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How to do the Ljung Box test for squared residuals?
So you have applied the Ljung-Box test on your original data, first with the option squared.residuals = FALSE and then squared.residuals = TRUE. In both cases you found the test statistic exceeds the critical value, hence you reject the null hypothesis.
Which is the null hypothesis of the Ljung Box test?
The Ljung-Box Q-test is a “portmanteau” test that assesses the null hypothesis that a series of residuals exhibits no autocorrelation for a fixed number of lags L, against the alternative that some autocorrelation coefficient ρ(k), k = 1., L, is nonzero.
What is the critical value of the Ljung Box?
I ran the Ljung-Box for a single series and find that the statistic is very high. I am using 20 lags so the critical value is 31.4104 and the statistic is greater than that. So my conclusion is that the data is not independently distributed. I also test the squared residuals for the same series. Again I have high values.
How is the Ljung test applied to a time series?
The test is applied to the residuals of a time series after fitting an ARMA(\\(p,q\\)) model to the data. The test examines \\(m\\) autocorrelations of the residuals. If the autocorrelations are very small, we conclude that the model does not exhibit significant lack of fit.
When to reject the null hypothesis in R-Ljung-Box?
In both cases you found the test statistic exceeds the critical value, hence you reject the null hypothesis. The null hypothesis in the first case is “there is no autocorrelation up to lag 20” and in the second case “there is no autocorrelation in the squares up to lag 20”.
How is the Ljung-Box test based on autocorrelation?
The Ljung-Box test is based on the autocorrelation plot. However, instead of testing randomness at each distinct lag, it tests the “overall” randomness based on a number of lags. For this reason, it is often referred to as a “portmanteau” test.