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A new Bayesian approach to quantile autoregressive time series model estimation and forecasting. (English) Zbl 1281.62184
Summary: This paper proposes a Bayesian approach to quantile autoregressive (QAR) time series model estimation and forecasting. We establish that the joint posterior distribution of the model parameters and future values is well defined. The associated Markov chain Monte Carlo algorithm for parameter estimation and forecasting converges to the posterior distribution quickly. We also present a combining forecasts technique to produce more accurate out-of-sample forecasts by using a weighted sequence of fitted QAR models. A moving window method to check the quality of the estimated conditional quantiles is developed. We verify our methodology using simulation studies and then apply it to currency exchange rate data. The results obtained show that an unequally weighted combining method performs better than other forecasting methodology.

MSC:
62M09 Non-Markovian processes: estimation
62F15 Bayesian inference
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M20 Inference from stochastic processes and prediction
62P20 Applications of statistics to economics
65C05 Monte Carlo methods
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