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> #Test ARCH effect > Box.test(m2$residuals^2,lag=10,type='Ljung') Box-Ljung test data: m2$residuals^2 X-squared = 17.628, df = 10, p-value = 0.06156

Question

Test ARCH effect

Box.test(m2$residuals^2, lag=10, type='Ljung')

Box-Ljung test
data: m2$residuals^2
X-squared: 17.628, df: 10, p-value: 0.06156

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Solution

The Box-Ljung test is a type of statistical test used to check if there is autocorrelation in a time series data. In this case, the test is applied to the squared residuals of a model (m2).

The output of the test provides three key pieces of information:

  1. X-squared: This is the test statistic. In this case, it is 17.628.

  2. df: This stands for degrees of freedom. It is the number of lags being tested. In this case, it is 10.

  3. p-value: This is the probability of observing the given result (or one more extreme) if the null hypothesis is true. In this case, the p-value is 0.06156.

The null hypothesis of the Box-Ljung test is that the data are independently distributed. In other words, the residuals are not autocorrelated. If the p-value is less than the significance level (usually 0.05), then we reject the null hypothesis and conclude that there is evidence of autocorrelation.

In this case, the p-value is greater than 0.05, so we do not reject the null hypothesis. This means that there is not enough evidence to suggest that the residuals are autocorrelated. However, the p-value is quite close to 0.05, so it might be worth investigating further.

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