Semiparametric estimation and forecasting for functional-coefficient autoregressive models.




Patrick, Joshua D. (Joshua Daniel).

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The functional-coefficient autoregressive (FCAR) model is a useful structure for reducing the size of the class of nonlinear time series models. Local linear regression has been shown to be an effective method for estimating the coefficient functions of these models. However, local linear regression suffers from the "curse of dimensionality" for high order models. We adapt a spline-backfitted kernel (SBK) method for estimating the coefficient functions. The SBK estimators are computationally expedient and theoretically reliable. We show the SBK estimator performs better than local linear regression in root mean square error through simulation results. Three forecasting methods for FCAR models have been examined in the literature after fitting the model with local linear regression. We adapt the three methods to the SBK estimators. We also examine methods for constructing prediction intervals for the forecasts. The performance of the three forecasting methods and the prediction intervals are compared through simulation results. Utility scale photovoltaic (PV) plants are becoming economically viable. Utility companies are interested in forecasting the short-term and long-term power generated from a PV plant. The power generated by the plant is correlated with the irradiance measured from the sun. We develop a spatio-temporal model for irradiance measurements from a 1.2 MW PV plant located in Lanai, Hawaii. We use the SBK method for estimating the time component of the model. We assume a separable covariance structure and find evidence that this assumption does not hold.