ARTICLE IN PRESS

Energy Policy 37 (2009) 3205–3211

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Energy Policy

0301-42

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/enpol

Long memory in US disaggregated petroleum consumption: Evidence fromunivariate and multivariate LM tests for fractional integration

Hooi Hooi Lean a, Russell Smyth b,�

a Economics Program, School of Social Sciences, Universiti Sains Malaysia, Malaysiab Department of Economics, Monash University, Australia

a r t i c l e i n f o

Article history:

Received 7 January 2009

Accepted 7 April 2009Available online 9 May 2009

Keywords:

Energy consumption

Fractional integration

Long memory

15/$ - see front matter & 2009 Elsevier Ltd. A

016/j.enpol.2009.04.017

esponding author.

ail address: Russell.Smyth@BusEco.monash.ed

a b s t r a c t

Previous studies that have tested for a unit root in aggregate energy consumption have potentially

reached misleading conclusions because they fail to allow for the possibility that energy consumption

might be fractionally integrated and do not distinguish between different types of energy consumption.

This study tests for long memory in disaggregated petroleum consumption in the United States using

univariate and multivariate Lagrange multiplier (LM) tests for fractional integration. The results point

strongly to the need to distinguish between different forms of energy consumption and allow for a

generalization of the I(0)/I(1) dichotomy when considering the order of integration of energy

consumption. Allowing for short-run dynamics, the univariate test suggests that less than 50% of the

series are fractionally integrated. Consistent with expectations the non-stationary series are found to

have the highest mean and standard deviation. The multivariate test suggests that petroleum

consumption in the commercial and industrial sectors is clearly fractionally integrated when allowing

for short-run dynamics, and, as such, exhibits persistent effects, while petroleum consumption in the

residential sector is a stationary process.

& 2009 Elsevier Ltd. All rights reserved.

1. Introduction

There is an emerging literature that tests for a unit root inenergy consumption. Some studies have used univariate unit roottests with and without structural breaks (see e.g. Altinay andKaragol, 2004; Lee and Chang, 2005; Narayan and Smyth, 2005).Other studies have used panel unit root tests with and withoutstructural breaks (see Al-Iriani, 2006; Chen and Lee, 2007; Hsuet al., 2008; Joyeux and Ripple, 2007; Lee, 2005; Lee and Chang,2008; Mishra et al., 2009; Narayan and Smyth, 2007). There arerelated literatures that test for a unit root in energy production(Maslyuk and Smyth, 2009; Narayan et al., 2008) and for a unitroot in energy spot and futures prices (see e.g. Elder and Serletis,2008; Serletis, 1992; Lee and Lee, 2009; Maslyuk and Smyth,2008). Whether energy consumption is stationary or containsa unit root is important for several reasons, which are nowwell documented in the literature (see e.g. Hsu et al., 2008,pp. 2317–2318; Lee and Lee, 2009, p. 469; Mishra et al., 2009,pp. 2318–2319).

First, if energy consumption is stationary, shocks to energyconsumption will be temporary; however, if energy consumptioncontains a unit root, shocks to energy consumption will have

ll rights reserved.

u.au (R. Smyth).

persistent effects. Second, if shocks to energy consumption arepersistent, given the importance of energy to other sectors in theeconomy, key macroeconomic variables can be expected to inheritthat persistence. Third, whether key macroeconomic variables arestationary has important implications for alternative economictheories, which suggest different conclusions on the issue of thedesirability and efficacy of government intervention through theuse of macroeconomic stabilization policies. Fourth, the analysisin this article addresses sectoral energy use, which implies thatour findings are also relevant for industrial policies and firm levelstrategies (i.e. investment in renewable energy sources) as wellas macroeconomic policies. Fifth, the issue of whether energyconsumption is stationary has important implications for model-ling. The correct approach to modelling, for example, energydemand or Granger causality between energy consumption andreal output, which both have important policy implications,depend on whether energy consumption contains a unit root.Fifth, the issue of whether energy consumption is stationary hasimportant implications for forecasting energy consumption. Ifenergy consumption is stationary, it is possible to forecast futuremovements in energy consumption based on past behaviour.However, if energy consumption is non-stationary then pastbehaviour is of no value in forecasting future demand and onewould need to look at other variables explaining energyconsumption in order to generate forecasts of energy demandinto the future.

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Studies have reached mixed conclusions about whether energyconsumption is stationary. The results from univariate unit roottests have failed to reach a consensus (see Chen and Lee, 2007 fora review). Among studies that have employed panel data tests, Lee(2005), Joyeux and Ripple (2007) and Narayan and Smyth (2007)find evidence of a panel unit root, Chen and Lee (2007) and Mishraet al. (2009) find evidence of panel stationarity and Hsu et al.(2008) reach different conclusions according to regional panels.These inconclusive findings might reflect two limitations with theextant literature, which this paper seeks to address.

First, the existing literature uses data on aggregate energyconsumption, but different forms of energy consumption mightexhibit different types of unit root behaviour. Yang (2000) arguedthat the use of aggregate energy data does not capture the degreeto which different countries or industries depend differently onenergy. The use of disaggregated data facilitates comparisons ofrelative energy intensities across uses by energy source (Ewinget al., 2007; Sari, et al., 2008). In the specific context of testingfor a unit root in energy consumption, some end users are largeconsumers, while others are less so. Energy consumption is morelikely to be non-stationary in sectors that are large consumers.The rationale is that for large consumers, shocks will generate abigger deviation from the long-run equilibrium path, resulting in ahigher level of persistence (Hsu et al., 2008). Second, some formsof energy consumption might be more volatile or more proneto disruption. Forms of energy and/or end users which experiencehigh volatility in energy consumption are more likely to beassociated with non-stationary energy consumption. The reason-ing is that for forms of energy use and/or end users thatexperience high volatility in energy consumption, deviations fromthe long-run equilibrium path, due to shocks that create volatilityin the first place, will be larger. Thus departure from theequilibrium path will be less likely to be temporary (see Maslyukand Smyth, 2009; Mishra et al., 2009; Narayan et al., 2008).

Second, the existing literature fails to consider that energyconsumption might be a long memory, fractionally integratedprocess. The presence of long memory can be defined from anempirical data-oriented approach in terms of the persistence ofautocorrelations. The extent of the persistence is consistent withessentially a stationary process, but where the autocorrelationstake much longer to decay than the exponential rate associatedwith the ARMA class (Baillie, 1996). Chen and Lee (2007) attributefailure to reject the unit root in energy consumption in somestudies to failure to take account of the existence of structuralbreak(s), which lowers the power of conventional tests (seePerron, 1989). However, equally, it is well known that standardunit root tests, such as the Augmented Dickey-Fuller test, havelow power if the alternatives are of a fractional form (see e.g.Diebold and Rudebusch, 1991; Hassler and Wolters, 1995; Lee andSchmidt, 1996; Caporale and Gil-Alana, 2008).

Fractional integration was first observed by statisticians in thenatural sciences in areas as diverse as climatology, geophysics andhydrology (see e.g. Hurst, 1951, 1957; Mandelbrot and Wallis,1968; Mandelbrot, 1972; McLeod and Hipel, 1978). Testing forfractional integration in econometrics is a more recent phenom-enon dating from the 1980s (Baillie, 1996). Several studies exist,testing for fractional integration in macroeconomic variables.These include studies for gross domestic product (Dieboldand Rudebusch, 1989, 1991; Gil-Alana, 2002b, 2003), inflation(Baillie et al., 1996; Kumar and Okimoto, 2007), exchange rates(Diebold et al., 1991; Baillie, 1996; Gil-Alana, 2002a), stock prices(Assaf, 2007) and unemployment (Caporale and Gil-Alana, 2008;Gil-Alana, 2002b). There are also a series of studies in the tourismeconomics literature, testing for fractional integration in interna-tional tourist arrivals for a range of countries including Spain andthe United States (Cunado et al., 2004, 2008; Gil-Alana et al.,

2004). There is only one related study in the energy unit rootliterature. Elder and Serletis (2008) test for fractional integrationin energy futures prices and find evidence that energy futureprices are long memory processes.

While much of the literature that has tested for a unit root inenergy consumption has emphasised the role of persistence ofshocks, testing for the presence of unit roots in autoregressiverepresentations of univariate and vector processes that areintegrated of order zero (I(0)) and integrated of order one (I(1))can be far too restrictive. Fractionally integrated processesrepresent a halfway house between I(0) and I(1) paradigms(Baillie, 1996). Moreover, fractional integration provides a meansto isolate persistence that is not consistent with either I(0) or I(1)processes. For this reason, fractional integration can be considereda generalization of the I(0)/I(1) dichotomy (Kumar and Okimoto,2007).

Apart from the fact that fractional integration provides a moregeneral framework to consider whether there is persistence inenergy consumption, another reason for considering fractionalintegration is increasing evidence of non-linearities in energymarkets. Serletis and Gogas (1999) tested for deterministic chaosin seven Mont Belview Texas hydrocarbon markets – crude oil,natural gas, ethane, propane, normal butane, iso-butane andnaptha – and find evidence consistent with a chaotic non-linearprocess in the five natural gas liquid markets. More recently,Maslyuk and Smyth (2009) find evidence of non-linearities incrude oil production for 17 OECD and non-OECD countries usingmonthly data over the period January 1973 to December 2007.Assaf (2007) and Elder and Serletis (2008) note that long memoryindicates evidence of non-linear dependence in the first andsecond moments.

This paper applies univariate and multivariate Lagrangemultiplier (LM) tests for fractional integration proposed byNielsen (2005) to monthly data on disaggregated petroleumconsumption in the United States over the period January 1973 toJuly 2008. The univariate LM test for fractional integration isapplied to 24 series of alternative forms of petroleum consump-tion. The multivariate LM test for fractional integration is appliedto five sector-based panels. The Nielsen (2005) multivariate LMtest for fractional integration generalizes the univariate testsdeveloped by Robinson (1994) and Tanaka (1999) among others.The multivariate fractional integration test has the advantage overthe univariate test applied to multiple time series that it is lesscumbersome and takes account of potentially important correla-tions between the elements of the multiple time series (Nielsen,2005). We employ the Nielsen (2005) LM test for fractionalintegration in preference to other available multivariate tests forfractional integration such as those proposed by Breitung andHassler (2002) and Gil-Alana (2003) because evidence fromsimulation studies reported in Nielsen (2005) suggests that theNielsen (2005) test performs better in terms of finite sampleproperties.

2. Disaggregated energy consumption in the United States

In the United States expenditure on energy accounts for 7% ofgross domestic product (Sari et al., 2008). In 2002, the commercialand residential sectors together accounted for 39.4% of energyconsumption, the industrial sector accounted for 33.4% of energyconsumption and the transportation sector accounted for 27.2% ofenergy consumption (Ewing et al., 2007). Approximately 20%of the United States energy needs are imported with petroleumcomprising the United States largest imported energy source. Thisfeature means that any disruption in oil production in other partsof the world has the potential to result in significant disruptions to

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H.H. Lean, R. Smyth / Energy Policy 37 (2009) 3205–3211 3207

the United States economy (Kilian, 2008). If shocks to petroleumproduction, and disaggregated petroleum consumption, havepersistent effects, disruptions to petroleum production andconsumption will have persistent effects on the United Stateseconomy. In this case, diversification away from petroleumproduction is most desirable since it would lessen dependenceon foreign energy and reduce the effects of oil disruptions on theUnited States real economy. Such policies would be consistentwith the development of renewable technologies and the moreefficient use of petroleum products via implementation ofdemand management policies (Economic Report of the President,2004). However, if energy production and consumption is an I(0)process, disruptions to petroleum production and consumptionwill be fleeting and the economy will return to its long-runequilibrium path (Narayan and Smyth, 2007; Narayan et al.,2008). If this is the case, this makes the search for alternatives topetroleum products less pressing.

3. Econometric methodology

We employ univariate and multivariate LM tests for fractionalintegration proposed by Nielsen (2005). Suppose we observe {yt,t ¼ 1,y, n} generated by

ð1þ LÞdþyyt ¼ etIðtX1Þ; t ¼ 0;�1;�2; . . . (1)

where I(.) denotes the indicator function and et is I(0); i.e., it iscovariance stationary and has spectral density that bounded awayfrom zero at the origin. The process yt generated by Eq. (1) is welldefined for all d, where d+y is the fractional order of integra-tion, and is sometimes called a multivariate type II fractionallyintegrated process.

The process in Eq. (1) allows a uniform definition, valid for all d

and y, whereas the alternative definition without truncation isvalid only for dþ y 2 ð�1

2;12Þ and partial summation would be

needed to generate a process with integration order outside thisrange. Deterministic terms can be added to Eq. (1), allowing fornonzero mean and trend.

In Eq. (1), we assume that d is specified a priori and wish to testthe hypothesis

H0 : y ¼ 0 (2)

against the alternative H1: ya0. For instance, the unit roothypothesis and the hypothesis of joint stationary (or moreprecisely, weak dependence) of yt are given by Eqs. (1) and (2)with d ¼ 1 and d ¼ 0, respectively. The objective is to test if anobserved K-vector time series yt is integrated of order d, denotedI(d), against the hypothesis that it is I(d+y) for ya0. Bydifferencing the observed time series, this is equivalent to testingif xt ¼ (1�L)dyt is I(0) against I(y). To put it in different terms, wetest the null hypothesis, H0: I(0), jointly stationary against H1: I(y),fractional integration. The LM statistic, which is chi-squared withone degree of freedom under the null, is

LM ¼trðP̂�1

S10Þ2

trðP̂�1

M11Þ

where

S10 ¼Xn

t¼2

x�t�1x0t ; x�t�1 ¼Xt�1

j¼1

j�1xt�j

M11 ¼ S11 þ12ðS20 þ S020Þ

S11 ¼Xn

t¼2

x�t�1x�0

t�1; S20 ¼Xn

t¼1

x��t�2x0t ; x��t�2 ¼Xt�2

j¼1

j�1x�t�j�1

4. Data

We examine 24 series of petroleum consumption by fivesectors for the United States. The five sectors are residential,commercial, industrial, transportation and electric power. Theseries are monthly consumption of different petroleum typesmeasured in thousand of barrels per day and are extracted fromthe Monthly Energy Review of the Energy Information Adminis-tration. The sample period covered is from January 1973 to July2008. The data were transformed to natural logarithms prior toanalysis. The 24 series broken down by sector are as follows:Distillate Fuel Oil Consumed by the Residential Sector; LiquefiedPetroleum Gases Consumed by the Residential Sector; DistillateFuel Oil Consumed by the Commercial Sector; Liquefied Petro-leum Gases Consumed by the Commercial Sector; Motor GasolineConsumed by the Commercial Sector; Residual Fuel Oil Consumedby the Commercial Sector; Asphalt and Road Oil Consumed by theIndustrial Sector; Distillate Fuel Oil Consumed by the IndustrialSector; Liquefied Petroleum Gases Consumed by the IndustrialSector; Lubricants Consumed by the Industrial Sector; MotorGasoline Consumed by the Industrial Sector; Petroleum CokeConsumed by the Industrial Sector; Residual Fuel Oil Consumedby the Industrial Sector; Other Petroleum Products Consumedby the Industrial Sector; Aviation Gasoline Consumed by theTransportation Sector; Distillate Fuel Oil Consumed by theTransportation Sector; Jet Fuel Consumed by the TransportationSector; Liquefied Petroleum Gases Consumed by the Transporta-tion Sector; Lubricants Consumed by the Transportation Sector;Motor Gasoline Consumed by the Transportation Sector; ResidualFuel Oil Consumed by the Transportation Sector; Distillate Fuel OilConsumed by the Electric Power Sector; Petroleum Coke Con-sumed by the Electric Power Sector; Residual Fuel Oil Consumedby the Electric Power Sector. Table 1 presents descriptive statisticsfor the 24 series of petroleum consumption. Motor GasolineConsumed by the Transportation Sector has the highest mean andstandard deviation while Liquefied Petroleum Gases Consumed bythe Transportation Sector has the lowest mean and standarddeviation.

5. Results

The results of the univariate LM test for fractional integrationare reported in Table 2. We allow for a nonzero mean followingNielsen (2005). We report the results without allowing short-rundynamics (p ¼ 0) as well as allowing VAR(p) dynamics with p ¼ 1,p ¼ 2, p ¼ 3 and p ¼ 4 in each case. When p ¼ 0, the univariateLM test rejects the null hypothesis for all 24 series at the 1%level. When p40 the results are more mixed. If p ¼ 1, the nullhypothesis is rejected for 15 of the 24 series or 62.5% at the 5%level or better. If p ¼ 2, the null hypothesis is rejected for 7 of the24 series or 29.2% at the 5% level or better. If p ¼ 3, the nullhypothesis is rejected for 9 of the 24 series or 37.5% at the 5% levelor better. If p ¼ 4, the null hypothesis is rejected for 11 of the24 series or 45.8% at the 5% level or better. Thus, allowing anonzero mean and short-run dynamics, we are generally able toreject the null hypothesis less than 50% of the time.

A possible explanation why the results with and withoutallowing for short-run dynamics differ is that the presenceof noise in the data due to measurement errors, outliers and

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Table 1Descriptive statistics of petroleum consumption by sector.

Variables Mean Std. Dev.

Distillate Fuel Oil Consumed by the Residential Sector 540.3524 269.0433

Liquefied Petroleum Gases Consumed by the Residential Sector 334.2098 84.21856

Distillate Fuel Oil Consumed by the Commercial Sector 251.1784 87.59911

Liquefied Petroleum Gases Consumed by the Commercial Sector 58.97820 14.86210

Motor Gasoline Consumed by the Commercial Sector 37.75951 16.21899

Residual Fuel Oil Consumed by the Commercial Sector 115.1384 95.96501

Asphalt and Road Oil Consumed by the Industrial Sector 466.1105 200.8024

Distillate Fuel Oil Consumed by the Industrial Sector 593.2772 153.3840

Liquefied Petroleum Gases Consumed by the Industrial Sector 1338.701 312.6678

Lubricants Consumed by the Industrial Sector 78.99796 10.07910

Motor Gasoline Consumed by the Industrial Sector 115.3892 36.70115

Petroleum Coke Consumed by the Industrial Sector 315.3257 75.59020

Residual Fuel Oil Consumed by the Industrial Sector 316.1405 259.3488

Other Petroleum Products Consumed by the Industrial Sector 1348.353 229.3466

Aviation Gasoline Consumed by the Transportation Sector 25.97950 10.12646

Distillate Fuel Oil Consumed by the Transportation Sector 1852.114 615.2228

Jet Fuel Consumed by the Transportation Sector 1369.891 265.7272

Liquefied Petroleum Gases Consumed by the Transportation Sector 19.64550 9.165747

Lubricants Consumed by the Transportation Sector 74.44845 9.237673

Motor Gasoline Consumed by the Transportation Sector 7469.993 919.1389

Residual Fuel Oil Consumed by the Transportation Sector 381.9936 109.7621

Distillate Fuel Oil Consumed by the Electric Power Sector 66.26098 44.46513

Petroleum Coke Consumed by the Electric Power Sector 30.47199 33.45523

Residual Fuel Oil Consumed by the Electric Power Sector 647.5584 448.3971

Table 2Univariate LM test for fractional integration with nonzero mean.

Sector Zt ¼ 1 p ¼ 0 p ¼ 1 p ¼ 2 p ¼ 3 p ¼ 4

Residential Distillate fuel oil 857.00*** 106.27***�11.018 �33.837 �20.560

Liquefied petroleum gases 1021.4*** 27.049***�2.9775 �5.3218 �6.4872

Commercial Distillate fuel oil 281.70*** 114.30*** 0.60743 �166.55 �63.631

Liquefied petroleum gases 1021.4*** 27.049***�2.9775 �5.3217 �6.4871

Motor gasoline 1683.6*** 3.0250* 0.0012339 0.021328 0.16536

Residual fuel oil 2096.7*** 22.629***�0.28784 �1.5838 �17.165

Industrial Asphalt and road oil 127.71*** 111.21*** 27.968*** 0.064291 155.14***

Distillate fuel oil 280.18***�30.513 �36.189 �8.2690 �80.748

Liquefied petroleum gases 1266.9*** 35.480***�2.0846 �5.0138 �5.6405

Lubricants 141.00***�67.733 �6.8805 �6.2425 �4.6751

Motor gasoline 1899.7*** 7.0519*** 0.10123 0.16623 0.38796

Petroleum coke 1497.4***�2.7839 �13.461 36.461*** 8.5052***

Residual fuel oil 2317.4*** 54.106*** 7.6109*** 6.7692*** 11.091***

Other petroleum products 1284.0*** 733.18*** 9.6911*** 4.0031** 5.4671**

Transportation Aviation gasoline 1039.7***�3.4338 �2.1814 �1.6040 �2.7543

Distillate fuel oil 2922.9*** 33.519*** 2.4500 9.3694*** 8.8451***

Jet fuel 2153.6*** 67.376*** 25.756*** 17.994*** 10.829***

Liquefied petroleum gases 1198.4*** 3.7215* 0.57662 4.7899** 6.0046**

Lubricants 125.78***�93.372 �10.358 �7.7110 �6.8597

Motor gasoline 2602.4*** 49.142*** 6.4683** 5.8171** 8.8695***

Residual fuel oil 314.96***�18.497 �3.9661 �6.1432 �6.6043

Electric Power Distillate fuel oil 625.79***�10.397 �13.017 �0.79633 186.29***

Petroleum coke 2427.4*** 7.3199*** 9.2697*** 10.321*** 3.9271**

Residual fuel oil 2074.1*** 4.9250** 46.563*** 32.727*** 15.863***

*, **, *** denote statistical significance at the 10%, 5% and 1% levels, respectively.

H.H. Lean, R. Smyth / Energy Policy 37 (2009) 3205–32113208

structural breaks can lead fractional integration tests to findspurious evidence of fractional integration. Financial data, whichwill normally be high quality and available at high samplingfrequency over long time periods, will have less noise. However,macroeconomic and energy time series, while typically availableover a long period, is only sampled at monthly or quarterlyintervals and, as such, has more noise. Haldrup and Nielsen (2007)

show that fractional integration tests which allow for short-rundynamics are less prone to finding spurious evidence of fractionalintegration due to non-persistent noise in the data.

There are nine series for which we reject the null hypothesis inat least three of the four cases allowing for short-run dynamics.These are Asphalt and Road Oil Consumed by the IndustrialSector; Residual Fuel Oil Consumed by the Industrial Sector; Other

ARTICLE IN PRESS

Table 3Multivariate test for fractional integration with nonzero mean.

p ¼ 0 p ¼ 1 p ¼ 2 p ¼ 3 p ¼ 4

Residential 3604.4*** 172.09***�0.29599 �10.536 �7.0088

Commercial 4914.8*** 45.196*** 14.689*** 12.705** 25.669***

Industrial 3994.2*** 281.01*** 45.893*** 27.024*** 27.183***

Transportation 4674.7***�52.379 51.170*** 44.247***

�181.49

Electric Power 3187.1***�7.0004 �15.927 11.451*** 33.372***

*, **, *** denote statistical significance at the 10%, 5% and 1% levels, respectively.

H.H. Lean, R. Smyth / Energy Policy 37 (2009) 3205–3211 3209

Petroleum Products Consumed by the Industrial Sector; DistillateFuel Oil Consumed by the Transportation Sector; Jet FuelConsumed by the Transportation Sector; Liquefied PetroleumGases Consumed by the Transportation Sector; Motor GasolineConsumed by the Transportation Sector; Petroleum Coke Con-sumed for Electric Power and Residual Fuel Oil Consumed forElectric Power. Most of these series have high means and/orstandard deviations. Seven of the nine series with the largestmean consumption and the largest standard deviation inconsumption are fractionally integrated (see Table 1). Of thoseseries which are fractionally integrated, the only series which donot have a large mean and standard deviation are LiquefiedPetroleum Gases Consumed by the Transportation Sectorand Petroleum Coke Consumed for Electric Power. This result isconsistent with expectations. Energy consumption is more likelyto be fractionally integrated in series with high average con-sumption because shocks will generate a bigger deviation fromthe long-run equilibrium path, resulting in a higher level ofpersistence (Hsu et al., 2008). Series with high volatility inconsumption, reflected in the standard deviation, are more likelyto be fractionally integrated because the deviations from the long-run equilibrium path, due to shocks that create volatility, will belarger. Thus, departure from the equilibrium path will be morelikely to be persistent (see Maslyuk and Smyth, 2009; Mishraet al., 2009; Narayan et al., 2008).

Table 3 presents the results of the multivariate LM test forfractional integration based on sector. Because the multivariateLM test for fractional integration takes account of potentiallyimportant correlations between the elements of the multiple timeseries, it could have more power than the univariate LM testfor fractional integration (Nielsen, 2005). The null hypothesis isrejected for each of the five sectors when no short-run dynamicsare permitted (p ¼ 0). When short-run dynamics are allowed(p40) the findings are mixed. The null hypothesis is clearlyrejected for the commercial and industrial sectors. The null isrejected with either p ¼ 2 or 3 for the transportation sector andeither p ¼ 3 or 4 for the electric power sector, but only if p ¼ 1 forthe residential sector. Thus, overall, allowing for short-rundynamics petroleum consumption in the commercial andindustrial sector is fractionally integrated. This result isconsistent with both sectors being large consumers of energy.The results for the electric power and transportation sectors arenot clear cut, while, petroleum consumption in the residentialsector appears to be jointly I(0) with nonzero means.

6. Policy implications

In discussing the policy implications we focus on the threesectors for which the results are relatively clear cut—thecommercial, industrial and residential sectors. These three sectorstogether are responsible for almost three quarters of total energyconsumption in the United States (Ewing et al., 2007). Thatpetroleum consumption in the commercial and industrial sectors

is fractionally integrated means that shocks to consumption,caused by disruptions to supply in the Middle East or elsewhere,will have persistent effects on the real economy, such as outputand employment, in these sectors. This result is consistent withthe findings of previous research suggesting that output andunemployment in the United States is fractionally integrated (Gil-Alana, 2002b). The results reported here suggest that it would beuseful for the commercial and industrial sectors to invest inrenewable technologies that would allow firms in these sectors tomove away from reliance on petroleum products. Another courseof action would be for the commercial and industrial sectors toimplement demand management policies that would result inmore efficient use of petroleum products. As petroleum con-sumption in the residential sector appears to be jointly I(0) withnonzero means, disruptions to consumption in this sector wouldbe temporary with no persistent effect on the real economy. Thedistinction between the commercial/industrial sectors and resi-dential sector in this context makes sense. The commercial andindustrial sectors are employers and generate output. Thus,shocks to petroleum consumption in these sectors are more likelyto be directly linked to more long-lasting disruptions to the realeconomy.

Depending on the size of the cyclical and secular component offluctuations, which is contested, if shocks to the real economy inthe commercial and industrial sector are persistent, this can beinterpreted as providing support for real business cycle theory aswell as other theories of the business cycle such as New Keynesianmodels (see Libanio, 2005 for a survey). If real output in thesesectors is persistent, this suggests that following a negative shockautomatic return to a equilibrium may not occur, and thereforeKeynesian stabilization policies to stimulate demand and movethe economy towards full employment have a role to perform(Libanio, 2005). However, a note of caution is needed. If realoutput is persistent, it is also possible to make a case against sharpcontractions to slow the economy in the event it is overheating orin response to currency or fiscal crises (Dutt and Ros, 2003), sincethe negative effects of such policies will not dissipate in the shortrun.

The results have implications for modelling energy consump-tion. Non-rejection of the null for petroleum consumption in theresidential sector implies standard methods can be employed forconducting, for example, Granger causality, structural vectorautoregression, or impulse response analysis. Rejection of thenull for petroleum consumption in the commercial and industrialsectors indicates the need to transform the data to make itsuitable for such analyses. For example, in Andersen et al. (2003) afractional difference is taken of the multivariate volatilityprocesses considered there and the resulting multivariate seriesare modelled by vector autoregressions. There is increasedrecognition that disaggregated energy consumption should beused when testing for Granger causality, impulse responsefunctions and the like to compare the relative strengths of therelationship between energy consumption and output and/oremployment by source (see e.g. Erbaykay, 2008; Ewing et al.,2007; Sari and Soytas, 2004; Sari et al., 2008; Wolde-Rufael, 2004;Yang, 2000). The findings from these studies have importantpolicy implications. For example in Granger causality studies, ifunidirectional Granger causality runs from energy consumption toreal output, it follows that reducing energy consumption couldlead to a fall in income; however if Granger causality runs in theopposite direction this provides strong justification for imple-menting energy conservation policies because economic growth isnot dependent on energy consumption. Drawing the appropriatepolicy implications from modelling exercises such as theserequires correctly identifying the order of integration as part ofthe preliminary analysis.

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7. Conclusion

Previous studies that have tested for a unit root in aggregateenergy consumption have potentially reached misleading conclu-sions because they fail to allow for the possibility that energyconsumption might be fractionally integrated and do notdistinguish between different types of energy consumption. Thisstudy has tested for long memory in disaggregated petroleumconsumption in the United States using univariate and multi-variate LM tests for fractional integration. The results pointstrongly to the need to distinguish between different forms ofenergy consumption and allow for a generalization of the I(0)/I(1)dichotomy when considering the order of integration of energyconsumption. The univariate tests suggest that, allowing for short-run dynamics, nine of the 24 series are fractionally integrated.Consistent with expectations these series tended to have thehighest mean and standard deviation. The multivariate testssuggest that petroleum consumption in the commercial andindustrial sectors is clearly fractionally integrated when allowingfor short-run dynamics while petroleum consumption in theresidential sector is jointly I(0) with nonzero means

A limitation of the Nielsen (2005) test employed in this studyis that it does not allow for the possibility of structural break(s).Previous research has attributed failure to find energy consump-tion stationary to failure to allow for structural breaks (Chen andLee, 2007). Fractional integration and structural breaks can beconfused (Granger and Hyung, 2004; Diebold and Inoue, 2001).For this reason, some recent studies that have tested for theorder of integration of, for example, macroeconomic variables(Gil-Alana, 2002b; Caporale and Gil-Alana, 2008) and interna-tional tourist arrivals (Cunado et al., 2008) have started usingfractional integration tests that allow for one or more structuralbreak. This would be a useful direction for future research in theenergy literature. Another limitation is that the Nielsen (2005)test does not explicitly allow for potential non-linearities in thedata. One study that applies a non-linear long memory model toUnited States unemployment is van Dijk et al. (2002). Applying atest such as this to disaggregated energy consumption or energyproduction would be another useful path for future research in theenergy literature.

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