> #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
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:
-
X-squared: This is the test statistic. In this case, it is 17.628.
-
df: This stands for degrees of freedom. It is the number of lags being tested. In this case, it is 10.
-
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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