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Title: Locally weighted mixture models for prediction from time series Authors:  Najla Qarmalah - Princess Norah bint Abdulrahman University (Saudi Arabia) [presenting]
Jochen Einbeck - Durham University (United Kingdom)
Frank Coolen - Durham University (UK)
Abstract: Locally weighted mixture models for time series data are introduced and used to obtain predictions based on the fitted models. Given data of the form $(t_{i}, y_{i})$,$i=1,...,T$, we suppose a mixture model with the $k-$th component as $y_{i}=m_{k}(t_{i})+\epsilon_{ik}$ with mixing proportion $\pi_{k}(t_{i})$, $k=1,...,K$ and $K$ is the number of components. The $m_{k}(t_{i})$ is a smooth unspecified regression function, and the error $\epsilon_{ik} \sim N(0,\sigma^{2})$ is independently distributed. Estimation of this model is achieved through a kernel-weighted version of the EM-algorithm, using exponential kernels with different bandwidths $h_k$ which have bigger effect on the forecast. By modelling a mixture of local regressions at a target quantity $t_T$ but with different bandwidths $h_k$, the estimated mixture probabilities are informative for the amount of information available in the data set at the scale of resolution corresponding to each bandwidth. Nadaraya-Watson and local linear estimators are used to carry out the localized estimation step. Based on the fitted model, several approaches for $m-$step-ahead predictions, $m=1$ and 2, at time $t_{T+m}$ are investigated. Real and simulated data are provided including data on energy use for Spain.