Use ?-0.05 to test the following time series for positive autocorrelation Period

Question

Use ?-0.05 to test the following time series for positive autocorrelation Period Sales Period Sales Period Sales 20 14 12 13 2 7 12 10 10 18 20 19 4 12 10 EEB Click the icon to view the critical values for the Durbin-Watson test for a 0.05 Identify the null and alternative hypotheses. Choose the correct answer below O B. H0: Negative autocorrelation is present H1: Positive autocorrelation is present A. Ho: No positive autocorrelation is present H1: Positive autocorrelation is present ° C. Ho: Positive autocorrelation is present 0 D. Ho: No negative autocorrelation is present H1: No positive autocorrelation is present H1: Negative autocorrelation is present Determine the Durbin-Watson statistic. (Round to two decimal places as needed.) ldentify the critical values (Round to two decimal places as needed.) State the conclusion. Choose the correct answer below 0 A. Fail to reject H0 and conclude that no positive autocorrelation is present. O B. Reject Ho and conclude that a positive autocorrelation is present. ° C. The test is inconclusive 0 D. Fail to reject Ho and conclude that a positive autocorrelation is present. 0 E. Reject Ho and conclude that no positive autocorrelation is present.

Explanation / Answer

1.)

Option A is correct.

Ho: No Positive Auto correlation is present

Ha: Positive Auto correlation is present

2.) The formula for Durbin Watson statistic is:

Durbin Watson Test Statistic = ?{t=2 to 20}(et-et-1)2 / ?{t=1 to 20} et2

Where, et = Observation value

Let's build AR model on above data for 1 lag only since if there is any auto correlation present it will be definitely resent at Lag-1.

AR model is given as:

Sales = a + b*Lag1

Basically, its regression equation between actual and lag value.

The equation after solving in excel is given as:

Sales = 5.14 + 0.68 * Lag1

Now, Predicting Sales Values with the help of above equation

Error is given as: et = Predicted-Actual

So, table is given below:

Checking mean of error is almost zero or not since this is assumption for Durbin Watson.

mean(et) = 2.36 * 1016 = 0(approximately)

Now, calculating the durbin watson statistic in tha table below:

Durbin Watson Statistic, d = 2.563

Now, finding critical values fron Durbin Watson table,

We are considering only 1 Lag, so k =1

For alpha = 0.05, k =1 and n= 15

dL = 1.08

dU = 1.36

In our case, d > dU which means negative Autocorrelation is present.

So, we fail to reject NULL Hypotheses.

Hence, answer A is correct

Period Sales    Lag-1 1 5 2 7 5 3 12 7 4 10 12 5 10 10 6 11 10 7 14 11 8 14 14 9 12 14 10 15 12 11 20 15 12 14 20 13 18 14 14 20 18 15 19 20

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