PERIODIC AUTOREGRESSIVE‐MOVING AVERAGE (PARMA) MODELING WITH APPLICATIONS TO WATER RESOURCES<sup>1</sup>

Vecchia, Aldo V.

doi:10.1111/j.1752-1688.1985.tb00167.x

Cited by 163 publications

(125 citation statements)

References 11 publications

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“…Since their introduction by Bennett (1958) and Gladyshev (1961Gladyshev ( , 1963) much attention has been given to periodically correlated (or ciclostationary) processes, partially because of their wide applicability to hydrology (Vecchia 1985, Salas 1993 It is worth to mention that all references given in the previous paragraph deal with the case of continuous-valued (i.e. conventional) periodically correlated processes.…”

Section: Introductionmentioning

confidence: 99%

Integer-valued autoregressive processes with periodic structure

Monteiro

Scotto

Pereira

2010

Journal of Statistical Planning and Inference

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In this paper the periodic integer-valued autoregressive model of order one with period T , driven by a periodic sequence of independent Poisson-distributed random variables, is studied in some detail. Basic probabilistic and statistical properties of this model are discussed.Moreover, parameter estimation is also addressed. Specifically, the methods of estimation under analysis are the method of moments, least squares-type and likelihood-based ones.Their performance is compared through a simulation study.

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Section: Introductionmentioning

confidence: 99%

Integer-valued autoregressive processes with periodic structure

Monteiro

Scotto

Pereira

2010

Journal of Statistical Planning and Inference

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“…Such models have been advocated by Vecchia, A.V. (1985aVecchia, A.V. ( , 1985b and others but some drawbacks to their use in actual applications are discussed in §2-5.…”

Section: Introductionmentioning

confidence: 99%

Diagnostic Checking of Periodic Autoregression Models With Application

McLeod

1994

Journal Time Series Analysis

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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“…Assim, modelos autorregressivos periódicos (PAR) são frequentemente adotados para representar esta característica (Vechia, 1985). O modelo PAR(p m ) para a série padronizada z t(r,m) > 0, r = 1, .…”

Section: O Modelos Par(p M )unclassified

Análise do erro de previsão de vazões mensais com diferentes horizontes de previsão

Andrade

Reis

Soares

et al. 2012

Sba Controle & Automação

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Analysis of Forecast Error of Monthly Streamflow with Different Forecast HorizonsThis paper addresses the problem of forecasting for monthly mean streamflow series, in which we call the forecast horizon (h), the interval of time between the last observation used in fitting the model prediction and the future value being predicted. The analysis of the forecast error is made on the basis of the forecast horizon. These series have a periodic behavior on average, ariance and autocorrelation function. Therefore, we consider the widely used approach to modeling these series that initially consists of removing the periodicity in mean and variance of the streamflow series and then calculating a standardized series for which stochastic models are adjusted. In this study we consider the series to the standard periodic autoregressive models PAR (p m ). Orders p m of the adjusted models for each month are determined from the analysis of periodic partial autocorrelation function (PePACF), using the Bayesian Information Criterion (BIC) applied to PAR models, proposed in (MecLeod, 1994) and analysis of PePACF proposed in (Stedinger, 2001). The forecast errors are calculated on the basis of parameters adjusted and evaluated for forecasting horizons h, ranging from 1 to 12 months on the RESUMOEste trabalho aborda o problema de previsão para séries de vazões médias mensais, no qual denomina-se de horizonte de previsão (h), o intervalo de tempo que separa a última observação usada no ajuste do modelo de previsão e o valor futuro a ser previsto. A análise do erro de previsão é feita em função deste horizonte de previsão. Estas séries possuem um comportamento periódico na média, na variância e na função de autocorrelação. Portanto, considera-se a abordagem amplamente usada para a modelagem destas séries que consiste inicialmente em remover a periodicidade na média e na variância das séries de vazões e em seguida calcular uma série padronizada para a qual são ajustados modelos estocásticos. Neste estudo considera-se para a série padronizada os modelos autorregressivos periódicos PAR(p m ). As ordens p m dos modelos ajustados para cada mês são determinadas usando os seguintes critérios: a análise clássica da função de autocorrelação parcial periódica (FACPPe); usando-se o Bayesian

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PERIODIC AUTOREGRESSIVE‐MOVING AVERAGE (PARMA) MODELING WITH APPLICATIONS TO WATER RESOURCES¹

Cited by 163 publications

References 11 publications

Integer-valued autoregressive processes with periodic structure

Integer-valued autoregressive processes with periodic structure

Diagnostic Checking of Periodic Autoregression Models With Application

Análise do erro de previsão de vazões mensais com diferentes horizontes de previsão

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PERIODIC AUTOREGRESSIVE‐MOVING AVERAGE (PARMA) MODELING WITH APPLICATIONS TO WATER RESOURCES1

Cited by 163 publications

References 11 publications

Integer-valued autoregressive processes with periodic structure

Integer-valued autoregressive processes with periodic structure

Diagnostic Checking of Periodic Autoregression Models With Application

Análise do erro de previsão de vazões mensais com diferentes horizontes de previsão

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PERIODIC AUTOREGRESSIVE‐MOVING AVERAGE (PARMA) MODELING WITH APPLICATIONS TO WATER RESOURCES¹