Which tests for autocorrelations to be zero?a. Jarque-Bera testb. Ljung-Box testc. Augmented Dicky-Fuller (ADF) testd. Dicky-Fuller test

The Ljung-Box test (option b) is used to test for autocorrelations to be zero.

Here are the steps to perform the Ljung-Box test:

1. Formulate the null and alternative hypotheses. The null hypothesis (H0) is that the data are independently distributed (i.e., the correlations in the population from which the sample is taken are 0, so that any observed correlations in the data result from randomness of the sampling process). The alternative hypothesis (H1) is that the data are not independently distributed; they exhibit serial correlation.

2. Compute the test statistic. The Ljung-Box test statistic is computed as: Q = n*(n+2)*sum([r[k]**2/(n-k) for k in range(1,h+1)]) where n is the sample size, r[k] is the autocorrelation at lag k, and h is the number of lags being tested.

3. Determine the p-value. The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. If the p-value is less than the chosen significance level (typically 0.05), we reject the null hypothesis.

4. Interpret the results. If the p-value is less than the chosen significance level, we conclude that the data are not independently distributed; they exhibit serial correlation. If the p-value is greater than the chosen significance level, we do not have enough evidence to conclude that the data are not independently distributed.

Note: The other tests mentioned (Jarque-Bera test, Augmented Dicky-Fuller (ADF) test, Dicky-Fuller test) are used for different purposes. The Jarque-Bera test is used to test if data have the skewness and kurtosis matching a normal distribution. The Augmented Dicky-Fuller (ADF) test and Dicky-Fuller test are used to test for stationarity or non-stationarity of time series data.