Some ARMA models for dependent sequences of poisson counts

McKenzie, E.

doi:10.2307/1427362

Cited by 256 publications

(147 citation statements)

References 17 publications

(23 reference statements)

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“…The class of integer-valued autoregressive processes denoted by INAR have been studied by many authors (e.g., Al-Osh and Alzaid, 1987;McKenzie, E., 1988, Brännäs, Hellström, 2001, Karlis, 2006. …”

Section: Methodsmentioning

confidence: 99%

Time series count data models: An empirical application to traffic accidents

Quddus

2008

Accident Analysis & Prevention

195

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Section: Methodsmentioning

confidence: 99%

Time series count data models: An empirical application to traffic accidents

Quddus

2008

Accident Analysis & Prevention

195

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“…the first-order integer autoregression (INAR(1)) model investigated by Al-Osh and Alzaid (1987) and McKenzie (1988). A brief account of the model is given here below.…”

Section: Time Series Models For Legal Abortions In Italymentioning

confidence: 99%

New Technologies and Statistics: Partners for Environmental Monitoring and City Sensing

Borga

Camporese

Iandelli

et al. 2014

Studies in Theoretical and Applied Statistics

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The agricultural investigation of the italian Parliament, published in 1884, also highlighted, especially in reports on individual territorial districts, the importance of chestnut in the italian mountains. Since the early twentieth century are available long time series collected by ISTAT (National Statistics Institute) data on surface and production of the chestnut and foreign trade of the chestnuts. Key words:Role of the chestnut, statistics, multifunctionality, agricultural policy Official statistics and role of the chestnutThe chestnut (Castanea sativa Miller) is the breadfruit and the tree of life that precedes and then accompanies the first man in history. Since Roman times, and even more in the Middle Ages and in Modern times, Italy is the european territory in which the chestnut spreads further contributing increasingly to the survival of the mountaineer.In the second half of the nineteenth century, the widespread presence of chestnut still identifies two particular social and economic situations: "The international poverty and the chestnut" portrays the role of the chestnuts in human nutrition in large parts of the Alps and the Apennines and "The civilization of the chestnut" photographs with a still of the customs, traditions, use of timber, fruit and use rules that govern the lives of many mountaineers from Piemonte to Veneto, from Lombardia to Calabria [1].The agricultural investigation of the italian Parliament, published in 1884-1886, also highlighted, especially in reports on individual territorial districts, the importance of chestnut in the italian mountains [2].Since the early twentieth century are available long time series collected by Ministry of Finance [3] and ISTAT (National Statistics Institute) [4, 5, 6] data on surface and production of the chestnut and foreign trade of the chestnuts.The examination of the many available statistical data to divide the evolution of italian chestnut by the unit to date in four historical periods.Adua Mario, Istituto Nazionale di Statistica (ISTAT), email: adua@istat.it 1951 1956 1961 1966 1971 1976 1981 1986 1991 1996 2001 Years The first period: "the autumn of the patriarch"The first period, from 1901 to 1950, "the autumn of the patriarch", is characterized by a general decrease in cultivation, however, maintains basically stable overall role of the italian mountain agro-forestry. In the early twentieth century, based on the conclusion of the Agricultural cadastre, it began the publishing of annual data of forestry; for 1910 it was estimated a total area in high forest of chestnut of 652 thousand hectares and a production of 607 thousand tons (Fig. 1). In 1911 it was observed the historical maximun of production: 830 thousand tons. In the thirties ISTAT (then Central Statistics Institute) [7] realizes the survey on the cultivation of chestnut in Italy -Years 1934. This survey is the picture sharper and more detailed on the role of the chestnut tree in the agricultural landscape and chestnuts in the diet. The survey shows a total area o...

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“…'s satisfying P [B s (β) = 1] = β and Z is a nonnegative integer-valued random variable (r.v.). Models based on thinning were first considered by McKenzie (1985) and have been elaborated on in subsequent papers by McKenzie (1986McKenzie ( , 1988, Alzaid (1987, 1988), Alzaid and Al-Osh (1988, 1990, 1993, Du and Li (1991), and Brännäs and Hall (2001) among other authors.…”

Section: Introductionmentioning

confidence: 99%

On the maximum of periodic integer-valued sequences with exponential type tails via max-semistable laws

Hall

Temido

2012

Journal of Statistical Planning and Inference

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In this work we study the limiting distribution of the maximum term of periodic integer-valued sequences with marginal distribution belonging to a particular class where the tail decays exponentially. This class does not belong to the domain of attraction of any max-stable distribution. Nevertheless, we prove that the limiting distribution is max-semistable when we consider the maximum of the first k n observations, for a suitable sequence {k n } increasing to infinity. We obtain an expression for calculating the extremal index of sequences satisfying certain local conditions similar to conditions D (m) (u n ), m ∈ N, defined by Chernick et al. (1991). We apply the results to a class of max-autoregressive sequences and a class of moving average models. The results generalize the ones obtained for the stationary case.

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Some ARMA models for dependent sequences of poisson counts

Cited by 256 publications

References 17 publications

Time series count data models: An empirical application to traffic accidents

Time series count data models: An empirical application to traffic accidents

New Technologies and Statistics: Partners for Environmental Monitoring and City Sensing

On the maximum of periodic integer-valued sequences with exponential type tails via max-semistable laws

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