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Abstract:
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A semi-parametric approach is developed to model nonlinear relationships in time series data using polynomial splines. Polynomial splines require little assumption on the functional form of the relationship, so are very flexible for highly nonlinear relationships. Polynomial splines are also computationally very efficient. The serial correlation in the data is removed using an ARMA process, by doing so, the efficiency in nonparametric estimation is improved and correct inferences can be obtained. The explicit structure of the ARMA model allows the correlation to be used to improve forecasting performance. An algorithm is developed to automatically select and estimate the polynomial splines model and the ARMA model through backfitting. This method is applied on a real-life data set to forecast hourly electricity usage. The nonlinear effect of temperature on hourly electricity usage is allowed to be different at different hours of the day and days of the week. The forecasting performance of the developed method is evaluated in post-sample forecasting. The model is compared with well-accepted models and found significant improvement in the forecasting performance. significant imp
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