Abstract
This paper considers the mixture autoregressive panel (MARP) model. This model can capture the burst and multi-modal phenomenon in some panel data sets. It also enlarges the stationarity region of the traditional AR model. An estimation method based on the EM algorithm is proposed and the assumption required of the model is quite low. To illustrate the method, we fitted the MARP model to the gray-sided voles data. Another MARP model with less restriction is also proposed.
Highlights
Panel time series data are collections of similar time series variables
We develop an estimation method based on the EM algorithm
If we study equation (2.2) closely, we will find that the mixture autoregressive panel (MARP) model is a mixture of N Gaussian AR models for each of the series
Summary
Panel time series data are collections of similar time series variables. A general linear dynamic model for a panel time series {Xjt}, j = 1, . . . , M , t = 1, . . . , Tj is given by p. Hjellvik and Tjφstheim (1999) treated the common factor ηt in model (1.1) as nuisance parameters and estimated them by averaging the observations across all the series at fixed time point t. Jin and Li (2005) considered the modeling of a contemporaneously correlated panel data with partial linear regression model These papers partly solved the problem of change points, nonlinearity and intercorrelation. Wong and Li (2000) extended GMTD model to time series analysis and suggested the mixture autoregressive model (MAR) to catch the multi-modal phenomena. Developing a mixture model to capture the multi-model characteristics in panel time series would be of importance. The gray-sided voles data are studied in section 4 as a real example of the application of our model.
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