scholarly journals Characterizing and Forecasting Climate Indices Using Time Series Models

2021 ◽  
Author(s):  
Taesam Lee ◽  
Taha B.M.J. Ouarda ◽  
Ousmane Seidou
Keyword(s):  
Time Series ◽  
Great Lakes ◽  
Southern Oscillation ◽  
Moving Average ◽  
Low Frequency ◽  
Arma Model ◽  
Water Levels ◽  
Climate Indices ◽  
Autoregressive Moving Average ◽  
Time Series Models

Abstract The objective of the current study is to present a comparison of techniques for the forecasting of low frequency climate oscillation indices with a focus on the Great Lakes system. A number of time series models have been tested including the traditional Autoregressive Moving Average (ARMA) model, Dynamic Linear model (DLM), Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model, as well as the nonstationary oscillation resampling (NSOR) technique. These models were used to forecast the monthly El Niño-Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO) indices which show the most significant teleconnection with the net basin supply (NBS) of the Great Lakes system from a preliminary study. The overall objective is to predict future water levels, ice extent, and temperature, for planning and decision making purposes. The results showed that the DLM and GARCH models are superior for forecasting the monthly ENSO index, while the forecasted values from the traditional ARMA model presented a good agreement with the observed values within a short lead time ahead for the monthly PDO index.

scholarly journals A Fuzzy Set-Valued Autoregressive Moving Average Model and Its Applications

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 324 ◽  
Author(s):  
Dabuxilatu Wang ◽  
Liang Zhang
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Empirical Analysis ◽  
Moving Average ◽  
Arma Model ◽  
Autoregressive Moving Average ◽  
Complex Data ◽  
Arma Models ◽  
Linguistic Data ◽  
Series Analysis

Autoregressive moving average (ARMA) models are important in many fields and applications, although they are most widely applied in time series analysis. Expanding the ARMA models to the case of various complex data is arguably one of the more challenging problems in time series analysis and mathematical statistics. In this study, we extended the ARMA model to the case of linguistic data that can be modeled by some symmetric fuzzy sets, and where the relations between the linguistic data of the time series can be considered as the ordinary stochastic correlation rather than fuzzy logical relations. Therefore, the concepts of set-valued or interval-valued random variables can be employed, and the notions of Aumann expectation, Fréchet variance, and covariance, as well as standardized process, were used to construct the ARMA model. We firstly determined that the estimators from the least square estimation of the ARMA (1,1) model under some L2 distance between two sets are weakly consistent. Moreover, the justified linguistic data-valued ARMA model was applied to forecast the linguistic monthly Hang Seng Index (HSI) as an empirical analysis. The obtained results from the empirical analysis indicate that the accuracy of the prediction produced from the proposed model is better than that produced from the classical one-order, two-order, three-order autoregressive (AR(1), AR(2), AR(3)) models, as well as the (1,1)-order autoregressive moving average (ARMA(1,1)) model.

scholarly journals Minimum Message Length in Hybrid ARMA and LSTM Model Forecasting

2021 ◽  
Author(s):  
Zheng Fang ◽  
David L. Dowe ◽  
Shelton Peiris ◽  
Dedi Rosadi
Keyword(s):  
Time Series ◽  
Deep Learning ◽  
Short Term Memory ◽  
Moving Average ◽  
Arma Model ◽  
Autoregressive Moving Average ◽  
Information Theoretic ◽  
Minimum Message Length ◽  
Message Length ◽  
Long Short Term Memory

We investigate the power of time series analysis based on a variety of information-theoretic approaches from statistics (AIC, BIC) and machine learning (Minimum Message Length) - and we then compare their efficacy with traditional time series model and with hybrids involving deep learning. More specifically, we develop AIC, BIC and Minimum Message Length (MML) ARMA (autoregressive moving average) time series models - with this Bayesian information-theoretic MML ARMA modelling already being new work. We then study deep learning based algorithms in time series forecasting, using Long Short Term Memory (LSTM), and we then combine this with the ARMA modelling to produce a hybrid ARMA-LSTM prediction. Part of the purpose of the use of LSTM is to seek capture any hidden information in the residuals left from the traditional ARMA model. We show that MML not only outperforms earlier statistical approaches to ARMA modelling, but we further show that the hybrid MML ARMA-LSTM models outperform both ARMA models and LSTM models.

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