The estimation of autoregressive, moving average and mixed autoregressive moving average systems with time-dependent parameters of non-stationary time series

1976 ◽  
Vol 23 (5) ◽  
pp. 647-656 ◽  
Author(s):  
M. Y. HUSSAIN ◽  
T. SUBBA RAO
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Time Dependent ◽  
Stationary Time Series ◽  
Autoregressive Moving Average ◽  
Stationary Time

scholarly journals PERAMALAN LAJU INFLASI DENGAN METODE AUTO REGRESSIVE INTEGRATED MOVING AVERAGE (ARIMA)

2017 ◽  
Vol 14 (4) ◽  
pp. 524 ◽  
Author(s):  
Djawoto Djawoto
Keyword(s):  
Time Series ◽  
Price Index ◽  
Inflation Rate ◽  
Moving Average ◽  
Arima Model ◽  
Consumer Price Index ◽  
Stationary Time Series ◽  
Stationary Time ◽  
Auto Regressive ◽  
Auto Regression

Auto Regression Integrated Moving Average (ARIMA) or the combination model of Auto Regression with moving average, is a linier model which is able to represent the stationary time series or non stationary time series. The purpose of this research is to forecast the inflation rate in November 2010 with the Consumer Price Index (CPI) by using ARIMA. The inflation indicator is very important to anticipate in making the Government’s policy and decision as well as for the citizen is for the information to determine what to do in related with savings and investment. By looking at the existing criteria, it is determined that the best model is ARIMA (1,1,0) or AR (1). Model ARIMA (1,1,0), the coefficient value AR (1) is significant,which has the most minimum value of Akaike Info Criterion (AIC) and Schwars Criterion (SC) compare toARIMA (0,1,1) or MA (1) and ARIMA (1,1,1) or AR (1) MA (1). In summarize, the ARIMA model used to forecast the valueof IHK is ARIMA (1,1,0).

Stationary Time Series Models with Exponential Dispersion Model Margins

1998 ◽  
Vol 35 (01) ◽  
pp. 78-92 ◽  
Author(s):  
Bent Jørgensen ◽  
Peter Xue-Kun Song
Keyword(s):  
Time Series ◽  
Dispersion Model ◽  
Moving Average ◽  
Stationary Time Series ◽  
Autoregressive Moving Average ◽  
Infinitely Divisible ◽  
Finite Moment ◽  
Exponential Dispersion Model ◽  
Exponential Dispersion Models ◽  
Moving Average Processes

We consider a class of stationary infinite-order moving average processes with margins in the class of infinitely divisible exponential dispersion models. The processes are constructed by means of the thinning operation of Joe (1996), generalizing the binomial thinning used by McKenzie (1986, 1988) and Al-Osh and Alzaid (1987) for integer-valued time series. As a special case we obtain a class of autoregressive moving average processes that are different from the ARMA models proposed by Joe (1996). The range of possible marginal distributions for the new models is extensive and includes all infinitely divisible distributions with finite moment generating functions, hereunder many known discrete, continuous and mixed distributions.

Modeling and Predicting Non-Stationary Time Series

1997 ◽  
Vol 07 (08) ◽  
pp. 1823-1831 ◽  
Author(s):  
Liangyue Cao ◽  
Alistair Mees ◽  
Kevin Judd
Keyword(s):  
Time Series ◽  
Time Dependent ◽  
Stationary Time Series ◽  
Industrial System ◽  
Experimental Time ◽  
Stationary Time ◽  
Experimental Time Series ◽  
System States

Many experimental time series are non-stationary. Modeling and predicting them is generally considered to be difficult. In this paper we introduce time-dependent regressive (TDR) models, which depend not only on system states but also on time. We test artificial time series which come from parameter-changing systems and are therefore non-stationary, and a simulated experimental time series from a model of a non-stationary industrial system. The TDR models work well on those time series, not only in prediction but also in extraction of the underlying bifurcations.

scholarly journals PERAMALAN LAJU INFLASI DENGAN METODE AUTO REGRESSIVE INTEGRATED MOVING AVERAGE (ARIMA)

2018 ◽  
Vol 14 (4) ◽  
pp. 524-538
Author(s):  
Djawoto Djawoto
Keyword(s):  
Time Series ◽  
Price Index ◽  
Inflation Rate ◽  
Moving Average ◽  
Arima Model ◽  
Consumer Price Index ◽  
Stationary Time Series ◽  
Stationary Time ◽  
Auto Regressive ◽  
Auto Regression

Auto Regression Integrated Moving Average (ARIMA) or the combination model of Auto Regression with moving average, is a linier model which is able to represent the stationary time series or non stationary time series. The purpose of this research is to forecast the inflation rate in November 2010 with the Consumer Price Index (CPI) by using ARIMA. The inflation indicator is very important to anticipate in making the Government’s policy and decision as well as for the citizen is for the information to determine what to do in related with savings and investment. By looking at the existing criteria, it is determined that the best model is ARIMA (1,1,0) or AR (1). Model ARIMA (1,1,0), the coefficient value AR (1) is significant,which has the most minimum value of Akaike Info Criterion (AIC) and Schwars Criterion (SC) compare toARIMA (0,1,1) or MA (1) and ARIMA (1,1,1) or AR (1) MA (1). In summarize, the ARIMA model used to forecast the valueof IHK is ARIMA (1,1,0).

scholarly journals SACF of the Errors of Stationary Time Series Models in the Presence of a Large Additive Outlier

2021 ◽  
pp. 31-40
Author(s):  
R. Suresh
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Stationary Time Series ◽  
Time Series Models ◽  
White Noise Process ◽  
First Order ◽  
Stationary Time ◽  
Additive Outlier ◽  
Distributed Process ◽  
Limiting Behaviour

In this paper, the limiting behaviour of the Sample Autocorrelation Function(SACF) of the errors {et} of First-Order Autoregressive (AR(1)), First-Order Moving Average (MA(1)) and First Order Autoregressive First-Order Moving Average (ARMA(1,1)) stationary time series models in the presence of a large Additive Outlier(AO) is discussed. It is found that the errors which are supposed to be uncorrelated due to either white noise process or normally distributed process are not so in the presence of a large additive outlier. The SACF of the errors follows a particular pattern based on the time series model. In the case of AR(1) model, at lag 1, the contaminated errors {et} are correlated, whereas at higher lags, they are uncorrelated. But in the MA(1) and ARMA(1,1) models, the contaminated errors {et} are correlated at all the lags. Furthermore it is observed that the intensity of correlations depends on the parameters of the respective models.

Stationary Time Series Models with Exponential Dispersion Model Margins

1998 ◽  
Vol 35 (1) ◽  
pp. 78-92 ◽  
Author(s):  
Bent Jørgensen ◽  
Peter Xue-Kun Song
Keyword(s):  
Time Series ◽  
Dispersion Model ◽  
Moving Average ◽  
Stationary Time Series ◽  
Autoregressive Moving Average ◽  
Infinitely Divisible ◽  
Finite Moment ◽  
Exponential Dispersion Model ◽  
Exponential Dispersion Models ◽  
Moving Average Processes

We consider a class of stationary infinite-order moving average processes with margins in the class of infinitely divisible exponential dispersion models. The processes are constructed by means of the thinning operation of Joe (1996), generalizing the binomial thinning used by McKenzie (1986, 1988) and Al-Osh and Alzaid (1987) for integer-valued time series. As a special case we obtain a class of autoregressive moving average processes that are different from the ARMA models proposed by Joe (1996). The range of possible marginal distributions for the new models is extensive and includes all infinitely divisible distributions with finite moment generating functions, hereunder many known discrete, continuous and mixed distributions.

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