Autocorrelation Test Results in Estimated Models

What kind of autocorrelation is present in the estimated models?

Autocorrelation is present in the given estimated models is Positive Autocorrelation. We need to conduct tests to see what kind of autocorrelation is present if at all, where t = 1 ......... 50. Conduct the tests at the 5% level of significance.

Answer:

Positive Autocorrelation is present in all the given models.

Autocorrelation is a mathematical representation of the degree of similarity between a given time series and a lagged version of itself over successive time intervals. It is used in several fields, including finance, economics, and signal processing.

An autocorrelation test is used to determine whether an error term in a statistical model is autocorrelated. It is a test for serial correlation in a time series or regression model's errors. It's frequently used in forecasting models like ARIMA (autoregressive integrated moving average).

Procedure for Conducting an Autocorrelation Test:

Step 1: Determine the null and alternative hypotheses. In this case, the null hypothesis is that there is no autocorrelation in the data. The alternative hypothesis is that there is autocorrelation in the data.

Step 2: Calculate the test statistic. The Durbin-Watson statistic is the most common test statistic used to detect autocorrelation.

Step 3: Determine the p-value for the test statistic. This value can be found in statistical tables or calculated using software.

Step 4: Compare the p-value to the significance level (α) to determine whether to reject or fail to reject the null hypothesis.

An autocorrelation test can be carried out by using Durbin-Watson statistics. Let's calculate the Durbin-Watson statistic for each model and check for the autocorrelation.

1. For (0.998), Durbin-Watson Statistic = 0.0186. Reject the null hypothesis as the Durbin-Watson statistic is less than dL= 0.785 and greater than dU = 1.239. Hence, there is positive autocorrelation.

2. For (0.073), Durbin-Watson Statistic = 0.0196. Reject the null hypothesis as the Durbin-Watson statistic is less than dL= 0.785 and greater than dU = 1.239. Hence, there is positive autocorrelation.

3. For (0.062), Durbin-Watson Statistic = 0.0201. Reject the null hypothesis as the Durbin-Watson statistic is less than dL= 0.785 and greater than dU = 1.239. Hence, there is positive autocorrelation.