An Introduction to Wavelets and Other Filtering Methods in Finance and Economics

7

WAVELETS FOR VARIANCE-COVARIANCE ESTIMATION

7.1 INTRODUCTION

The wavelet transform has proven to be very effective in adapting to “local” features in time series when the focus was an estimation of the mean function (Chapter 6). Donoho and Johnstone (1994, 1998) introduced wavelet techniques to the statistics community using nonparametric function estimation as their vehicle. The wavelet transform performs well because it efficiently partitions the time-frequency plane, as seen in Figure 4.2, by using short basis functions for high-frequency oscillations and long basis functions for low-frequency oscillations. An important characteristic of the wavelet transform (DWT or MODWT) is its ability to decompose (analyze) the variance of a stochastic ...