Summary: Rank-Based Estimation for Autoregressive
Moving Average Time Series Models
February 6, 2007
We establish asymptotic normality and consistency for rank-based estimators of
autoregressive-moving average model parameters. The estimators are obtained by mini-
mizing a rank-based residual dispersion function similar to the one given in L.A. Jaeckel
[Estimating regression coefficients by minimizing the dispersion of the residuals, Ann.
Math. Statist. 43 (1972) 14491458]. These estimators can have the same asymptotic ef-
ficiency as maximum likelihood estimators and are robust. The quality of the asymptotic
approximations for finite samples is studied via simulation.
AMS 2000 subject classifications. Primary 62M10; secondary 62E20, 62F10.
Key words and phrases. Autoregressive moving average models, rank estimation.
Rank-Based Estimation for ARMA Models 1
In this paper, we use a rank-based technique to estimate the parameters of autoregressive-moving average
(ARMA) models, the standard linear time series models for stationary data. The rank (R) estimators we
consider minimize the sum of mean-corrected model residuals weighted by a function of residual rank; they