RUI: Inference and Variable Selection in Volatility Models

The University Corporation, Northridge, Northridge CA

Investigators

Abstract

As the need for data collection and storage soars, better predictive models are critical for making informed decisions, understanding trends, forecasting outcomes, and optimizing processes in various industries and sectors. This research project will develop mathematical and statistical methods to establish reliable procedures and algorithms that can analyze data in applications where data is observed through time, which is called time series data. This includes stock market analysis and predictions, weather forecasting, medical and astronomy data analysis. More specifically, this project focuses on studying how external factors influence trends in time series data. It involves not only testing the significance of these effects but also filtering through various potential factors that could be causing external influences. By including graduate and undergraduate students in this research and incorporating relevant research components in related graduate curricula, this project will engage students in STEM fields, especially underrepresented groups. This project specifically aims at studying the effects of exogenous factors in time series volatility models. Although exogenous covariates have been consistently used in time series applications, formal hypothesis testing, inference and model selection procedures in volatility models such as the Autoregressive Conditional Heteroscedasticity remain substantially under-developed, especially when there are several possible factor effects and when these effects may be nonlinear. This research will develop mathematical and statistical theoretical background for model building using exogenous variables in ARCH models, which have not been thoroughly investigated in the literature of statistics and econometrics. Models developed in this project will be used for a number of possible applications in time series data, particularly in the financial fields. More specifically, the objectives include a) developing a variable selection method for identifying significant exogenous covariates in an ARCH model, b) developing a novel hypothesis test for the significance of a set of exogenous variables when their effect in the ARCH volatility is fully nonparametric, and c) showing that the multiple nonparametric hypothesis tests for the covariates can be used to consistently select exogenous covariates even when their effect is nonlinear. The variable selection procedures will be based on a multiple testing correction approach and the consistency of the results will be established using asymptotic properties of the estimators when the sample size increases. The nonparametric effects of the external factors will be estimated with kernel regression estimators and the nonparametric variable selection will be performed using the asymptotic theory of the Analysis of Variance when the number of factor levels increases with the sample size. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.