A0316
Title: An asymptotic behaviour of a finite-section of the optimal causal filter
Authors: Junho Yang - Academia Sinica (Taiwan) [presenting]
Abstract: An $L_1$-bound between the coefficients of the optimal causal filter applied to the data-generating process and its approximation based on finite sample observations is derived. The data-generating process is assumed to be second-order stationary with either short or long-memory autocovariance. First, to obtain the $L_1$-bound, an exact expression of the causal filter coefficients and their approximation in terms of the absolute convergent series of the multistep ahead infinite and finite predictor coefficients, respectively, are provided. Then, a so-called uniform-type Baxter's inequality is proved to obtain a bound for the difference between the two multistep ahead predictor coefficients (under short and memory time series). The $L_1$-approximation error bound of the causal filter coefficients can be used to evaluate the quality of the time series predictions through the mean squared error criterion.
