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Abstract:
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For the Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of models. First, estimating the parameters of a time series model can be difficult with sampling-based approaches when the model's likelihood is intractable and/or when the data set being used is large. Second, once samples from a parameter posterior are obtained on a fixed window of data, it is not clear how they will be used to generate forecasts, nor is it clear how, and in what sense, they will be "updated" as interest shifts to newer posteriors as new data arrive. This paper provides an applied analysis of financial returns data using a well-established stochastic volatility model with several forecasting algorithms. Its principal aim is to provide guidance on how to tune different algorithms, how to quantify the uncertainty of different scoring measures, and to describe a variety of pitfalls with each approach.
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