Statistical model validation through white noise hypothesis testing in regression analysis and ARIMA models

Abstract

In the domain of finance and economics, ensuring the validity and dependability of forecasting models is crucial. In this paper, the White Noise Hypothesis Test is elucidated as an essential model validation tool for both the regression and ARIMA models. In the case of regression analysis, there is a need for residual independence and homoscedasticity to confirm that the estimates of the parameters are not biased, that is, the chances of the parameter estimated to be true is high. In the case of an ARIMA model, residuals are checked for the white noise characteristics, and so as to ensure that all the relevant patterns associated with the time series have been detected. The paper uses simulated stock market data and risk management scenarios to demonstrate how these tests enhance model reliability, since when white noise characteristics are ascertained, the residuals are confirmed random and independent. The importance of validating models is discussed in the context of economic forecasting and policy analysis, where the validated models are indispensable for anticipating a market upheaval or to make right economic decisions. Therefore, when white noise test is used to confirm that the model meets the white noise criteria, this improves the credibility of predictions and thus influences strategic decision making in the uncertain environment.