Comparison of Methods Used for Estimation of Number of Factors for High Dimensional Factor-Augmented Functional-Coefficient Forecasting Models

Jiraroj  Tosasukul

Authors

Jiraroj Tosasukul Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand

Keywords:

Factor models, functional-coefficient models, number of common factors, eigenvalues, principal component analysis

Abstract

Estimating the number of common factors is challenging particularly in nonparametric high dimensional time series model where the dimensions are bigger than the sample size being considered. In this article, we study the different techniques for determining the number of common factors which are considered in the context of reducing dimensions in the factor-augmented functional-coefficient model with high dimensions. The concept behind all the estimate techniques that are used in this research is based on the evaluation of eigenvalues derived from the correlation and covariance matrix. The performance of the estimators is compared using percentages and the average of the estimated factor numbers. The results of the simulation experiments showed that the growth rates of residual variances technique exhibits outstanding performance compared to other methods in situations when the dimension is greater than or equal to the large sample size. Nevertheless, both modified eigenvalues thresholding and the eigenvalue difference criterion techniques provide better results in comparison to other methods in cases when the dimension is smaller than the small sample size. This study employed an empirical approach, using an actual dataset of Australia's quarterly consumer price index (CPI) to provide evidence for the estimating techniques used for determining the factor number.

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