Open Access
2020 The local partial autocorrelation function and some applications
Rebecca Killick, Marina I. Knight, Guy P. Nason, Idris A. Eckley
Electron. J. Statist. 14(2): 3268-3314 (2020). DOI: 10.1214/20-EJS1748


The classical regular and partial autocorrelation functions are powerful tools for stationary time series modelling and analysis. However, it is increasingly recognized that many time series are not stationary and the use of classical global autocorrelations can give misleading answers. This article introduces two estimators of the local partial autocorrelation function and establishes their asymptotic properties. The article then illustrates the use of these new estimators on both simulated and real time series. The examples clearly demonstrate the strong practical benefits of local estimators for time series that exhibit nonstationarities.


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Rebecca Killick. Marina I. Knight. Guy P. Nason. Idris A. Eckley. "The local partial autocorrelation function and some applications." Electron. J. Statist. 14 (2) 3268 - 3314, 2020.


Received: 1 May 2019; Published: 2020
First available in Project Euclid: 10 September 2020

zbMATH: 1448.62133
MathSciNet: MR4147585
Digital Object Identifier: 10.1214/20-EJS1748

Keywords: Haar cross-correlation wavelet , integrated local wavelet periodogram , locally stationary time series , practical estimation , Wavelets

Vol.14 • No. 2 • 2020
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