Analysis of Time Series Data via Quasi-Least Squares Technique
Mingrui Li · Journal of Applied Mathematics and Computation · 2024
In this paper, we proceed to analyze and dispose of time series data that are measured repeatedly on the basis of AR(p) via an approach called 'quasi-least squares'. We first briefly provide an overview and description of the quasi-least squares method, making it easy to illustrate the iterative steps and convergence criteria of the algorithm based on the parameter estimation process of the generalized linear model. Next, as an application of the quasi-least squares method, we assume to construct a model that can be used to handle time series data with errors taken by repeated measures with the help of an autoregressive model. In order to improve the efficiency of parameter estimators, we are supposed to take advantage of the quasi-least squares to present an integral iterative procedure for the regression coefficients and autoregressive coefficients of AR(p), thereupon then further verifying the practicability of the model and algorithm. Most importantly, under some wild regularity conditions, we show that the resulting estimators are asymptotically normal.