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Large deviations for posterior distributions on the parameter of a multivariate \(\mathrm{AR}(p)\) process. (English) Zbl 1273.62216

Summary: We prove the large deviation principle for the posterior distributions on the (unknown) parameter of a multivariate autoregressive process with i.i.d. normal innovations. As a particular case, we recover a previous result for univariate first-order autoregressive processes. We also show that the rate function can be expressed in terms of the divergence between two spectral densities.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60F10 Large deviations
62F15 Bayesian inference
62M15 Inference from stochastic processes and spectral analysis
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