Abstract
Modeling and analysis of time series are important in applications including economics, engineering, environmental science and social science. Selecting the best time series model with accurate parameters in forecasting is a challenging objective for scientists and academic researchers. Hybrid models combining neural networks and traditional Autoregressive Moving Average (ARMA) models are being used to improve the accuracy of modeling and forecasting time series. Most of the existing time series models are selected by information-theoretic approaches, such as AIC, BIC, and HQ. This paper revisits a model selection technique based on Minimum Message Length (MML) and investigates its use in hybrid time series analysis. MML is a Bayesian information-theoretic approach and has been used in selecting the best ARMA model. We utilize the long short-term memory (LSTM) approach to construct a hybrid ARMA-LSTM model and show that MML performs better than AIC, BIC, and HQ in selecting the model—both in the traditional ARMA models (without LSTM) and with hybrid ARMA-LSTM models. These results held on simulated data and both real-world datasets that we considered.We also develop a simple MML ARIMA model.
Highlights
Forecasting in time series is a difficult task due to the presence of trends and/or seasonal components
We extended the traditional Autoregressive Moving Average model (ARMA) time series model to form the hybrid ARMA-LSTM by combining the neural network of long short-term memory (LSTM) in order to test the performance of Minimum Message Length (MML) in model selection
We compare the ARMA-LSTM selected by MML with the ARMA model selected by MML. These results show that MML outperforms when compared to Akaike Information Criterion (AIC) [20], Bayesian information criterion (BIC) [20], and HQ [21] in terms of selecting a model with lower prediction error, and this holds whether our modeling is enhanced by LSTM or instead is ARMA unassisted by LSTM
Summary
Forecasting in time series is a difficult task due to the presence of trends and/or seasonal components. We extended the traditional ARMA time series model to form the hybrid ARMA-LSTM by combining the neural network of long short-term memory (LSTM) in order to test the performance of MML in model selection. The ARMA model was introduced by Box and Jenkins in 1976 [13], and it is popular and widely used in the time series science community and provides accurate forecasts in both in-sample and out-of-sample data when the parameters are correctly estimated [14] It is a hybrid (or mixture) of autoregressive (AR) and moving average (MA) processes, but the ARMA model can only be used in stationary time series [15]. The Bayesian information-theoretic MML principle provides more reliable and highly accurate results in the model selection of the hybrid ARMA-LSTM model than other traditional methods (AIC, BIC, HQ).
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