OverviewRecently there has been a thriving stream of studies (for example, Asche et al., 2006, Hartley et al., 2008, Brigida, 2014) on the relationship between oil price and natural gas price. It is highly necessary to understand the underlying mechanism of how oil price is linked with natural gas price when we consider the new features of both the international oil market and the natural gas market. Most of these existing studies focus on the US market and it is shown that the pattern of this relationship has been changing over time. This is especially true when the recent development of the shale gas/oil market has dramatically changed the local/international market. This paper adopts a long memory approach to study the oil-gas relationship in three distinctive major international markets of, namely, the US, Europe and Japan. Our empirical results contribute to current discussions on the pass-through from oil price to natural gas price. It is consistent with the fact that for oil there has been a worldwide market, whereas for natural gas the markets are largely segmented. While acknowledging the fact that price mechanisms differ significantly across these markets, we have found interesting empirical results that may help to understand the pricing relationship and offer potential policy suggestions.MethodsLong memory or long range dependence has been used in hydrology and climatology since the 1950s and been extended to economics and finance only since the 1980s. First noted by Hurst (1951) and then Mandelbrot and Wallis (1968), the long range dependence is defined as the persistence of autocorrelations, in which the decaying process is far longer than what an ARMA model would predict. For example, Lo (1991, Table 1, pp1285) shows the difference in autocorrelation structure between an AR(1) process with 0.5 as the AR coefficient and a fractional alternative that the order of integration equals 1/3. The first four autocorrelations for the first case are 0.5, 0.25, 0.125 and 0.063, and are reduced to 0.001 at the 10th order. On the other hand, the first four autocorrelations for the factional integrated case are 0.5, 0.4, 0.35 and 0.318, and it only decreased to 0.235 after 10 periods. In many current works, testing unit roots in autoregressive process has played an essential role. However, it is arguable that the dichotomy between I(1) and I(0) is too restrictive to model the underlying processes.Techniques on finding long memory have been well developed in recent years, for example, the ‘Rescaled Range’ or ‘Range over Standard Deviation’ or ‘R/S’ statistic, first proposed by Hurst (1951) and then Mandelbrot and Wallis (1969). Geweke and Porter-Hudak (1983, GPH in short) propose an estimator of the order of integration based on the OLS regression of the log periodogram on the log frequency. Shimotsu and Phillips (2006) develop the Exact Local Whittle estimator whose asymptotics are based on the exact frequency domain (or its estimate which will give rise to FELW estimator) of the data generating process. This paper will adopt these two approaches to estimate the order of integration of the oil-gas price ratio in three markets. To further consider the potential time varying feature of this relationship, we extend the analysis using a rolling windows approach.ResultsStandard unit root tests (such as the ADF and KPSS test) on the oil-gas price ratios show some contradicting results especially for Europe and Japan. There are two possibilities of such inconsistency between the ADF and KPSS results. First, the KPSS test has power to test for fractional integration. Rejecting stationary null hypothesis by the KPSS test means that the underlying series may have long memory. Second, the inconsistency may reflect that the relationship is time varying.Although there are occasional differences subject to the model specification, the results using GPH or ELW estimation are generally consistent with each other. Taking ELW estimation as an example, there are three clearly different results for each region. The European relationship is stationary with long memory, whereas the US relationship is clearly nonstationary and Japan’s in between, meaning nonstationary with mean-reverting.The rolling windows estimation shows that the level of persistence (measured by the order of integration) has been increasing across three markets. And again, we can identify clear distinctive features from these series. The European relationship remains stationary, although the level of persistence increases when the window moves to July/1990–Dec./2006 and remains at a relatively higher level afterwards. Japan’s case is slightly more complicated, since it is moving from a stationary regime to nonstationary (but mean-reverting) when the window moves to ??Oct./1988–Mar./2005, reflecting a potential structural change from early 2005. The order of integration for the US shows generally nonstationary results. When the windows move to those including Feb./2011 onwards, it exhibits not only nonstationarity but also potentially explosive process.ConclusionsTo summarize, this paper adopts the long memeory/fractional integration approach to study the oil-gas pricing relationship in Europe, Japan and the US respectively. We have found the following results:There are evidences of long memory in all series, meaning the shocks to the oil-gas relationship tend to persist even when the ratio is stationary. While the European and the Japanese relationships are shown to have the tendency of stationary or reverting back to the relationship, the US results demonstrate clear evidence of a breaking up of the oil-gas bundle from 2011 onwards. Evidences of potential impact of structural changes on the markets also can be identified by the rolling windows estimation. For the European case, Decemeber 2006 is likely to be the breaking point, whereas March 2005 for Japan. Undoutedly, further investigations on the market conditions for these critical time points are also needed.
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