Fang Zheng, Dowe David L, Peiris Shelton, Rosadi Dedi
Department of Data Science and Artificial Intelligence, Monash University, Clayton, VIC 3800, Australia.
School of Mathematics and Statistics, University of Sydney, Camperdown, NSW 2006, Australia.
Entropy (Basel). 2021 Nov 29;23(12):1601. doi: 10.3390/e23121601.
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.
时间序列的建模与分析在包括经济学、工程学、环境科学和社会科学等应用领域中都很重要。在预测中选择具有准确参数的最佳时间序列模型，对科学家和学术研究人员来说是一个具有挑战性的目标。结合神经网络和传统自回归移动平均（ARMA）模型的混合模型正被用于提高时间序列建模和预测的准确性。现有的大多数时间序列模型是通过信息论方法来选择的，如AIC、BIC和HQ。本文重新审视了基于最小消息长度（MML）的模型选择技术，并研究了其在混合时间序列分析中的应用。MML是一种贝叶斯信息论方法，已被用于选择最佳的ARMA模型。我们利用长短期记忆（LSTM）方法构建了一个混合ARMA-LSTM模型，并表明在选择模型时，无论是在传统ARMA模型（无LSTM）还是混合ARMA-LSTM模型中，MML的表现都优于AIC、BIC和HQ。这些结果在我们所考虑的模拟数据和实际数据集上均成立。我们还开发了一个简单的MML ARIMA模型。
