Kalman filter estimation for periodic autoregressive-moving average models

Jimenez, C.; McLeod, A. Ian; Hipel, Keith W.

doi:10.1007/bf01543862

Cited by 25 publications

(15 citation statements)

References 24 publications

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“…Each evaluation of the likelihood function involves very lengthy computations when s ≥ 12 (Vecchia, 1985a;Li and Hui, 1988;Jiménez, McLeod and Hipel, 1989 [ Figure 4 about here]…”

Section: Par Identificationmentioning

confidence: 99%

Diagnostic Checking of Periodic Autoregression Models With Application

McLeod

1994

Journal Time Series Analysis

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124

101

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Abstract. An overview of model building with periodic autoregression (PAR) models is given emphasizing the three stages of model development: identification, estimation and diagnostic checking. New results on the distribution of residual autocorrelations and suitable diagnostic checks are derived. The validity of these checks is demonstrated by simulation. The methodology discussed is illustrated with an application. It is pointed out that the PAR approach to model development offers some important advantages over the more general approach using periodic autoregressive moving-average (PARMA) models.I have written S functions for the periodic autoregressive modelling methods discussed in my paper. Complete S style documentation for each function is provided. To obtain, e-mail the following message: send pear from S to statlib@temper.stat.cmu.edu or use anonymous ftp to connect to fisher.stats.uwo.ca and download the shar archive file, pear.sh, located in the directory pub/pear.

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“…Each evaluation of the likelihood function involves very lengthy computations when s ≥ 12 (Vecchia, 1985a;Li and Hui, 1988;Jiménez, McLeod and Hipel, 1989 [ Figure 4 about here]…”

Section: Par Identificationmentioning

confidence: 99%

Diagnostic Checking of Periodic Autoregression Models With Application

McLeod

1994

Journal Time Series Analysis

Self Cite

124

101

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“…in which the matrix coefficients A T ,0 and A T ,1 (see [7, 18, p. 1932] for the expression of A T ,0 and A T ,1 ) are periodic with period S, such that pS is the least common multiple of p and S. From equation (4), which is equivalent to equation (1), one can easily verify that a necessary and sufficient causality condition for model (1) is that the eigenvalues of the matrix…”

Section: Periodic Stationarity Conditionsmentioning

confidence: 99%

“…Periodic linear time series models have been extensively used in recent years in a variety of theoretical and practical research fields, such as hydrology, economics, electrical engineering and many others [1][2][3][4][5][6][7][8][9][10]. The success of these models is due to their efficient representation of many stochastic phenomena exhibiting periodic autocorrelation structure that are not adequately explained by the classical SARIMA models.…”

Section: Introductionmentioning

confidence: 99%

Causality conditions and autocovariance calculations in PVAR models

Aknouche

2007

Journal of Statistical Computation and Simulation

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This paper studies the causality conditions and autocovariance calculations in periodic vector autoregressions. A state-space representation is exploited to extract a simple, necessary and sufficient condition for periodic stationarity, under which the autocovariances can be expressed in a simple but tractable form. The proposed methods compute the autocovariances for distinct seasons separately, thereby facilitating efficient computation for models with a large period.

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“…Pagano [11] and Salas et al. [14] studied moment estimation of PARMA models, Vecchia [17,18] and Jimenez et al [6] investigated maximum likelihood estimation of PARMA models. Basawa and Lund [3] derived the asymptotic properties of the weighted least squares estimates of PARMA models for periodic independent and identically distributed (i.i.d) mean zero noise, their results are an extension of those for periodic autoregressive (PAR) models in Pagano [11] and Troutman [16].…”

Section: Introductionmentioning

confidence: 99%