Wavelet-M-Estimation for Time-Varying Coefficient Time Series Models

Abstract

This paper proposes wavelet-M-estimation for time-varying coefficient time series models by using a robust-type wavelet technique, which can adapt to local features of the time-varying coefficients and does not require the smoothness of the unknown time-varying coefficient. The wavelet-M-estimation has the desired asymptotic properties and can be used to estimate conditional quantile and to robustify the usual mean regression. Under mild assumptions, the Bahadur representation and the asymptotic normality of wavelet-M-estimation are established.

Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient Models

“…It has been a major statistical theory issue since Bahadur's pioneering work on quantiles [30]; see [31], among others. Recently, reference [32] investigated the Bahadur representation for sample quantiles under ϕ-mixing sequence; reference [33] gave an M-estimation for time-varying coefficient models with α-mixing errors and established Bahadur representation in probability. In the paper, we will establish Bahadur representation with probability 1 (almost surely) for quantile-wavelet estimates in the models Equations ( 1) and (2).…”