Rank‐based estimation for autoregressive moving average time series models

Abstract

We establish asymptotic normality and consistency for rank-based estimators of autoregressive-moving average model parameters. The estimators are obtained by minimizing a rank-based residual dispersion function similar to the one given in L.A. Jaeckel

A Smooth Block Bootstrap for Statistical Functionals and Time Series

“…Shao, ) as a robust assessment of location. See Tran (), Hallin and Puri () and Andrews (), and references therein, for other rank‐based estimation with time series. Example For a function Ψ( x , t ), an M‐estimator T ( F n ) can be defined as the solution to , estimating a parameter T ( F ) for which holds. This class of estimators can contain maximum likelihood estimators and various robust estimators for time series models.…”

“…Shao, 2003) as a robust assessment of location. See Tran (1988), Hallin and Puri (1991) and Andrews (2008), and references therein, for other rank-based estimation with time series. Example 4 (M-estimators).…”

Robust model order selection for ARMA models based on the bounded innovation propagation τ-estimator

“…, N, is zero-mean Gaussian with σ W = κσ X , where κ = 5. We compare our proposed approaches to (i) the information criterion that is based on Gaussian maximum likelihood IC ML and provides a benchmark for the "clean data" case and (ii) a criterion IC RA that is of the same type as IC 1 but uses robust rank-based ARMA parameter estimates from [13] and the normalized median absolute deviation [12] as robust standard deviations estimate.…”

“…For recent advances on robust ARMA parameter estimation, the interested reader is referred, e.g., to [3,5,[12][13][14][15] and references therein. All presented approaches are based on the bounded innovation propaga- .…”

Rank-Based Estimation for Garch Processes

“…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 )…”