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On some nonstationary, nonlinear random processes and their stationary approximations

Part of: Inference from stochastic processes Parametric inference

Published online by Cambridge University Press:  08 September 2016

Suhasini Subba Rao
Suhasini Subba Rao*
Affiliation:
Universität Heidelberg
*
∗ Current address: Department of Statistics, Texas A&M University, 3143 TAMU, College Station, TX 77843-3143, USA. Email address: suhasini@stat.tamu.edu
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Abstract

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In this paper our object is to show that a certain class of nonstationary random processes can locally be approximated by stationary processes. The class of processes we are considering includes the time-varying autoregressive conditional heteroscedastic and generalised autoregressive conditional heteroscedastic processes, amongst others. The measure of deviation from stationarity can be expressed as a function of a derivative random process. This derivative process inherits many properties common to stationary processes. We also show that the derivative processes obtained here have alpha-mixing properties.

Keywords

Derivative processlocal stationaritynonlinearitynonstationaritystate space model

MSC classification

Primary: 62M10: Time series, auto-correlation, regression, etc.
Secondary: 62F10: Point estimation
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 38 , Issue 4 , December 2006 , pp. 1155 - 1172
Copyright
Copyright © Applied Probability Trust 2006 

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