Sensitivity of Response Spectra to ARMA Model Process

2008 ◽  
Author(s):  
Malek Brahimi ◽  
Sidi Berri
Keyword(s):  
Time Series ◽  
Sensitivity Analysis ◽  
Moving Average ◽  
Arma Model ◽  
Response Spectra ◽  
Envelope Function ◽  
Damage Effect ◽  
Autoregressive Moving Average ◽  
Response Data ◽  
The One

The sensitivity analysis in this study focuses on the sensitivity of response spectra to the number of peaks in the envelope function and the order of the Autoregressive Moving Average of order p, q (ARMA( p,q)) process used to represent an earthquake time series. Results consist of two sets of response spectra: one set corresponds to the one peak for envelope function and ARMA(2,1), the second set involves a change in the number of peaks assumed and the order p, q of fitted ARMA(2,1) models. For comparison purposes, response data were normalized by dividing all spectral ordinates by the corresponding ordinates for the one peak, ARMA(2,1) models for the same earthquake. It was conclude that, models of order (2,1) are sufficient to estimate the damage effect of an earthquake with relatively few parameters.

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.

Generation of 10-day flow of the Brahmaputra River using a time series model

2012 ◽  
Vol 44 (6) ◽  
pp. 1071-1083 ◽  
Author(s):  
M. Shahjahan Mondal ◽  
Jahir Uddin Chowdhury
Keyword(s):  
Time Series ◽  
River Flow ◽  
Model Building ◽  
Moving Average ◽  
Arma Model ◽  
Autoregressive Moving Average ◽  
Brahmaputra River ◽  
Negative Power ◽  
Diagnostic Checking ◽  
Autoregressive Parameter

Time series models are used in hydrology for the generation of river flow data. The development of such a model, namely deseasonalized Autoregressive Moving Average (ARMA), for the generation of 10-day flows of the Brahmaputra River in Bangladesh is described. The model was fitted following systematic stages of identification, estimation and diagnostic checking of model building. A negative power transformation for the Brahmaputra flow was found to be necessary for model construction. The seasonality of the flow was removed by Fourier analysis using five harmonics for 10-day means and 13 harmonics for standard deviations. The fitted model was ARMA (1, 3) having one autoregressive parameter and three moving average parameters. The validation forecasts made with the model indicated that the deseasonalized ARMA model could capture the 10-day variability of the Brahmaputra flow reasonably well. To further validate and verify the model 200 synthetic flow sequences, each with a length of 50 years, were generated. The fitted ARMA model was found to be capable of preserving both short-term statistics (variance and autocorrelation) and long-term statistics (Hurst coefficient and rescaled adjusted range) of the historic Brahmaputra flow.

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.

Modeling of System Dynamics and Disturbance From Paper-Making Process Data

1976 ◽  
Vol 98 (2) ◽  
pp. 197-199 ◽  
Author(s):  
S. M. Pandit ◽  
T. N. Goh ◽  
S. M. Wu
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Estimation Procedure ◽  
Autoregressive Moving Average ◽  
Process Data ◽  
Paper Making ◽  
Response Data ◽  
On Line ◽  
Modeling Strategy ◽  
Input Response

A new method is described to simultaneously model the dynamics and disturbance for a paper-making process from a set of on-line step input response data. The response is decomposed into two parts — a deterministic part represented by the response of an nth order linear system, and a stochastic part characterized by an Autoregressive Moving Average time series model. The differential equations representing the dynamics of the noise are also obtained and discussed. A general modeling strategy and estimation procedure for arbitrary inputs and unkown deal-time is outlined.

scholarly journals Autocovariance and autocorrelation structures of the generalised autoregressive moving average (GARMA(1,3;δ,1)) model

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Suguneswary Ellappan ◽  
Norhashidah Awang ◽  
Thulasyammal Ramiah Pillai
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Moving Average ◽  
Arma Model ◽  
Series Data ◽  
Autoregressive Moving Average ◽  
Numerical Examples ◽  
New Class ◽  
Autocorrelation Structure ◽  
Special Case

Generalized ARMA (GARMA) model is a new class of model that has been introduced to reveal some unknown features of certain time series data. The objective of this paper is to derive the autocovariance and autocorrelation structure of GARMA(1,3;δ,1)  model in order to study the behaviour of the model. It is shown that the results of this model can be reduced to the autocovariance and autocorrelation of the standard ARMA model as well as a special case. Numerical examples are used to illustrate the behaviour of the autocovariance and autocorrelation at different δ values to show the various structures that the model can represent

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.

Throughput Bottleneck Prediction of Manufacturing Systems Using Time Series Analysis

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Lin Li ◽  
Qing Chang ◽  
Guoxian Xiao ◽  
Saumil Ambani
Keyword(s):  
Time Series ◽  
Production Line ◽  
Manufacturing Systems ◽  
Moving Average ◽  
Arma Model ◽  
Cost Effective ◽  
System Throughput ◽  
Autoregressive Moving Average ◽  
Production Improvement ◽  
Detection Schemes

Throughput bottlenecks define and constrain the productivity of a production line. The most cost-effective way to improve system throughput is to mitigate bottlenecks toward a balanced system. Most of the currently used bottleneck detection schemes found in literature utilize long-term analysis to identify the bottlenecks for a known period and ignore the operation dynamics leading to bottleneck shifts. This paper proposes a method for predicting the throughput bottlenecks of a production line using autoregressive moving average (ARMA) model. We consider the production blockage and starvation times of each station to be a time series used to predict throughput bottlenecks. It is realized that the blockage and starvation times of a production line are critical indicators reflecting the production system dynamics and its internal material flow. As the first attempt in literature for throughput bottleneck prediction, the results demonstrate that the ARMA model can accurately predict blockage and starvation information of each station and hence can accurately predict the system throughput bottleneck, which will lead to the most significant production improvement.

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