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New weighted portmanteau statistics for time series goodness of fit testing. (English) Zbl 1261.62079

Summary: We exploit ideas from high-dimensional data analysis to derive new portmanteau tests that are based on the trace of the square of the m th order autocorrelation matrix. The resulting statistics are weighted sums of the squares of the sample autocorrelation coefficients that, unlike many other tests appearing in the literature, are numerically stable even when the number of lags considered is relatively close to the sample size. The statistics behave asymptotically as a linear combination of chi-squared random variables and their asymptotic distribution can be approximated by a gamma distribution. The proposed tests are modified to check for nonlinearity and to check the adequacy of a fitted nonlinear model. Simulation evidence indicates that the proposed goodness of fit tests tend to have higher power than other tests appearing in the literature, particularly in detecting long-memory nonlinear models. The efficacy of the proposed methods is demonstrated by investigating nonlinear effects in Apple, Inc., and Nikkei-300 daily returns during the 2006–2007 calendar years.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G10 Nonparametric hypothesis testing
62J20 Diagnostics, and linear inference and regression
65C60 Computational problems in statistics (MSC2010)
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