ECON301_Handout_12_1213_02

Of forecast errors prediction errors of the

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of forecast errors (prediction errors) of the corresponding years (The proof is beyond the scope of this lecture). In order to test for structural change in 2001, 2002 and 2003; we can test 2001 e , 2002 e and 2003 e individually (t test) and jointly (F test) different from zero.
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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 10 I. Individual Test For example, we can individually test the statistical significance of 2001 e as follows: 0 2001 :0 He 0 2001 Generalizing the individual test of the statistical significance of t e is 0 t t A Note that if this null hypothesis is not rejected this does not necessarily imply that the coefficients pertaining to the two subsamples will be equal. If, however, the null hypothesis is rejected this will imply that at least one of the coefficients is different for two subsamples. o In other words, although the rejection of null hypothesis would imply a structural change, the non-rejection of null hypothesis does not necessarily imply parameter stability for two subsamples. II. Joint Test
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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 11 Below, note the summary of the basic steps of the Predictive test to test for the following hypothesis: 0 1 1 3 : ... 0 t H e e e e 0 : at least one of them is non zero H where t e is the expected value of prediction error. Note that For our example, the restricted model is: (1) 0 1 1 2 2 t t t t Y X X u t =1991, 1992, …,2003 The unrestricted model is (2) 0 1 1 2 2 1 2001 2 2002 3 2003 t t t t Y X X e I e I e I u 1991,1992,. ..,2003 t Step 1. Estimate the equation (1) and retrieve the sum of squared residuals, R S . Note that for our example t =1991, 1992, …,2003 and hence T=13. Step 2. Estimate the equation (2) and retrieve the sum of squared residuals, U S . Step 3. Calculate the following test statistic:     / /1 RU U S S p Q S T k 
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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 12 where 1 Tk  is the degrees of freedom in unrestricted model 2 and p is the number of restrictions in null hypothesis 3 . The calculated Q statistic is distributed as F with [ p , 1 ] degrees of freedom: ,1 p T k QF .Reject the null hypothesis of parameter constancy if p T k . Note that, due to mathematical reasons , the SSR of the following models will be the same: (2) 0 1 1 2 2 1 2001 2 2002 3 2003 tt Y X X e I e I e I u 1991,1992,. ..,2003 t ; SSR= U S (1*) 0 1 1 2 2 Y X X u ..,2000 t ; SSR= * U S Hence instead of equation (2), we can estimate equation (1*) and use its SSR as the unrestricted model’s SSR: * UU SS Let us denote the number of observations in equation (1*) as T 1 . In our example, T 1 =10 and T =13.
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of forecast errors prediction errors of the corresponding...

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