Energy Consumption in the GCC Countries: Evidence on Persistence

This paper examines the statistical properties of energy consumption in the GCC countries applying fractional integration methods to annual data from 1980 to 2014. The results indicate that both the raw and the logged series exhibit a (statistically significant) linear time trend in the case of Bahrain, Oman and Qatar, and the raw series only in the case of Saudi Arabia. Mean reversion (i.e., statistical evidence of d < 1) is found in the case of Bahrain for both the raw and logged data, and in Qatar for the logged series. In the remaining cases, the I(1) hypothesis cannot be rejected except for the logged data in Saudi Arabia, since d is found to be statistically higher than 1 in that country. The implication of these findings is that in the case of Bahrain and Qatar exogenous shocks to energy consumption have transitory effects, which disappear in the long run without the need for policy action, whilst the permanent nature of the effects of shocks elsewhere means that appropriate policies have to be designed to restore equilibrium. C000, C220, E210, Q400.


Introduction
In the last two decades numerous studies have analysed the causal linkages between energy consumption and economic growth as well as other macroeconomic variables; however, many of them have not paid proper attention to the stochastic properties of the energy variables. (Note 1) Narayan and describes the data and discusses the main empirical results. Section 4 offers some concluding remarks.

Methodology
The analysis below is based on the concept of long memory. In the time domain, a process {x t , t = 0, ±1, …} with an autocovariance (or pseudo-autocovariance) function γ u = Cov(x t , x t+u ) is said to exhibit long memory if the sum of its autocovariances is γ u , i.e., In the frequency domain, consider the same process {x t , t = 0, ±1, …} and assume that it has a spectral density function (or a pseudo spectral density function), which is the Fourier transform of the The category of short-memory or I(0) processes includes white noise but also stationary and invertible ARMA processes.
Long memory is a property of unit-root or I(1) processes that become I(0) or stationary by taking first differences. More specifically, a process {x t , t = 0, ±1, …} is said to be I(1) if it can be represented as ,..., ) and t u is a   0 I process defined as above, which can be a white noise or an ARMA process. Note that if u t is ARMA(p,q), then x t is said to be an ARIMA (P, 1, q) process. The differencing parameter for making a series I(0) is not necessarily an integer (e.g., 1 as in (6) above) but can be any real number. In other words, one can consider more general models of the form: ,..., where d can be a fraction between 0 or 1, or even exceed 1. In fact, one can use a Binomial expansion such that, for all real value d, and therefore the left-hand side of (7) can be expressed as This type of processes was introduced by Granger (1980Granger ( , 1981, Granger and Joyeux (1980) and Hosking (1981) after noticing that many series appeared to be over differenced after differencing them to achieve stationarity. They were made popular in the nineties by Baillie (1996), Gil-Alana and Robinson (1997) and Silverberg and Verspagen (1999), and since then have been widely applied to analyse time series data in various sectors including the energy one (see, e.g., Gil-Alana et al., 2010).
In this context, the parameter d plays a very important role as a measure of the degree of persistence. In particular, if d belongs to the interval (0, 0,5) x t in (7) is covariance stationary, whereas if d ≥ 0.5 the process is non-stationary. Also, values of d below 1 imply mean reversion, i.e., the effects of shocks are transitory and disappear in the long run, whilst if d ≥ 1 they are permanent. Finally, note that if u t in (7) is an ARMA(p, q) process, then x t is a fractionally integrated ARMA or ARFIMA(p, d, q) process.
We estimate the fractional differencing parameter using the Whittle function in the frequency domain (Dahlhaus, 1989) applying a parametric testing procedure proposed by Robinson (1994) that is valid even in the presence of non-stationarity. This method allows to test for any real value d in the model given by (6), where x t can be the errors of a regression model including deterministic terms such as an intercept and/or a linear trend. Moreover, the limit distribution is standard Normal and is not affected by the inclusion of deterministic components or the modelling assumptions about the I(0) disturbance term u t in (6).

Data
We use data on energy consumption per capita expressed in terms of kg of oil equivalent, annually,   accelerated. Despite the fact that the economy boomed, growing by 5.6% p.a., energy demand increased by only 3.8% p.a., which implies that energy intensity dropped on average by 1.7% p.a.

Empirical Results
We estimate the following model: where y t is the time series of interest, β 0 and β 1 are unknown coefficients corresponding respectively to an intercept and a linear time trend, and x t is assumed to be integrated of order d (or I(d)), which implies that u t in the second equation in (3) is I(0). Table 1  As can be seen, a time trend is required in four cases (Bahrain, Oman, Qatar and Saudi Arabia) for the original series and in three (the same countries except Saudi Arabia) for the logged series. The I (1) hypothesis, i.e., d = 1, cannot be rejected in the majority of cases, the confidence interval including one, the exceptions being Bahrain with the raw data and Bahrain and Qatar with the logged ones-in these cases there is evidence of mean reversion, since the estimated value of d is significantly smaller than one. Table 2 reports the estimated values for the intercept and the time trend coefficients for each series.
The latter are biggest in the case of Qatar with the raw data and Oman with the logged ones.