A time-reversed model selection approach to time series forecasting

In this paper, we introduce a novel model selection approach to time series forecasting. For linear stationary processes, such as AR processes, the direction of time is independent of the model parameters. By combining theoretical principles of time-reversibility in time series with conventional modeling approaches such as information criteria, we construct a criterion that employs the backwards prediction (backcast) as a proxy for the forecast. Hereby, we aim to adopt a theoretically grounded, data-driven approach to model selection. The novel criterion is named the backwards validated information criterion (BVIC). The BVIC identifies suitable models by trading off a measure of goodness-of-fit and a models ability to predict backwards. We test the performance of the BVIC by conducting experiments on synthetic and real data. In each experiment, the BVIC is examined in contrast to conventionally employed criteria. Our experimental results suggest that the BVIC has comparable performance as conventional information criteria. Specifically, in most of the experiments performed, we did not find statistically significant differences between the forecast error of the BVIC under certain parameterizations and that of the different information criteria. Nonetheless, it is worth emphasizing that the BVIC guarantees are established by design where the model order penalization term depends on strong mathematical properties of time-reversible time series forecasting properties and a finite data assessment. In particular, the penalization term is replaced by a weighted trade-off between functional dimensions pertaining to forecasting.That said, we observed that the BVIC recovered more accurately the real order of the underlying process than the other criteria, which rely on a static penalization of the model order. Lastly, leveraging the latter property we perform the assessment of the order model (or, memory) of time series pertaining to epileptic seizures recorded using electrocorticographic data. Our results provide converging evidence that the order of the model increases during the epileptic events.