Upgrade from ARIMA to ARIMAX to Improve Forecasting Accuracy of Nonlinear Time-Series: Create Your Own Exogenous Variables Using Wavelet Analysis
نویسنده
چکیده
This paper proposes a technique to implement wavelet analysis (WA) for improving a forecasting accuracy of the autoregressive integrated moving average model (ARIMA) in nonlinear time-series. With the assumption of the linear correlation, and conventional seasonality adjustment methods used in ARIMA (that is, differencing, X11, and X12), the model might fail to capture any nonlinear pattern. Rather than directly model such a signal, we decompose it to less complex components such as trend, seasonality, process variations, and noises, using WA. Then, we use them as exogenous variables in the autoregressive integrated moving average with explanatory variable model (ARIMAX). We describe a background of WA. Then, the code and a detailed explanation of WA based on multi-resolution analysis (MRA) in SAS/IML® software are demonstrated. The idea and mathematical basis of ARIMA and ARIMAX are also given. Next, we demonstrate our technique in forecasting applications using SAS® Forecast Studio. The demonstrated time-series are nonlinear in nature from different fields. The results suggest that WA effects are good regressors in ARIMAX, which captures nonlinear patterns well.
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