Alex Gonzaga

A wavelet Whittle estimator of generalized long-memory stochastic volatility

We consider a k-GARMA generalization of the long-memory stochastic volatility model, discuss the properties of the model and propose a wavelet-based Whittle estimator for its parameters. Its consistency is shown. Monte Carlo experiments show that the small sample properties are essentially indistinguishable from those of the Whittle estimator, but are favorable with respect to a wavelet-based approximate maximum likelihood estimator. An application is given for the Microsoft Corporation stock, modeling the intraday seasonal patterns of its realized volatility.

Asymptotic decorrelation of between-scale wavelet coefficients of generalized fractional process

Recent interest on the wavelet transform of digital random signals with long-memory is significantly due to the approximate decorrelation of their wavelet coefficients, which simplifies system identification and estimation. In this paper, we show that for a fairly general model of long-memory across-scale autocovariances of wavelet coefficients converge rapidly to zero, and we determine the rate of converge. The result provides useful groundwork for wavelet-based processing of long-memory random signals.

Seasonal long-memory stochastic volatility

In this paper, we propose an alternative approach to estimation of seasonal long-memory stochastic volatility based on the generalized long-memory stochastic volatility (GLMSV) model. We show that the estimator is consistent. We investigate the small sample performance of the estimator by simulation. An application to actual data is also presented.