Multivariate integer-valued time series with flexible autocovariances and their application to major hurricane counts

This paper examines a bivariate count time series with some curious statistical features: Saffir–Simpson Category 3 and stronger annual hurricane counts in the North Atlantic and eastern Pacific Ocean Basins. As land and ocean temperatures on our planet warm, an intense climatological debate has ari...

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Published in:The Annals of Applied Statistics
Main Authors: Livsey, James, Lund, Robert, Kechagias, Stefanos, Pipiras, Vladas
Format: Text
Language:English
Published: The Institute of Mathematical Statistics 2018
Subjects:
Online Access:https://projecteuclid.org/euclid.aoas/1520564478
https://doi.org/10.1214/17-AOAS1098
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spelling ftculeuclid:oai:CULeuclid:euclid.aoas/1520564478 2023-05-15T17:35:32+02:00 Multivariate integer-valued time series with flexible autocovariances and their application to major hurricane counts Livsey, James Lund, Robert Kechagias, Stefanos Pipiras, Vladas 2018-03 application/pdf https://projecteuclid.org/euclid.aoas/1520564478 https://doi.org/10.1214/17-AOAS1098 en eng The Institute of Mathematical Statistics 1932-6157 1941-7330 Copyright 2018 Institute of Mathematical Statistics Count time series hurricanes long-range dependence multivariate negative autocorrelation Poisson Text 2018 ftculeuclid https://doi.org/10.1214/17-AOAS1098 2018-10-06T13:08:43Z This paper examines a bivariate count time series with some curious statistical features: Saffir–Simpson Category 3 and stronger annual hurricane counts in the North Atlantic and eastern Pacific Ocean Basins. As land and ocean temperatures on our planet warm, an intense climatological debate has arisen over whether hurricanes are becoming more numerous, or whether the strengths of the individual storms are increasing. Recent literature concludes that an increase in hurricane counts occurred in the Atlantic Basin circa 1994. This increase persisted through 2012; moreover, the 1994–2012 period was one of relative inactivity in the eastern Pacific Basin. When Atlantic activity eased in 2013, heavy activity in the eastern Pacific Basin commenced. When examined statistically, a Poisson white noise model for the annual severe hurricane counts is difficult to resoundingly reject. Yet, decadal cycles (longer term dependence) in the hurricane counts is plausible. This paper takes a statistical look at the issue, developing a stationary multivariate count time series model with Poisson marginal distributions and a flexible autocovariance structure. Our auto- and cross-correlations can be negative and have long-range dependence; features that most previous count models cannot achieve in tandem. Our model is new in the literature and is based on categorizing and super-positioning multivariate Gaussian time series. We derive the autocovariance function of the model and propose a method to estimate model parameters. In the end, we conclude that severe hurricane counts are indeed negatively correlated across the two ocean basins. Some evidence for long-range dependence is also presented; however, with only a 49-year record, this issue cannot be definitively judged without additional data. Text North Atlantic Project Euclid (Cornell University Library) Pacific The Annals of Applied Statistics 12 1
institution Open Polar
collection Project Euclid (Cornell University Library)
op_collection_id ftculeuclid
language English
topic Count time series
hurricanes
long-range dependence
multivariate
negative autocorrelation
Poisson
spellingShingle Count time series
hurricanes
long-range dependence
multivariate
negative autocorrelation
Poisson
Livsey, James
Lund, Robert
Kechagias, Stefanos
Pipiras, Vladas
Multivariate integer-valued time series with flexible autocovariances and their application to major hurricane counts
topic_facet Count time series
hurricanes
long-range dependence
multivariate
negative autocorrelation
Poisson
description This paper examines a bivariate count time series with some curious statistical features: Saffir–Simpson Category 3 and stronger annual hurricane counts in the North Atlantic and eastern Pacific Ocean Basins. As land and ocean temperatures on our planet warm, an intense climatological debate has arisen over whether hurricanes are becoming more numerous, or whether the strengths of the individual storms are increasing. Recent literature concludes that an increase in hurricane counts occurred in the Atlantic Basin circa 1994. This increase persisted through 2012; moreover, the 1994–2012 period was one of relative inactivity in the eastern Pacific Basin. When Atlantic activity eased in 2013, heavy activity in the eastern Pacific Basin commenced. When examined statistically, a Poisson white noise model for the annual severe hurricane counts is difficult to resoundingly reject. Yet, decadal cycles (longer term dependence) in the hurricane counts is plausible. This paper takes a statistical look at the issue, developing a stationary multivariate count time series model with Poisson marginal distributions and a flexible autocovariance structure. Our auto- and cross-correlations can be negative and have long-range dependence; features that most previous count models cannot achieve in tandem. Our model is new in the literature and is based on categorizing and super-positioning multivariate Gaussian time series. We derive the autocovariance function of the model and propose a method to estimate model parameters. In the end, we conclude that severe hurricane counts are indeed negatively correlated across the two ocean basins. Some evidence for long-range dependence is also presented; however, with only a 49-year record, this issue cannot be definitively judged without additional data.
format Text
author Livsey, James
Lund, Robert
Kechagias, Stefanos
Pipiras, Vladas
author_facet Livsey, James
Lund, Robert
Kechagias, Stefanos
Pipiras, Vladas
author_sort Livsey, James
title Multivariate integer-valued time series with flexible autocovariances and their application to major hurricane counts
title_short Multivariate integer-valued time series with flexible autocovariances and their application to major hurricane counts
title_full Multivariate integer-valued time series with flexible autocovariances and their application to major hurricane counts
title_fullStr Multivariate integer-valued time series with flexible autocovariances and their application to major hurricane counts
title_full_unstemmed Multivariate integer-valued time series with flexible autocovariances and their application to major hurricane counts
title_sort multivariate integer-valued time series with flexible autocovariances and their application to major hurricane counts
publisher The Institute of Mathematical Statistics
publishDate 2018
url https://projecteuclid.org/euclid.aoas/1520564478
https://doi.org/10.1214/17-AOAS1098
geographic Pacific
geographic_facet Pacific
genre North Atlantic
genre_facet North Atlantic
op_relation 1932-6157
1941-7330
op_rights Copyright 2018 Institute of Mathematical Statistics
op_doi https://doi.org/10.1214/17-AOAS1098
container_title The Annals of Applied Statistics
container_volume 12
container_issue 1
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