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A single series representation of multiple independent ARMA processes
Author(s) -
Bowden Ross S.,
Clarke Brenton R.
Publication year - 2012
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2011.00766.x
Subject(s) - univariate , series (stratigraphy) , autoregressive–moving average model , mathematics , interleaving , representation (politics) , time series , moving average , moving average model , statistics , econometrics , algorithm , autoregressive integrated moving average , autoregressive model , computer science , multivariate statistics , paleontology , politics , political science , law , biology , operating system
This article shows that multiple independent time series from the same ARMA process can be represented by a single univariate ARMA time series through an interleaving of the original series. Using this result, existing univariate modelling software can be used to fit a single ARMA time series model simultaneously to multiple independent realizations of the same ARMA process. The interleaving approach and its properties will be presented and compared with alternative estimation options. It will be applied to the modelling of 66 years of daily maximum temperatures for Perth, Western Australia and to other time series models.