آزمون های کارایی غیرخطی و روزانه در بازارهای آتی انرژی

Using high frequency data, this paper first time comprehensively examines the intraday efficiency of four major energy (crude oil, heating oil, gasoline, natural gas) futures markets. In contrast to earlier studies which focus on in-sample evidence and assume linearity, the paper employs various nonlinear models and several model evaluation criteria to examine market efficiency in an out-of-sample forecasting context. Overall, there is evidence for intraday market inefficiency of two of the four energy future markets (heating oil and natural gas), which exists particularly during the bull market condition but not during the bear market condition. The evidence is also robust against the data-snooping bias and the model overfitting problem, and its economic significance can be very substantial.

For most of its scientific life, the field of finance has debated the question of market efficiency (Chordia et al., 2005). The weak-form market efficiency suggests that the security prices traded in a (weak-form) efficient market follow a random walk (or more precisely a martingale) and cannot be predicted based on historical price information.1 Hence, randomness or unpredictability of asset returns can generally be claimed to closely relate to market efficiency. The inference on market efficiency carries important implications to practitioners, for example, to portfolio managers for the design of trading strategies, and to financial managers for the equity financing decision. Numerous earlier works have been conducted to examine weak-form market efficiency in the context of asset return predictability based on past returns. In particular, these works typically use the autocorrelation test and/or the variance ratio test of Lo and MacKinlay (1988). The works using the autocorrelation test include Lee et al. (2000), Chordia et al. (2005) on stock markets and Liu and He (1991) and Liu (2007) on currency markets, while the works using the variance ratio test include Lee et al. (2000), Chaudhuri and Wu (2003), Patro and Wu (2004) and Bianco and Renò (2006) on stock markets, and Liu and He (1991) and Pan et al. (1997) on currency markets. Noteworthy, however, both the autocorrelation test and the variance ratio test assume linearity and only investigate serial uncorrelatedness rather than martingale difference, which was already pointed out in Hsieh (1991) and McQueen and Thorley (1991) and more recently reemphasized by Hong and Lee (2003). Theoretically, as discussed in McQueen and Thorley (1991), existence of fads or rational speculative bubbles suggests the possibility of nonlinear patterns in asset returns. Or, if the world is governed by a not-too-complex chaotic process, it should have short-term nonlinear predictability (in mean) but not linear predictability (Hsieh, 1991, p.1845). Empirically, a nonlinear time series can have zero autocorrelation but a non-zero mean conditional on its past history (Hong and Lee, 2003). Hence, both the autocorrelation test and the variance ratio test may fail to capture predicable nonlinearities in mean and could yield misleading conclusions in favor of the random walk (martingale) hypothesis. This study examines intraday market efficiency and return predictability on major energy futures markets. We seek to contribute to the literature in the following important aspects. First, although few earlier studies explore intraday volatility behaviors of electricity futures markets (e.g., Higgs and Worthington, 2005) or use nonlinear models to investigate daily oil futures market efficiency and return predictability (Fujihara and Mougoué, 1997, Moshiri and Foroutan, 2006, Matilla-Garcia, 2007 and Shambora and Rossiter, 2007), our study is the first to investigate intraday return predictability on major energy futures markets (crude oil, heating oil, gasoline, natural gas). It is surprising to note that despite intraday transactions are nowadays common and surveys of market participants indicate that technical analysis is placed with more emphasis the shorter the time horizon, the study of predictability based on past returns with high frequency data is still very limited ( Bianco and Renò, 2006 and Marshall et al., 2008). Also, even casual observations can clearly reveal that intraday price behavior can be vastly different from daily price behavior, as a large swing within the day can end up with little change in the end-of-day closing price. To this end, our study on intraday price behavior (especially in the context of exploiting potential nonlinearity-in-mean) fills an important gap on energy markets in particular and (to a large extent) financial markets in general. 2 Second, we extend the literature by applying a number of nonlinear models that allow for both potential nonlinearity-in-mean and nonlinearity-in-variance. In particular, some variants of the popular nonlinear models used in many previous studies are used in this study.3 While the studies cited above using the autocorrelation test and/or the variance ratio test only focus on in-sample evidence and typically fail to allow for potential nonlinearity-in-mean, recent studies on energy markets (Moshiri and Foroutan, 2006, Matilla-Garcia, 2007, Shambora and Rossiter, 2007 and Agnolucci, 2009) have focused on nonlinear models and out-of-sample performance, which also mitigates the concern of in-sample overfitting for nonlinear models. This study further extends these recent studies by using the recent White's Reality Check test (Sullivan et al., 1999) to address the concern of data-snooping bias (i.e., spuriously superior predicative ability of some complex models due to chance).4 When several forecast models using the same data are compared, it is crucial to take into account the dependence among these models, which otherwise may result in misleading inference due to data-snooping bias.5 Finally, similar to Swanson and White (1997), Gencay, 1998 and Gencay, 1999, Hong and Lee (2003) and Yang et al. (2008), this study presents evidence based on both statistical and economic criteria. Few earlier random walk behavior studies on futures markets have considered economic criteria as measured by magnitude of trading returns and particularly the direction of forecasted price changes, which have practical value to investors and other decision-makers. For example, Moshiri and Foroutan (2006) and Matilla-Garcia (2007) focus on statistical criteria, while only Shambora and Rossiter (2007) have explored the importance of trading rule profitability (as an economic criterion) to evaluate the forecasting performance on energy futures markets. Moreover, the direction of changes as an alternative economic criterion has been little explored on futures markets. From a perspective of decision-making under uncertainty, there exist important circumstances under which this criterion is exactly the right one for maximizing the economic welfare of the forecaster (Leitch and Tanner, 1991 and Hong and Lee, 2003). Directional predictability in asset returns also has important implications for market timing and the resulting active asset allocation management. Hence, we are perhaps the first to comprehensively report evidence on both (out-of-sample) trading rule profitability (particularly based on multiple nonlinear models) and the predictability of direction of changes for major energy futures markets. The rest of this paper is organized as follows: Section 2 presents econometric methodology; Section 3 describes the data; and discusses the empirical results; and finally, Section 4 concludes the paper.

Using high frequency data, this paper first time comprehensively examines the intraday predictability of four major energy (crude oil, heating oil, gasoline, natural gas) futures markets. The paper employs various nonlinear models (neural network, semiparametric functional coefficient model, nonparametric kernel regression, GARCH), in addition to a linear model, and several evaluation criteria based on both statistical and economic accuracy to examine market efficiency in an out-of-sample forecasting context. Overall, more thorough allowance for nonlinearity and market conditions (bear and bull markets) still only suggests somewhat limited evidence for intraday market inefficiency of energy future prices. Among the four energy futures markets, only two markets (heating oil and natural gas) show robust evidence of predictability (against the data-snooping bias as well as the overfitting problem) during the bull market condition. No such robust evidence of predictability is present for any markets during the bear market condition. Nevertheless, it is worthy to note that for these cases with the evidence of predictability, the economic significance can be very substantial. Interestingly, the evidence for predictability is detected only by economic criteria (i.e., trading rule profitability and the direction of price changes), but not by traditional statistical criteria. Furthermore, the evidence is primarily detected by using the linear model and a popular nonlinear-in-mean model (i.e., nonparametric kernel regression) and their combinations with some other models, while the nonlinear-in-variance GARCH model and other nonlinear-in-mean models (including the NN model) generally do not help. The little contribution of the GARCH model to out-of-sample predictability stands in contrast with earlier studies on daily stock and currency returns (e.g., Hsieh, 1991, 1993) and daily energy returns (Moshiri and Foroutan, 2006; Matilla-Garcia, 2007; Shambora and Rossiter, 2007). The little success of the NN model in this study also differs from several earlier studies on the crude oil market (Moshiri and Foroutan, 2006; Shambora and Rossiter, 2007). Certainly, the differences of financial markets and particularly difference of data frequencies (intraday versus daily) under study might account for such different findings. Finally, the allowance for the data-snooping bias using White's Reality Check test renders apparently stronger predictability of these markets (particularly based on forecast combinations) to be tenuous. Thus, the findings of the paper underscore the importance of allowing for data-snooping in addition to the well-known overfitting problem of nonlinear models. In this context, the predictability of asset returns in general and energy market returns in particular might not be as widespread as previously thought when the data-snooping bias was typically ignored (e.g., Moshiri and Foroutan, 2006; Matilla-Garcia, 2007; Shambora and Rossiter, 2007). On the other hand, Hong et al. (2007) demonstrate further benefits of using nonlinear models when the forecasts of the entire asset return density distribution are evaluated. These issues should deserve more attention in future research of asset return predictability.