Estimation of Regression Model with Interacted Autoregressive Integrated Moving Average (INTARIMA) Errors

Baskaran  Thangarajan; Nimitha  John

Authors

Baskaran Thangarajan Department of Statistics and Data Science, CHRIST (Deemed to be University), Bengaluru, Karnataka, India
Nimitha John Department of Statistics and Data Science, CHRIST (Deemed to be University), Bengaluru, Karnataka, India

Keywords:

INTARIMA, regression with correlated errors, interacted lagged variables, regression with AR errors

Abstract

Regression analysis assumes independence of errors. Failure of it makes the model untenable.
This article introduces a new method for estimating a regression model when the errors are correlated,
specifically in the Interacted Autoregressive Integrated Moving Average (INTARIMA) structure. The
proposed method outperforms traditional methods dealing with regression models with independent
or ARIMA errors. The method is unique in the sense that it deals with the autocorrelated error with
interactions, which hitherto not been addressed. The superiority of the new approach is established
through a simulation analysis. To validate the suitability of the suggested method for real-world
applications, we apply it to the Nelson-Plosser macroeconomic time series data on the Consumer
Price Index (CPI) and Interest Rate of the United States. The data analysis with the new method
provides better parameter estimates over the methods featuring ARIMA or independent errors. While
the magnitude of this gain in accuracy is over 40 percent compared to the technique for ARIMA
errors, it is still higher when compared to the method for independent errors. Practitioners in fields
like economics, data analysis, or others would benefit using the INTARIMA model in real world
scenarios whenever they face a situation wherein the regression model has autocorrelated error with
interactions. Thus, this article establishes the proposed method as the most effective approach for
regression models for addressing serially correlated errors with significant interaction effects.

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