Self-Identification Deep Learning ARIMA

Abstract

The aspiration to predict the future values as close to the actual values as possible leads to the invention of time series models, the autoregressive integrated moving average (ARIMA) model which requires appropriate parameters of model identification, the ARIMA order, prior to fit coefficients of the models using the Box-Jenkins method. Statisticians for a decade identified the order via the sample autocorrelation function (ACF) and the sample partial autocorrelation function (PACF) which were very challenging for a human eye. To circumvent this issue, the recent model identification development uses a likelihood based-method that automatically generates orders and fits coefficients by varying the ARIMA order and pick the best one having the smallest Akaike information criterion (AIC) or Bayesian information criterion (BIC). The acquired ARIMA model may fail residual diagnostics. Consequently, this paper proposes the convolution neural network model, called the self-identification deep learning (SID) model, to automatically identify the ARIMA order via sample ACF/PACF. Accordingly, randomly simulated time series data with stationary and invertibility properties are generated by ARIMA model. Next, the time series data are converted into ACF/PACF graphs in order to feed into the SID model. The derived ARIMA order will be passed to determine the best fit coefficients of the ARIMA model via the Box-Jenkin methods for forecasting future values. The complete algorithm is called the self-identification deep learning ARIMA (SIDA) algorithm. The performance of identifying the ARIMA order from the SID model outperforms the likelihood based-method and ResNET50 which accepts the time series data directly in terms of precision, recall and F1-scores. Moreover, the SIDA algorithm applying to the real world dataset shows a better performance over the likelihood-based method via the mean absolute percentage error, the symmetric mean absolute percentage error, the mean absolute error and the root mean square error.