TY - JOUR
T1 - Multivariate α-stable distributions
T2 - VAR(1) processes, measures of dependence and their estimations
AU - Karling, Maicon J.
AU - Lopes, Sílvia R.C.
AU - de Souza, Roberto M.
N1 - Funding Information:
M.J. Karling was supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) - Brazil ( 1736629 ) and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) - Brazil ( 170168/2018-2 ). S.R.C. Lopes’ research was partially supported by CNPq - Brazil ( 303453/2018-4 ).
Publisher Copyright:
© 2022 Elsevier Inc.
PY - 2023/5
Y1 - 2023/5
N2 - Measuring the dependency between lagged random vectors in time series is extremely important to detect appropriate models for fitting real data. Vector autoregressive processes (VAR), in particular, are among the most popular multivariate time series that allow modeling schemes for two or more random variables. However, if the series of innovations process does not have finite second-order moments, the classical analysis that uses the empirical auto-covariance function is not adequate as its theoretical counterpart is not defined. After perceiving the lack of a suitable multivariate version of the codifference function, we propose an adaptation of this tool to measure interdependence in multivariate α-stable processes. We establish such a function based on notions presented in the existing literature. We also show some of its properties and give an estimator based on the empirical characteristic function. Subsequently, we evaluate another measure of dependence with different properties but similar usage for comparison reasons. These two measures are computed for VAR(1) processes with α-stable innovations, proving to be useful in the identification of associated patterns related to them. Finally, we demonstrate how these measures can be applied with real data sets by analyzing the monthly number of patients with community-acquired pneumonia and the registered values of PM10 in the city of São Paulo, Brazil, from January 2008 to December 2021.
AB - Measuring the dependency between lagged random vectors in time series is extremely important to detect appropriate models for fitting real data. Vector autoregressive processes (VAR), in particular, are among the most popular multivariate time series that allow modeling schemes for two or more random variables. However, if the series of innovations process does not have finite second-order moments, the classical analysis that uses the empirical auto-covariance function is not adequate as its theoretical counterpart is not defined. After perceiving the lack of a suitable multivariate version of the codifference function, we propose an adaptation of this tool to measure interdependence in multivariate α-stable processes. We establish such a function based on notions presented in the existing literature. We also show some of its properties and give an estimator based on the empirical characteristic function. Subsequently, we evaluate another measure of dependence with different properties but similar usage for comparison reasons. These two measures are computed for VAR(1) processes with α-stable innovations, proving to be useful in the identification of associated patterns related to them. Finally, we demonstrate how these measures can be applied with real data sets by analyzing the monthly number of patients with community-acquired pneumonia and the registered values of PM10 in the city of São Paulo, Brazil, from January 2008 to December 2021.
KW - Bayesian techniques
KW - Codifference
KW - Measures of dependence
KW - Multivariate α-stable distributions
KW - Simulations
KW - Spectral covariance
KW - Vector autoregressive processes
UR - http://www.scopus.com/inward/record.url?scp=85145190988&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2022.105153
DO - 10.1016/j.jmva.2022.105153
M3 - Article
AN - SCOPUS:85145190988
SN - 0047-259X
VL - 195
JO - JOURNAL OF MULTIVARIATE ANALYSIS
JF - JOURNAL OF MULTIVARIATE ANALYSIS
M1 - 105153
ER -