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.

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.

On-Line Structural Damage Feature Extraction Based on Autoregressive Statistical Pattern of Time Series

2014 ◽  
Author(s):  
Ming-Hui Hu ◽  
Shan-Tung Tu ◽  
Fu-Zhen Xuan ◽  
Zheng-Dong Wang
Keyword(s):  
Time Series ◽  
Feature Extraction ◽  
Structural Damage ◽  
Power Plants ◽  
Damage Identification ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Statistical Pattern ◽  
On Line ◽  
The Relationship

The main aim of this paper is to demonstrate an autoregressive statistical pattern analysis method for the on-line structural health monitoring based on the damage feature extraction. The strain signals obtained from sensors are modeled as autoregressive moving average (ARMA) time series to extract the damage sensitive features (DSF) to monitor the variations of the selected features. One algebra combination of the first three AR coefficients is defined as damage sensitive feature. Using simple theory of polynomial roots, the relationship between the first three AR coefficient and the roots of the characteristic equation of the transfer function is deduced. Structural damage detection is conducted by comparing the DSF values of the inspected structure. The corresponding damage identification experiment was investigated in X12CrMoWVNbN steel commonly used for rotor of steam turbine in power plants. The feasibility and validity of the proposed method are shown.

Intervention Modeling

2017 ◽  
Author(s):  
Richard McCleary ◽  
David McDowall ◽  
Bradley J. Bartos
Keyword(s):  
Time Series ◽  
Autocorrelation Function ◽  
Moving Average ◽  
Intervention Model ◽  
Noise Component ◽  
Autoregressive Integrated Moving Average ◽  
Noise Function ◽  
Modeling Strategy ◽  
The Impact ◽  
True Structure

The general AutoRegressive Integrated Moving Average (ARIMA) model can be written as the sum of noise and exogenous components. If an exogenous impact is trivially small, the noise component can be identified with the conventional modeling strategy. If the impact is nontrivial or unknown, the sample AutoCorrelation Function (ACF) will be distorted in unknown ways. Although this problem can be solved most simply when the outcome of interest time series is long and well-behaved, these time series are unfortunately uncommon. The preferred alternative requires that the structure of the intervention is known, allowing the noise function to be identified from the residualized time series. Although few substantive theories specify the “true” structure of the intervention, most specify the dichotomous onset and duration of an impact. Chapter 5 describes this strategy for building an ARIMA intervention model and demonstrates its application to example interventions with abrupt and permanent, gradually accruing, gradually decaying, and complex impacts.

scholarly journals The time series regression analysis in evaluating the economic impact of COVID-19 cases in Indonesia

2021 ◽  
Vol 16 (3) ◽  
pp. 197-210
Author(s):  
Utriweni Mukhaiyar ◽  
Devina Widyanti ◽  
Sandy Vantika
Keyword(s):  
Time Series ◽  
Exchange Rate ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Transfer Function Model ◽  
Function Model ◽  
Time Series Regression ◽  
Vector Autoregressive ◽  
Daily Data ◽  
The Impact

This study aims to determine the impact of COVID-19 cases in Indonesia on the USD/IDR exchange rate using the Transfer Function Model and Vector Autoregressive Moving-Average with Exogenous Regressors (VARMAX) Model. This paper uses daily data on the COVID-19 case in Indonesia, the USD/IDR exchange rate, and the IDX Composite period from 1 March to 29 June 2020. The analysis shows: (1) the higher the increase of the number of COVID-19 cases in Indonesia will significantly weaken the USD/IDR exchange rate, (2) an increase of 1% in the number of COVID-19 cases in Indonesia six days ago will weaken the USD/IDR exchange rate by 0.003%, (3) an increase of 1% in the number of COVID-19 cases in Indonesia seven days ago will weaken the USD/IDR exchange rate by 0.17%, and (4) an increase of 1% in the number of COVID-19 cases in Indonesia eight days ago will weaken the USD/IDR exchange rate by 0.24%.

ARMA processes have maximal entropy among time series with prescribed autocovariances and impulse responses

1985 ◽  
Vol 17 (04) ◽  
pp. 810-840 ◽  
Author(s):  
Jürgen Franke
Keyword(s):  
Time Series ◽  
Impulse Response ◽  
Moving Average ◽  
Autoregressive Process ◽  
Natural Generalization ◽  
Maximal Entropy ◽  
Autoregressive Moving Average ◽  
Moving Average Process ◽  
Arma Process ◽  
Arma Processes

The maximum-entropy approach to the estimation of the spectral density of a time series has become quite popular during the last decade. It is closely related to the fact that an autoregressive process of order p has maximal entropy among all time series sharing the same autocovariances up to lag p. We give a natural generalization of this result by proving that a mixed autoregressive-moving-average process (ARMA process) of order (p, q) has maximal entropy among all time series sharing the same autocovariances up to lag p and the same impulse response coefficients up to lag q. The latter may be estimated from a finite record of the time series, for example by using a method proposed by Bhansali (1976). By the way, we give a result on the existence of ARMA processes with prescribed autocovariances up to lag p and impulse response coefficients up to lag q.

scholarly journals Estimation for Nonnegative Lévy-Driven Ornstein-Uhlenbeck Processes

2007 ◽  
Vol 44 (04) ◽  
pp. 977-989 ◽  
Author(s):  
Peter J. Brockwell ◽  
Richard A. Davis ◽  
Yu Yang
Keyword(s):  
Continuous Time ◽  
Lévy Process ◽  
Moving Average ◽  
Asymptotic Properties ◽  
Estimation Procedure ◽  
Financial Econometrics ◽  
Levy Process ◽  
Efficient Estimation ◽  
Autoregressive Moving Average ◽  
Continuous Time Processes

Continuous-time autoregressive moving average (CARMA) processes with a nonnegative kernel and driven by a nondecreasing Lévy process constitute a very general class of stationary, nonnegative continuous-time processes. In financial econometrics a stationary Ornstein-Uhlenbeck (or CAR(1)) process, driven by a nondecreasing Lévy process, was introduced by Barndorff-Nielsen and Shephard (2001) as a model for stochastic volatility to allow for a wide variety of possible marginal distributions and the possibility of jumps. For such processes, we take advantage of the nonnegativity of the increments of the driving Lévy process to study the properties of a highly efficient estimation procedure for the parameters when observations are available of the CAR(1) process at uniformly spaced times 0,h,…,Nh. We also show how to reconstruct the background driving Lévy process from a continuously observed realization of the process and use this result to estimate the increments of the Lévy process itself when h is small. Asymptotic properties of the coefficient estimator are derived and the results illustrated using a simulated gamma-driven Ornstein-Uhlenbeck process.

Continuous Autoregressive Moving Average Models

2021 ◽  
pp. 118-141
Author(s):  
Yakup Ari
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Discrete Time ◽  
Moving Average ◽  
Likelihood Estimation ◽  
Real Data ◽  
Autoregressive Moving Average ◽  
The Difference

The financial time series have a high frequency and the difference between their observations is not regular. Therefore, continuous models can be used instead of discrete-time series models. The purpose of this chapter is to define Lévy-driven continuous autoregressive moving average (CARMA) models and their applications. The CARMA model is an explicit solution to stochastic differential equations, and also, it is analogue to the discrete ARMA models. In order to form a basis for CARMA processes, the structures of discrete-time processes models are examined. Then stochastic differential equations, Lévy processes, compound Poisson processes, and variance gamma processes are defined. Finally, the parameter estimation of CARMA(2,1) is discussed as an example. The most common method for the parameter estimation of the CARMA process is the pseudo maximum likelihood estimation (PMLE) method by mapping the ARMA coefficients to the corresponding estimates of the CARMA coefficients. Furthermore, a simulation study and a real data application are given as examples.

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