Memories of the Gold Foreign Exchange Market Based on a Moving V-Statistic and Wavelet-Based Multiresolution Analysis

Abstract

Memory in finance is the foundation of a well-established forecasting model, and new financial theory research shows that the stochastic memory model depends on different time windows. To accurately identify the multivariate long memory model in the financial market, this paper proposes the concept of a moving V-statistic on the basis of a modified R/S method to determine whether the time series has a long-range dependence and subsequently to apply wavelet-based multiresolution analysis to study the multifractality of the financial time series to determine the initial data windows. Finally, we check the moving V-statistic estimation in wavelet analysis in the same condition; the paper selects the volatilities of the gold foreign exchange rates to evaluate the moving V-statistic. According to the results, the method of testing memory established in this paper can identify the breakpoint of the memories effectively. Furthermore, this method can provide support for forecasting returns in the financial market.