A Perturbative Approach to Novelty Detection in Autoregressive Models
We propose a new method to perform novelty detection in dynamical systems governed by linear autoregressive models. The method extends information theoretic concepts recently introduced for i.i.d. data to the time-series scenario. It is based on a perturbative expansion whose leading term is the classical F-test, and whose O( 1 n) correction can be approximated as a function of the number of training points and the model order. We demonstrate on several synthetic examples that the first correction to the F-test can dramatically improve the control over the false positive rate of the system. We also test the approach on some real time series data, demonstrating that the method still retains a good accuracy in detecting novelties.