Time-Varying Long-Memory in Volatility: Detection and Estimation with Wavelets

Previous analysis of high frequency nancial time series data has found volatility to follow a long-memory process and to display an intradaily U-shape pattern. These ndings implicitly assume that a stable environment exists in the nancial world. To better capture the nonstationary behavior associated with market collapses, political upheavals and news annoucements, we propose a nonstationary class of stochastic volatility models that features time-varying parameters. The generality of our nonstationary stochastic volatility model better accommodates several empirical features of volatility and nests stationary stochastic volatility models within it. To estimate the time-varying long-memory parameter, we use the log linear relationship between the local variance of the maximum overlap discrete wavelet transform's coeecients and their scaling parameter to produce a semiparameteric, OLS estimator. Because wavelets are a set of well localized basis functions in time and scale, they are an ideal tool for analyzing nonstationary behavior. We apply our estimator to a years worth of ve-minute Deutsche mark-U.S dollar return data.