A robust regression model for a first-order autoregressive time series with unequal spacing: application to water monitoring

Thirty fetuses were observed for 24 hours and one fetus was observed for 20 hours during the last 10 weeks of gestation. Observations were made of the amount of gross fetal body movement in each successive 5 minute observation epoch, thus resulting in 30 time series of 288 observations and one time series of 240 observations. Spectral analysis of these time series demonstrated the presence of significant power in the frequency range of 0.002 to 0.0175 cpm. Application of Box-Jenkins techniques to the time series resulted in the choice of a first-order auto-regression model to fit the data. It was concluded that the incidence of episodes of gross fetal body movements were non-random and were, in fact, pseudoperiodic.

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MARGINALS OF MULTIVARIATE FIRST-ORDER AUTOREGRESSIVE TIME SERIES MODELS

Journal of Time Series Analysis ◽

10.1111/j.1467-9892.1988.tb00456.x ◽

1988 ◽

Vol 9 (1) ◽

pp. 89-97 ◽

Cited By ~ 1

Author(s):

Antonie Stam ◽

Steven C. Hillmer

Keyword(s):

Time Series ◽

Time Series Models ◽

Autoregressive Time Series ◽

First Order

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

Advances in Applied Probability ◽

10.2307/1426975 ◽

1981 ◽

Vol 13 (4) ◽

pp. 826-845 ◽

Cited By ~ 78

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.

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Changes of Variance in First-Order Autoregressive Time Series Models-With an Application

Journal of the Royal Statistical Society Series C (Applied Statistics) ◽

10.2307/2347232 ◽

1976 ◽

Vol 25 (3) ◽

pp. 248 ◽

Cited By ~ 63

Author(s):

Dean W. Wichern ◽

Robert B. Miller ◽

Der-Ann Hsu

Keyword(s):

Time Series ◽

Time Series Models ◽

Autoregressive Time Series ◽

First Order

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NEAR-INTEGRATED RANDOM COEFFICIENT AUTOREGRESSIVE TIME SERIES

Econometric Theory ◽

10.1017/s0266466608080535 ◽

2008 ◽

Vol 24 (5) ◽

pp. 1343-1372 ◽

Cited By ~ 7

Author(s):

Alexander Aue

Keyword(s):

Time Series ◽

Serial Correlation ◽

Critical Value ◽

Random Coefficient ◽

Autoregressive Time Series ◽

Limiting Behavior ◽

First Order ◽

Finite Dimensional ◽

Serial Correlation Coefficient ◽

Random Coefficient Autoregressive

We determine the limiting behavior of near-integrated first-order random coefficient autoregressive RCA(1) time series. It is shown that the asymptotics of the finite-dimensional distributions crucially depends on how the critical value 1 is approached, which determines whether the process is near-stationary, has a unit root, or is mildly explosive. %In a second part, we derive the limit distribution of the serial correlation coefficient in the near stationary and the mildly explosive settings under very general conditions on the parameters. The results obtained are in accordance with those available for first-order autoregressive time series and can hence serve as an addition to existing literature in the area.

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