Bayesian Forecasting of Vector Moving Average Processes | ||
| The Egyptian Statistical Journal | ||
| Article 6, Volume 59, Issue 1, June 2015, Pages 68-89 PDF (21.38 M) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/esju.2015.314457 | ||
| Author | ||
| Sherif S.Ali | ||
| Cairo university, Egypt | ||
| Abstract | ||
| Forecasting is the final and one of the most important phases of a multivariate time series analysis. This article develops an approximate Bayesian methodology to forecast the future observations of vector moving average processes. By employing an approximate conditional likelihood and a matrix normal-Wishart, or Jeffreys vague prior, the proposed Bayesian forecasting methodology is based on deriving an approximate posterior probability density of the future observations in a convenient form. Then one may easily calculate the posterior mean vector and precision of the future vector of observations and hence develops a Highest Predictive Density (HPD) region for the future observations. Four simulation studies, with Jeffreys' vague prior, have been conducted in order to demonstrate the idea of the proposed methodology and test its adequacy in solving the forecasting problems of vector moving average processes. The numerical results show that the proposed methodology can efficiently forecast the vector moving average processes with high precision for moderate and large time series length. | ||
| Keywords | ||
| Forecasting; Vector Moving Average Processes; Likelihood Function; Matrix Normal; Wishart Distribution; Predictive Density | ||
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