Question

Breusch-Godfrey test for autocorrelation up to order 5 OLS, using observations 1959-1995 (T = 37) Dependent variable: uhat coefficient std. error t-ratio p-value const time y uhat_1 uhat_2 uhat_3 uhat_4 uhat_5 978.820 436.150 34.1167 15.3719 -0.116854 0.0521510 0.456929 0.170204 -0.00137933 0.193113 -0.130481 0.193568 -0.230634 0.207956 -0.420982 0.187454 Unadjusted R-squared 0.495061 Test statistic: LMF = 5.686546, with p-value = P(F(5,29) > 5.68655) Alternative statistic: TR^2 = 18.317273, with p-value = P(Chi-square(5) > 18.3173) = Ljung-Box Q' = 26.2097, with p-value = P(Chi-square(5) > 26.2097) - a. What is the null hypothesis? (1 point) b. What are the steps for the calculated test statistic? (1 point) c. What is the correct critical value with degrees of freedom? Do an internet search or use the correct table in the back of your book (1 point)

Answer 1

A. The null hypothesis for the Breusch Godfrey test for AR (P) SCHEME would be :

H_{​​​​​​0} : P_{​​​​​​1} = P_{​​​​​​2} = P₃ = P_​​​4 = P_5​​​​​_​​​ = 0

H_{​​​​0} show that in the regression, autocorrelation does not exist.

B. The steps for the calculated test statistic are :

2 Ut : .: 94 calao ato value > b) The steps for the calculated test statisha :- Assume Ut ~ AR (S) scheme © Estimate regusion & obtain residuals. ① Reguess it on explainatory variables ie. time, UttUt-2, Ut-3, Utru futs. &, + 42 time t&plut-it pêut-2 & på ut 3 + pû ut 4 + Ås ut-s & vê & obtain R² from this auxilliary regression. ② setting the hypothesis :- P A = P2 = P3 = pu= 15 20 HA 2 Atleast one of them is of sample size is large then. (n-p) R² ~ 2² p degree of freedom=p critical then Ho rejected to autocorrelation exist. If calculated value < critical value , then Mo accepted So auto correlation doesn't exist Ho = non - 2010

3) Coruct at the of critical valu 57. level significance of degue of freedom = 5. => 11.0705 Cat dof=s, significance level = 5% = 0.05
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