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From the literature I do not understand the null hypothesis of this test. I used it's implementation in R to confirm my multivariate model captures the ARCH effects present in the data. I use this line of code:

Weighted.LM.test(fit1@model$residuals[,1], fit1@model$sigma[,1]^2, lag = 25,type = c("correlation", "partial"),fitdf = 1, weighted = TRUE)

To obtain the standardized residuals and put them in the test. The results are:

Weighted X-squared on Squared Residuals for fitted ARCH process = 5.1043, Shape = 9.5018, Scale = 1.3640, p-value = 0.8705

Does the pvalue indicate I fail to reject the null hypothesis of no autocorrelation, and therefore there is still autocorrelation present, and thus my model is flawed? Or am I misinterpreting this test. Any recommendations on how to solve this?

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The $p$-value is high, so you do not reject $H_0$ of no autocorrelation in squared standardized residuals. No autocorrelation is what you want as the model assumes the standardized innovations to be i.i.d. All looks fine.

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  • $\begingroup$ Thank you Richard for the confirmation. It seems I indeed misinterpreted and am glad that my model is adequate. The LM function is from a specific package: 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), as proposed by Fisher and Gallagher (2012). $\endgroup$
    – Guest
    Commented Feb 23, 2021 at 13:11
  • $\begingroup$ @Guest, thanks for correcting me. I have updated my answer accordingly. $\endgroup$
    – Richard Hardy
    Commented Feb 23, 2021 at 14:41

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