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Local Gaussian Autocorrelation and Tests for Serial Independence
Author(s) -
Lacal Virginia,
TjØstheim Dag
Publication year - 2017
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/jtsa.12195
Subject(s) - autocorrelation , mathematics , heteroscedasticity , measure (data warehouse) , autoregressive model , series (stratigraphy) , gaussian , autocorrelation technique , independence (probability theory) , moving average model , statistics , autoregressive conditional heteroskedasticity , econometrics , time series , computer science , autoregressive integrated moving average , biology , volatility (finance) , paleontology , physics , quantum mechanics , database
The traditional and most used measure for serial dependence in a time series is the autocorrelation function. This measure gives a complete characterization of dependence for a Gaussian time series, but it often fails for nonlinear time series models as, for instance, the generalized autoregressive conditional heteroskedasticity model (GARCH), where it is zero for all lags. The autocorrelation function is an example of a global measure of dependence. The purpose of this article is to apply to time series a well‐defined local measure of serial dependence called the local Gaussian autocorrelation. It generally works well also for nonlinear models, and it can distinguish between positive and negative dependence. We use this measure to construct a test of independence based on the bootstrap technique. This procedure requires the choice of a bandwidth parameter that is calculated using a cross validation algorithm. To ensure the validity of the test, asymptotic properties are derived for the test functional and for the bootstrap procedure, together with a study of its power for different models. We compare the proposed test with one based on the ordinary autocorrelation and with one based on the Brownian distance correlation. The new test performs well. Finally, there are also two empirical examples.