Localized mixture models for prediction with application

Abstract

This paper explores how localized mixture models can be used for prediction using time series data. The estimation method presented in this study is a kernel-weighted version of an EM-algorithm, where exponential kernels with different bandwidths are used as weight functions. Nadaraya–Watson and local linear estimators are used to carry out localized estimations. Furthermore, in order to demonstrate suitability for prediction at a future time point, a methodology for bandwidth selection and adequate methods are outlined for each model, and then compared with competing forecasting routines. A simulation study is executed to assess the performance of these models for prediction. Furthermore, real data is used to investigate the performance of the localized mixture models for prediction. The data used is predominately taken from the International Energy Agency (IEA).

Keywords:

• Localized mixture model
• EM-algorithm
• forecasting
• and bandwidth

Acknowledgments

I am grateful to Prof. Frank Coolen and Dr. Jochen Einbeck from the Department of Mathematical Sciences at Durham University. Both have been sincere in guiding me to develop this paper and in their suggestions and comments. I would also like to thank Prof. Guy Nason from the University of Bristol for his suggestions about forecasting approaches. His advice led me to develop new insights and conclusions from my results. This research was funded by the Deanship of Scientific Research at Princess Nourah bint Abdulrahman University through the Fast track research Funding Program.

Notes

1 International Energy Agency, available at: http://www.iea.org/.

2 All values shown in the tables are multiplied by 1,000.