Asymptotic decorrelation of discrete wavelet packet transform of generalized long-memory stochastic volatility

We derive the asymptotic properties of discrete wavelet packet transform (DWPT) of generalized long-memory stochastic volatility (GLMSV) model, a relatively general model of stochastic volatility that accounts for persistent (or long-memory) and seasonal (or cyclic) behavior at several frequencies. We derive the rates of convergence to zero of between-scale and within-scale wavelet packet coefficients at different subbands. Wavelet packet coefficients in the same subband can be shown to be approximately uncorrelated by appropriate choice of basis vectors using a white noise test. These results may be used to simplify the variance-covariance matrix into a diagonalized matrix, whose diagonal elements have the least distinct variances to compute.