Are the scaling properties of bull and bear markets identical? : evidence from oil and gold markets

In this study, the scaling properties of the oil and gold return volatilities have been analyzed in the context of bull and bear periods. In the determination of bull and bear turning points, we used the Modified Bry-Boschan Quarterly (MBBQ) algorithm. Results showed that the business cycle phase shapes of the bear periods in the oil market are almost linear, whereas the bull and bear periods of the gold and bull period of the oil market are convex. This means that there are sharper declines in the bear period of the oil market. Following the detection of bull and bear periods, scaling exponent H analysis was performed via the aggregated variance, Higuchi's statistic, Peng's statistic, rescaled range, boxed periodogram and wavelet fit models, which are from the time, frequency and wavelet domains. As there are conflicts about the credibility of these methods in the literature, we have used the shuffling procedure in order to determine the most robust methods. According to the results, bear periods have higher volatility persistency than bull periods.