Rank-based estimation for all-pass time series models

Abstract

An autoregressive-moving average model in which all roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models are useful for identifying and modeling noncausal and noninvertible autoregressive-moving average processes. We establish asymptotic normality and consistency for rank-based estimators of all-pass model parameters. The estimators are obtained by minimizing the rank-based residual dispersion function given by Jaeckel [Ann. Math. Statist. 43 (1972) 1449--1458]. These estimators can have the same asymptotic efficiency as maximum likelihood estimators and are robust. The behavior of the estimators for finite samples is studied via simulation and rank estimation is used in the deconvolution of a simulated water gun seismogram.Comment: Published at http://dx.doi.org/10.1214/009053606000001316 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Rank-Based Estimation for Garch Processes

“…Using a proof similar to that of Lemma 16 on page 88 of Andrews (2003), it can be shown that sup x∈I R |f n (x) − f n (x)| P → 0, and so this lemma holds.…”

“…The weight function λ t7 is plotted in Figure 3.1, along with λ N . Note that λ t7 (x) and λ N (x) are fairly similar except near x = 1. relatively efficient (see, for example, Hettmansperger and McKean, 1998, Andrews, Davis, and Breidt, 2007, and Andrews, 2008. In the case of linear model estimation, λ W is the optimal weight function when the noise distribution is logistic and, for R-estimation of GARCH model parameters, λ W is optimal when ln(Z 2 t )…”

Robust Factor Models with Explanatory Proxies

“…For instance, it has been extensively studied in the time series literature (e.g., Andrews et al (2007);Hill (2015)). The quantile regression is another type of robust estimation.…”

Rosenblatt’s Contributions to Deconvolution

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