| Jun Liu |
In this paper a semi-parametric approach is developed to model non-linear relationships in time series data using
polynomial splines. Polynomial splines require very little assumption about the functional form of the underlying
relationship, so they are very flexible and can be used to model highly non-linear relationships. Polynomial splines are
also computationally very efficient. The serial correlation in the data is accounted for by modelling the noise as
an autoregressive integrated moving average (ARIMA) process, by doing so, the efficiency in nonparametric estimation is
improved and correct inferences can be obtained. The explicit structure of the ARIMA model allows the correlation
information to be used to improve forecasting performance. An algorithm is developed to automatically select and
estimate the polynomial spline model and the ARIMA model through backfitting. This method is applied on a real-life data
set to forecast hourly electricity usage. The non-linear 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 and compared with several well-accepted models. The
results show the
performance of the proposed model is comparable with a long short-term memory deep learning model. |