Dimension Reduction in High Dimensional Multivariate Time Series Analysis
The vector autoregressive (VAR) and vector autoregressive moving average (VARMA) models have been widely used to model multivariate time series, because of their capability to represent the dynamic relationships among variables in a system and their usefulness in forecasting unknown future values. However, when the dimension is very high, the number of parameters often exceed the number of available observations, and it is impossible to estimate the parameters. A suitable solution is clearly needed. After introducing some existing methods, we will suggest the use of contemporal aggregation as a dimension reduction method, which is very natural and simple to use. We will compare our proposed method with other existing methods in terms of forecast accuracy through both simulations and empirical examples. The presentation is based on the invited talk at the 2017 ICSA Applied Statistics Symposium in Chicago.
KeywordsVARMA model Regularization Starma model Clustering High dimension Aggregation
The author wants to thank his PhD student, Zeda Li, who helped him develop software code for the analyses of many data sets in the presentation.
- Gehman, A.: The effects of spatial aggregation on spatial time series modeling and forecasting, PhD dissertation, Temple University (2015)Google Scholar
- Lütkepohl, H.: Forecasting contemporaneously aggregated vector ARMA processes. J. Bus. Econ. Stat. 2, 201–214 (1984)Google Scholar
- MacQueen, J.: Some methods for classification and analysis of multivariate observations. In: Cam, L.M., Neyman J. (eds.) Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 281–297. University of California Press (1967)Google Scholar
- Nicholson, W.B., Bien, J., Matteson, D.S.: High dimensional forecasting via interpretable vector autoregression, arXiv:1412.5250v3 [stat.ME] (2018)Google Scholar
- Song, S., Bickel, P.: Large vector autoregressions, arXiv: 1106.3915v1 [stat.ML] (2011)Google Scholar
- Stock, J.H., Watson, M.W.: Macroeconomic forecasting using diffusion index. J. Bus. Econ. Stat. 20, 1147–1162 (2002b)Google Scholar
- Tryon, R.C.: Cluster analysis: correlation profile and orthometric (factor) analysis for the isolation of unities in mind and personality. Edwards Brothers, Ann Arbor (1939)Google Scholar
- Tsay, R.S.: Multivariate Time Series Analysis with R and Financial Applications. Wiley, Hoboken (2013)Google Scholar