Maximum likelihood 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 generate uncorrelated (white noise) time series, but these series are not independent in the non-Gaussian case. An approximate likelihood for a causal all-pass model is given and used to establish asymptotic normality for maximum likelihood estimators under general conditions. Behavior of the estimators for finite samples is studied via simulation. A two-step procedure using all-pass models to identify and estimate noninvertible autoregressive-moving average models is developed and used in the deconvolution of a simulated water gun seismogram.

Optimal forecasting of noncausal autoregressive time series

“…Thus, we assume that the error term t is nonGaussian and that its distribution has a (Lebesgue) density f (x; ) = 1 f ( 1 x; ) which depends on the parameter vector (d 1) in addition to the scale parameter already introduced. The function f (x; ) is assumed to satisfy the regularity conditions stated in Andrews et al (2006) and Lanne and Saikkonen (2008). These conditions imply that f (x; ) is twice continuously di¤erentiable with respect to (x; ), non-Gaussian, and positive for all x 2 R and all permissible values of .…”

“…However, no practically useful forecasting method seems to be available although forecasting is probably the most important application of univariate models. In addition, forecasts are needed in computing impulse responses on which measures of persistence in economic time series can be 1 Noncausal and potentially noninvertible autoregressive moving average models, as well as their their special cases referred to as all-pass models, have also been studied in the statistical literature (see, inter alia, Lii and Rosenblatt (1996), Huang and Pawitan (2000), Breidt et al (2001), and Andrews et al (2006)). 1 based.…”

Autoregression-based estimation of the new Keynesian Phillips curve

“…The function f (x; !) is assumed to satisfy the regularity conditions stated in Andrews et al (2006) and Lanne and Saikkonen (2011a). These conditions imply that f (x; !)…”

Noncausality and inflation persistence

“…The function f (x; !) is assumed to satisfy the regularity conditions stated in Andrews et al (2006), and Lanne and Saikkonen (2011). These conditions imply that f (x; !)…”