Hybrid time series models with interacted lagged variables

Abstract

Time series forecasting predicts the future trend based on historical data. This doctoral research introduces a new concept called Interacted Lagged Variables (ILVs) to address the limitation of neglecting potential interactions among lagged variables in newlinetraditional Autoregressive Integrated Moving Average (ARIMA) models and propels it forward by developing a distinctive model known as Interacted-ARIMA (INTARIMA). The new approach captures interactions among lagged variables and integrates into the traditional ARIMA approach. It promises to surpass the limitations of ARIMA and raise the precision and reliability of time series forecasting. newlineWhile developing the INTARIMA model, the research proposes a methodology for newlineidentifying interactions among the lagged variables and including them in the model. newlineWith interactions, it defnes the INTARIMA process and explores its characteristic newlineproperties such as mean, variance, autocovariance function, and autocorrelation newlinefunction. The research also sheds light on the stationarity conditions and devises newlineparameter estimation procedures. It further delves into the algorithm for forecasting newlineusing the proposed INTARIMA model. The validity and the superiority of the model newlinein terms of forecast-accuracy is established through simulation and empirical analysis. Simulation studies also confrm the credibility of the expressions derived for the properties of the INTARIMA model and authenticate the parameter estimation procedures. A notable feature of the INTARIMA model is that it seamlessly transforms itself into the traditional ARIMA model, when the interactions are absent in the process. All the properties also reduce to those of the ARIMA model in such cases. The research further extends the scope and utility of the INTARIMA model by developing a hybrid model by amalgamating INTARIMA with Artifcial Neural Network (ANN). The credibility of the hybrid model is demonstrated through empirical analysis of real-world datasets.