Kōsaku Takanashi, Kenichiro McAlinn
arXiv 20 Nov 2019 · Mathematics — Statistics Theory
arXiv:1911.08662 · PDF · DOI · OpenAlex · Extracted main text
We discuss the finite sample theoretical properties of online predictions in non-stationary time series under model misspecification. To analyze the theoretical predictive properties of statistical methods under this setting, we first define the Kullback-Leibler risk, in order to place the problem within a decision theoretic framework. Under this framework, we show that a specific class of dynamic models -- random walk dynamic linear models -- produce exact minimax predictive densities. We first show this result under Gaussian assumptions, then relax this assumption using semi-martingale processes. This result provides a theoretical baseline, under both non-stationary and stationary time series data, for which other models can be compared against. We extend the result to the synthesis of multiple predictive densities. Three topical applications in epidemiology, climatology, and economics, confirm and highlight our theoretical results.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | McAlinn, K. and M. West (2019) Dynamic bayesian predictive synthesis in time series forecasting self | 0.956 | 8 | 3 | 88% |
| 2 | Bernaciak, D. and J. E. Griffin (2022) A loss discounting framework for model averaging and selection in time series models | 0.644 | 2 | 2 | 100% |
| 3 | Liang, F. and A. Barron (2004) Exact minimax strategies for predictive density estimation, data compression, and model selection | 0.511 | 3 | 2 | 33% |
| 4 | West, M. and P. J. Harrison (1997) Bayesian Forecasting and Dynamic Models\/ (2nd ed.) | 0.511 | 2 | 2 | 50% |
| 5 | Genest, C. and M. J. Schervish (1985) Modelling expert judgements for Bayesian updating | 0.511 | 2 | 1 | 100% |
| 6 | West, M. and J. Crosse (1992) Modelling of probabilistic agent opinion | 0.511 | 2 | 1 | 100% |
| 7 | West, M (1992) Modelling agent forecast distributions | 0.511 | 2 | 1 | 100% |
| 8 | Aastveit, K. A., K. R. Gerdrup, A. S. Jore, and L. A. Thorsrud (2014) Nowcasting GDP in real time: A density combination approach | 0.405 | 1 | 1 | 100% |
| 9 | Cogley, T. and T. J. Sargent (2005) Drifts and volatilities: Monetary policies and outcomes in the post WWII U.S | 0.405 | 1 | 1 | 100% |
| 10 | Genre, V., G. Kenny, A. Meyler, and A. Timmermann (2013) Combining expert forecasts: Can anything beat the simple average? | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 37 scored citations.