Bivariate exponential and geometric autoregressive and autoregressive moving average models

1988 ◽  
Vol 20 (4) ◽  
pp. 798-821 ◽  
Author(s):  
H. W. Block ◽  
N. A. Langberg ◽  
D. S. Stoffer
Keyword(s):  
Moving Average ◽  
Real Data ◽  
Autoregressive Moving Average ◽  
Positive Dependence ◽  
Data Set ◽  
Associated Random Variables ◽  
Bivariate Exponential ◽  
Moving Average Models ◽  
Special Cases ◽  
Autoregressive Moving Average Models

We present autoregressive (AR) and autoregressive moving average (ARMA) processes with bivariate exponential (BE) and bivariate geometric (BG) distributions. The theory of positive dependence is used to show that in various cases, the BEAR, BGAR, BEARMA, and BGARMA models consist of associated random variables. We discuss special cases of the BEAR and BGAR processes in which the bivariate processes are stationary and have well-known bivariate exponential and geometric distributions. Finally, we fit a BEAR model to a real data set.

Bivariate exponential and geometric autoregressive and autoregressive moving average models

1988 ◽  
Vol 20 (04) ◽  
pp. 798-821
Author(s):  
H. W. Block ◽  
N. A. Langberg ◽  
D. S. Stoffer
Keyword(s):  
Moving Average ◽  
Real Data ◽  
Autoregressive Moving Average ◽  
Positive Dependence ◽  
Data Set ◽  
Associated Random Variables ◽  
Bivariate Exponential ◽  
Moving Average Models ◽  
Special Cases ◽  
Autoregressive Moving Average Models

We present autoregressive (AR) and autoregressive moving average (ARMA) processes with bivariate exponential (BE) and bivariate geometric (BG) distributions. The theory of positive dependence is used to show that in various cases, the BEAR, BGAR, BEARMA, and BGARMA models consist of associated random variables. We discuss special cases of the BEAR and BGAR processes in which the bivariate processes are stationary and have well-known bivariate exponential and geometric distributions. Finally, we fit a BEAR model to a real data set.

scholarly journals Multivariate geometric autoregressive and autoregressive moving average models

2021 ◽  
Vol 12 (2) ◽  
pp. 12-18
Author(s):  
S.M. Umar ◽  
S. Bala
Keyword(s):  
Autoregressive Model ◽  
Geometric Distribution ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Positive Dependence ◽  
Associated Random Variables ◽  
Moving Average Models ◽  
Multivariate Geometric Distribution ◽  
Special Case ◽  
Autoregressive Moving Average Models

We present Autoregressive (AR) and autoregressive moving average (ARMA) processes with multivariate geometric (MG) distribution. The theory of positive dependence is used to show that in many cases, multivariate geometric autoregressive (MGAR) and multivariate autoregressive moving average (MGARMA) models consist of associated random variables. We also provide a special case of the multivariate geometric autoregressive model in which it is stationary and has multivariate geometric distribution.

Moving-average models with bivariate exponential and geometric distributions

1987 ◽  
Vol 24 (01) ◽  
pp. 48-61
Author(s):  
Naftali A. Langberg ◽  
David S. Stoffer
Keyword(s):  
Moving Average ◽  
Random Variables ◽  
Moment Inequalities ◽  
Random Vectors ◽  
Positive Dependence ◽  
Associated Random Variables ◽  
Bivariate Exponential ◽  
Moving Average Models ◽  
Joint Probabilities

Two classes of finite and infinite moving-average sequences of bivariate random vectors are considered. The first class has bivariate exponential marginals while the second class has bivariate geometric marginals. The theory of positive dependence is used to show that in various cases the two classes consist of associated random variables. Association is then applied to establish moment inequalities and to obtain approximations to some joint probabilities of the bivariate processes.

Moving-average models with bivariate exponential and geometric distributions

1987 ◽  
Vol 24 (1) ◽  
pp. 48-61 ◽  
Author(s):  
Naftali A. Langberg ◽  
David S. Stoffer
Keyword(s):  
Moving Average ◽  
Random Variables ◽  
Moment Inequalities ◽  
Random Vectors ◽  
Positive Dependence ◽  
Associated Random Variables ◽  
Bivariate Exponential ◽  
Moving Average Models ◽  
Joint Probabilities

Two classes of finite and infinite moving-average sequences of bivariate random vectors are considered. The first class has bivariate exponential marginals while the second class has bivariate geometric marginals. The theory of positive dependence is used to show that in various cases the two classes consist of associated random variables. Association is then applied to establish moment inequalities and to obtain approximations to some joint probabilities of the bivariate processes.

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