Behaviours of Error-Prone Variables on Low-Chaotic Autoregressive Models

Abstract

Nowadays, both measurement errors and chaotic structures in data are frequently included in the literature. The main reasons for this are biased parameter estimations in the presence of measurement error and the unpredictability of chaotic structures. Although it has been investigated whether the confusion in the data is due to the measurement error or to the chaotic structure, the issue of how these two concepts affect each other has not been found in the literature. This study researched how time series with a low-chaotic structure were affected by measurement error, using Lyapunov exponents. This effect was demonstrated by various simulations for low-chaotic AR(1) and AR(2) autoregressive models. The results showed that the maximal Lyapunov exponent attenuated toward zero with an increase in the measurement error. It was also found that the Lyapunov exponent was affected by the sample size and the number of delays of the models.