The Effect of Over-Differencing on Model Validity

Abstract

We examine the effect of unnecessary differencing (over-differencing) on the appropriateness of the proposed models (Autoregressive of order one AR(1), Autoregressive of order two AR(2), and Moving Average of order two MA(2)). Our interest arises from the fact that in practical applications the fitted model due to inappropriately differenced data can still suitably describe the data sample based on the goodness of fit test using residual analysis. Given that we use simulation study to detect the consequences of unnecessary differencing on the fitted model. While the simulation study can be controlled using different scenarios, it becomes more challenging when dealing with real data. The validity and performance of the fitted models was checked by observing the changes in the estimated coefficients, the associated standard errors (SE), the residual variance, and Akaike information (AIC) by comparing them with the true parameters of the system (true model). The uniqueness of this paper is to examine how the fitted model is sensitive (valid) to the over-differencing.