z-logo
open-access-imgOpen Access
Stable Parameter Estimation for Autoregressive Equations with Random Coefficients
Author(s) -
V. B. Goryainov,
Elena Goryainova
Publication year - 2014
Publication title -
nauka i obrazovanie
Language(s) - English
Resource type - Journals
ISSN - 1994-0408
DOI - 10.7463/1214.0742725
Subject(s) - autoregressive model , mathematics , estimation , star model , nonlinear autoregressive exogenous model , estimation theory , statistics , econometrics , autoregressive integrated moving average , time series , economics , management

In recent yearsthere has been a growing interest in non-linear time series models. They are more flexible than traditional linear models and allow more adequate description of real data. Among these models a autoregressive model with random coefficients plays an important role. It is widely used in various fields of science and technology, for example, in physics, biology, economics and finance. The model parameters are the mean values of autoregressive coefficients. Their evaluation is the main task of model identification. The basic method of estimation is still the least squares method, which gives good results for Gaussian time series, but it is quite sensitive to even small disturbancesin the assumption of Gaussian observations. In this paper we propose estimates, which generalize the least squares estimate in the sense that the quadratic objective function is replaced by an arbitrary convex and even function. Reasonable choice of objective function allows you to keep the benefits of the least squares estimate and eliminate its shortcomings. In particular, you can make it so that they will be almost as effective as the least squares estimate in the Gaussian case, but almost never loose in accuracy with small deviations of the probability distribution of the observations from the Gaussian distribution.

The main result is the proof of consistency and asymptotic normality of the proposed estimates in the particular case of the one-parameter model describing the stationary process with finite variance. Another important result is the finding of the asymptotic relative efficiency of the proposed estimates in relation to the least squares estimate. This allows you to compare the two estimates, depending on the probability distribution of innovation process and of autoregressive coefficients. The results can be used to identify an autoregressive process, especially with nonGaussian nature, and/or of autoregressive processes observed with gross errors.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.
Having issues? You can contact us here