Question #9 - Reading 2 Time-Series Analysis

Reading: Reading 2 Time-Series Analysis

PDF File: Reading 2 Time-Series Analysis.pdf

Page: 4

Status: Unattempted

Correct Answer: A

Shared Context

of 101 The primary concern when deciding upon a time series sample period is which of the following factors? A) The length of the sample time period. B) Current underlying economic and market conditions. C) The total number of observations. Diem Le is analyzing the financial statements of McDowell Manufacturing. He has modeled the time series of McDowell's gross margin over the last 16 years. The output is shown below. Assume 5% significance level for all statistical tests. Autoregressive Model Gross Margin – McDowell Manufacturing Quarterly Data: 1st Quarter 1985 to 4th Quarter 2000 Regression Statistics R-squared 0.767 Standard error of forecast 0.049 Observations 64 Durbin-Watson 1.923 (not statistically significant) Coefficient Standard Error t-statistic Constant 0.155 0.052 ????? Lag 1 0.240 0.031 ????? Lag 4 0.168 0.038 ????? Autocorrelation of Residuals Lag Autocorrelation Standard Error t-statistic 1 0.015 0.129 ????? 2 –0.101 0.129 ????? 3 –0.007 0.129 ????? 4 0.095 0.129 ????? Partial List of Recent Observations Quarter Observation 4th Quarter 2002 0.250 1st Quarter 2003 0.260 2nd Quarter 2003 0.220 3rd Quarter 2003 0.200 4th Quarter 2003 0.240 Abbreviated Table of the Student's t-distribution (One-Tailed Probabilities) df p = 0.10 p = 0.05 p = 0.025 p = 0.01 p = 0.005 50 1.299 1.676 2.009 2.403 2.678 60 1.296 1.671 2.000 2.390 2.660 70 1.294 1.667 1.994 2.381 2.648

Question

Le can conclude that the model is:

Answer Choices:

A. properly specified because the Durbin-Watson statistic is not significant

B. properly specified because there is no evidence of autocorrelation in the residuals

C. not properly specified because there is evidence of autocorrelation in the residuals and the Durbin-Watson statistic is not significant

Explanation

The Durbin-Watson test is not an appropriate test statistic in an AR model, so we cannot use it to test for autocorrelation in the residuals. However, we can test whether each of the four lagged residuals autocorrelations is statistically significant. The t-test to accomplish this is equal to the autocorrelation divided by the standard error with 61 degrees of freedom (64 observations less 3 coefficient estimates). The critical t-value for a significance level of 5% is about 2.000 from the table. The appropriate t-statistics are: Lag 1 = 0.015/0.129 = 0.116 Lag 2 = -0.101/0.129 = -0.783 Lag 3 = -0.007/0.129 = -0.054 Lag 4 = 0.095/0.129 = 0.736 None of these are statically significant, so we can conclude that there is no evidence of autocorrelation in the residuals, and therefore the AR model is properly specified.

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