AR and ARMA model order selection for time-series modeling with ImageNet classification

Abstract

We propose model order selection methods for autoregressive (AR) and autoregressive moving average (ARMA) time-series modeling based on ImageNet classifications with a 2-dimensional convolutional neural network (2-D CNN). We designed two models for two realistic scenarios: (1) a general model which emulates the scenario that validation and test datasets do not necessarily have the same dynamics as the training data, (2) a specific model which emulates the opposite scenario—the validation and test datasets share the dynamics of the training data. The results were compared to those of both Akaike Information criterion (AIC) and Bayesian Information criterion (BIC). Using simulation examples, we trained 2-D CNN-based Inception-v3 and ResNet50-v2 models for either AR or ARMA order selection for each of the two scenarios. The proposed ResNet50-v2 to use both time-frequency and the original time series data outperformed AIC and BIC for all scenarios. For the general model, the average of relative error reduction (ARER) when compared to the BIC method in the clean and three noisy environments was 19.07% (±14.22%) for the AR order for an AR process, and 5.67% (±2.83%) for the ARMA order for an ARMA process. The ARERs significantly improved to 73.92% (±30.95%) and 65.58% (±38.61%) for the AR and ARMA models, respectively, for the specific model scenario.