50, and 44 annual data sets respectively. While, this study adopts seasonally adjusted data sets, e.g., 112 and 72 quarterly data sets for two sample periods, respectively.

Furthermore, due to the rapid growth in both economy and EC in Taiwan, forecasting both variables is of the utmost signiﬁcance to the reconstruction process going on in Taiwan, especially to that of the energy generation systems. Thus, this study proposes a new ECSTSP model to forecast both EL and real GDP simulta-neously, taking the cointegration relationship into account. The out-of-sample forecasting ability of the ECSTSP model is to be compared with both STSP and SARIMA multivariate and univar-iate benchmark models over six forecast horizons. The investi-gation results suggest that all of the models have strong forecasting performance with MAPE less than 5.4%, but the ECSTSPs have the smallest average values of MAPEs over six forecasting horizons for both EL and GDP, which are 2.50% and 1.74%, respectively, while the average values of MAPE for SARIMA are 3.06% and 2.68%. Both STSP and ECSTSP models have smaller variance of MAPEs over six forecasting horizons than SARIMA models. These results indicate that the forecasting accuracies of STSP models are not sensitive to the length of forecast horizon, but SARIMA models are. For short-term prediction, the univariate SARIMA models are as good as ECSTSP ones for both series. These results may be expected since the SARIMA model is available for short prediction periods. For long-term prediction, both STSP and ECSTSP models are better than SARIMA models, because the STSP model is appropriate for jointly forecasting several related time series that dynamically interact. For long-term prediction, the best models are ECSTSP for two variables, because the cointe-gration relationship between real GDP and EC is taken into account in this method.

In the future, it will be possible to explore the causality rela-tionship between industrial sector EC and other economic factors, e.g., employment or income, and to forecast EC in Taiwan using multivariate linear or nonlinear models.

Acknowledgments

The author would like to thank two anonymous referees and the Editor for their valuable suggestions and helpful comments which have greatly enhanced the quality of this paper.

Appendix A. Electricity consumption and real GDP forecast results during 2007–2013

The forecasts of two variables over the 2008–2013 periods, together with the actual data in 2007, are presented in detail in

Table A1. It shows that the ECSTST model tends to give values that are neither too large nor too small for long-term forecast among the three different models.

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Table A1

Forecasts for electricity consumption and real GDP for Taiwan, 2007–2013.

Electricity consumption (kwh) Real GDP

Date Actual ECSTSP STSP SARIMA Actual ECSTSP STSP SARIMA

Mar-2007 50,701,637 51,663,499 52,488,618 51,090,844 3,152,427 3,168,121 3,177,247 3,168,466 Jun-2007 56,315,383 58,113,668 58,101,558 57,121,193 3,135,149 3,148,132 3,153,063 3,098,508 Sep-2007 64,305,493 63,457,851 62,091,182 63,098,841 3,358,002 3,284,883 3,275,344 3,296,605 Dec-2007 57,873,290 59,501,202 58,365,758 58,419,147 3,446,720 3,444,997 3,437,911 3,481,292 Mar-2008 53,720,909 53,761,967 52,956,674 3,380,523 3,361,709 3,358,718 Jun-2008 60,905,753 59,879,718 58,843,202 3,379,799 3,358,989 3,326,597 Sep-2008 66,087,459 64,364,457 65,896,274 3,517,143 3,478,496 3,514,669 Dec-2008 60,113,690 59,819,927 60,230,636 3,578,985 3,535,885 3,610,174 Mar-2009 56,167,044 56,887,821 55,106,383 3,510,861 3,487,286 3,527,566 Jun-2009 62,965,585 62,362,795 61,000,369 3,516,151 3,494,367 3,495,445 Sep-2009 67,757,661 66,145,193 68,060,900 3,644,962 3,598,897 3,683,517 Dec-2009 62,245,092 61,936,993 62,402,721 3,702,079 3,649,687 3,779,022 Mar-2010 58,729,371 59,526,853 57,285,926 3,640,588 3,608,794 3,696,414 Jun-2010 65,110,064 64,766,702 63,187,371 3,648,319 3,621,145 3,664,292 Sep-2010 69,521,095 68,101,977 70,255,360 3,769,301 3,720,470 3,852,365 Dec-2010 64,440,719 64,096,745 64,604,639 3,822,853 3,766,625 3,947,870 Mar-2011 61,312,826 62,096,062 59,495,303 3,767,750 3,730,061 3,865,261 Jun-2011 67,297,363 67,142,102 65,404,207 3,777,856 3,746,671 3,833,140 Sep-2011 71,356,982 70,092,276 72,479,654 3,891,798 3,841,991 4,021,212 Dec-2011 66,675,933 66,279,145 66,836,392 3,942,324 3,884,165 4,116,718 Mar-2012 63,898,043 64,644,191 61,734,514 3,893,310 3,851,468 4,034,109 Jun-2012 69,509,822 69,497,618 67,650,877 3,905,678 3,871,823 4,001,988 Sep-2012 73,246,732 72,099,360 74,733,783 4,013,219 3,963,352 4,190,060 Dec-2012 68,935,762 68,479,825 69,097,979 4,061,134 4,001,997 4,285,566 Mar-2013 66,474,656 67,177,063 64,003,560 4,017,867 3,973,034 4,202,957 Jun-2013 71,736,846 71,836,013 69,927,381 4,032,342 3,996,714 4,170,836 Sep-2013 75,178,310 74,121,107 77,017,746 4,134,023 4,084,562 4,358,908 Dec-2013 71,211,018 70,696,651 71,389,401 4,179,661 4,120,077 4,454,414

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