A new autoregressive time series model in exponential variables (NEAR(1))

1981 ◽  
Vol 13 (4) ◽  
pp. 826-845 ◽  
Author(s):  
A. J. Lawrance ◽  
P. A. W. Lewis
Keyword(s):  
Time Series ◽  
Autoregressive Model ◽  
Marginal Distribution ◽  
Sample Path ◽  
Cross Coupling ◽  
Time Series Model ◽  
Autoregressive Time Series ◽  
First Order ◽  
Joint Distributions ◽  
Two Parameter

A new time series model for exponential variables having first-order autoregressive structure is presented. Unlike the recently studied standard autoregressive model in exponential variables (ear(1)), runs of constantly scaled values are avoidable, and the two parameter structure allows some adjustment of directional effects in sample path behaviour. The model is further developed by the use of cross-coupling and antithetic ideas to allow negative dependency. Joint distributions and autocorrelations are investigated. A transformed version of the model has a uniform marginal distribution and its correlation and regression structures are also obtained. Estimation aspects of the models are briefly considered.

A new autoregressive time series model in exponential variables (NEAR(1))

1981 ◽  
Vol 13 (04) ◽  
pp. 826-845 ◽  
Author(s):  
A. J. Lawrance ◽  
P. A. W. Lewis
Keyword(s):  
Time Series ◽  
Autoregressive Model ◽  
Marginal Distribution ◽  
Sample Path ◽  
Cross Coupling ◽  
Time Series Model ◽  
Autoregressive Time Series ◽  
First Order ◽  
Joint Distributions ◽  
Two Parameter

A new time series model for exponential variables having first-order autoregressive structure is presented. Unlike the recently studied standard autoregressive model in exponential variables (ear(1)), runs of constantly scaled values are avoidable, and the two parameter structure allows some adjustment of directional effects in sample path behaviour. The model is further developed by the use of cross-coupling and antithetic ideas to allow negative dependency. Joint distributions and autocorrelations are investigated. A transformed version of the model has a uniform marginal distribution and its correlation and regression structures are also obtained. Estimation aspects of the models are briefly considered.

First-order autoregressive models for gamma and exponential processes

1990 ◽  
Vol 27 (2) ◽  
pp. 325-332 ◽  
Author(s):  
C. H. Sim
Keyword(s):  
Laplace Transform ◽  
Autoregressive Model ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Higher Order ◽  
Gamma Process ◽  
Correlation Structure ◽  
First Order ◽  
Joint Distributions ◽  
Two Parameter

In this paper we propose an autoregressive representation for a particular type of stationary Gamma(θ–1, v) process whose n-dimensional joint distributions have Laplace transform |In + θSnVn|–v, where Sn = diag(s1, · ··, sn), Vn is an n × n positive definite matrix with elements υ ij = p|i–j|i2, i, j = 1, ···, n and p is the lag-1 autocorrelation of the gamma process. We also generalize the two-parameter NEAR(1) model of Lawrance and Lewis (1981) to an exponential first-order autoregressive model with three parameters. The correlation structure and higher-order properties of the two proposed models are also given.

A Bivariate First-Order Autoregressive Time Series Model in Exponential Variables (BEAR(1))

1989 ◽  
Vol 35 (10) ◽  
pp. 1236-1246 ◽  
Author(s):  
Lee S. Dewald ◽  
Peter A. W. Lewis ◽  
Ed McKenzie
Keyword(s):  
Time Series ◽  
Time Series Model ◽  
Autoregressive Time Series ◽  
First Order

First-order autoregressive models for gamma and exponential processes

1990 ◽  
Vol 27 (02) ◽  
pp. 325-332 ◽  
Author(s):  
C. H. Sim
Keyword(s):  
Laplace Transform ◽  
Autoregressive Model ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Higher Order ◽  
Gamma Process ◽  
Correlation Structure ◽  
First Order ◽  
Joint Distributions ◽  
Two Parameter

In this paper we propose an autoregressive representation for a particular type of stationary Gamma(θ –1, v) process whose n-dimensional joint distributions have Laplace transform |In + θSnVn | –v , where Sn = diag(s 1, · ··, sn ), Vn is an n × n positive definite matrix with elements υ ij = p|i–j|i 2, i, j = 1, ···, n and p is the lag-1 autocorrelation of the gamma process. We also generalize the two-parameter NEAR(1) model of Lawrance and Lewis (1981) to an exponential first-order autoregressive model with three parameters. The correlation structure and higher-order properties of the two proposed models are also given.

scholarly journals Modeling a nonlinear process using the exponential autoregressive time series model

2018 ◽  
Vol 95 (3) ◽  
pp. 2079-2092 ◽  
Author(s):  
Huan Xu ◽  
Feng Ding ◽  
Erfu Yang
Keyword(s):  
Time Series ◽  
Nonlinear Process ◽  
Time Series Model ◽  
Autoregressive Time Series
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