CLASSIFICATION OF VARIANCE REGIME FOR MULTIPHASED TIME SERIES USING LARGE DEVIATION THEORY

Abstract

Heteroscedasticity in time series data poses a substantial difficulty in modeling, as it influences the forecasting process. Multiphased, time series variables are prone to fluctuations in variance during both the observation periods and the forecasting phase. This presents a hurdle in accurately modeling and predicting such series. Experts acknowledge the regime switch model as an accurate method for predicting and forecasting such series. However, it relies on the precise identification of the series phases. The current strategies have been shown capable of identifying variance breaks within multiphased time series data. However, they are unable to ascertain the specific types of variance breaks that occur within the time series. The study introduces an alternative method for identifying variance breaks, as well as characterizing their nature and categorizing the variance regimes within multiphased time series. The devised method employs Large Deviation Theory to estimate the probabilities of break occurrences. The method involves partitioning the complete series $X(t)$ for $t>0$ into subsections of size $\delta t$. Thereafter, the variance of each subsection, represented as $\operatorname{var}(X(\delta t))$, and the standardized variance of each subsection, represented as $v_{5 t}$, are computed. The Gärtner-Ellis technique is utilized to derive the rate function for $v_{5 t}$, which is necessary for calculating $\operatorname{Pr}\left(v_{\delta t} \geq a\right)$ given a positive threshold $a$. The technique identified three variance regimes (low variance, average variance, and high variance) for classifying the subsection variances of the series relative to the benchmark variance $\sigma_t^2$. The simulation study and empirical data application demonstrated that the method effectively identified variance breaks and classified the variances of subsections relative to benchmark variance.

Received: July 22, 2025;
Revised: August 19, 2025;
Accepted: September 15, 2025