Weighted Portmanteau Test for Fitted ARCH process

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Description

A weighted portmanteau test for testing the null hypothesis of adequately fitted ARCH process. This is essentially a weighted version of the statistic proposed by Li and Mak (1994)

Usage

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Weighted.LM.test(x, h.t, lag = 1, 
                type = c("correlation", "partial"),
                fitdf = 1, weighted = TRUE)

Arguments

x

a numeric vector or univariate time series, or residuals of a fitted time series

h.t

a numeric vector of the conditional variances

lag

the statistic will be based on lag autocorrelation coefficients.

type

type of test to be performed, either based on the autocorrelations or partial-autocorrelations.

fitdf

the number of ARCH parameters fit to the model, default=1 since at least some ARCH model must be fit to find h.t

weighted

A flag determining if the weighting scheme should be utilized. TRUE by default, if FALSE, it performs the test from Li and Mak (1994)

Details

These test can be performed after fitting an ARCH process to a time series. The theoretical work was originally developed in Li and Mak (1994) and has recently been extended in Fisher and Gallagher (2012).

Value

A list with class "htest" containing the following components:

statistic

the value of the test statistic

parameter

The approximate shape and scale parameters for the weighted statistic or degrees of freedom of the chi-squared distribution if the weighted flag is set to FALSE.

p.value

The p-value of the test

method

a character string indicating which type of test was performed.

data.name

a character string giving the name of the data

Note

Similiar to the Box.test() and Weighted.Box.test() functions

Author(s)

Thomas J. Fisher

References

Fisher, T. J. and Gallagher, C. M. (2012), New Weighted Portmanteau Statistics for Time Series Goodness-of-Fit Testing. Journal of the American Statistical Association, accepted.

Li, W. K. and Mak, T. K. (1994), On the squared residual autocorrelations in non-linear time series with conditional heteroskedasticity. Journal of Time Series Analysis 15(6), 627-636.