2940603 Advanced Econometrics (Assoc. Prof. Pongsa Pornchaiwiseskul)
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Final Exam (0900-1200hr, January 26, 2004) 2940603 Advanced Econometrics (Assoc. Prof. Pongsa Pornchaiwiseskul) Instructions: a) Textbooks, lecture notes and calculators are allowed. b) Each must work alone. Cheating will not be tolerated. c) There are four(4) tests. Attempt all the tests. Each carries equal weights. d) Use only the provided test-books. e) All the hypothesis testing will use 0.05 as the level of significance. TEST#1 (20 points)
Difference between trade volume in the morning and the afternoon sessions (Vt) of a particular commodity on trading day t is assumed (no need to prove this) to follow an independent AR(1) process without drift as follows :
Vt = Vt-1 + t ------(1.1) where t = IID normal noise in period t 2 Var(t) = for all t The price spread (St) on day t is postulated to depend on the trade value as follows:
St = 1 + 2 Vt + t ------(1.2) where t = another IID normal noise in period t 2 Var(t) = for all t Given printouts below,
Page 1/6 Final Exam (0900-1200hr, January 26, 2004) 2940603 Advanced Econometrics (Assoc. Prof. Pongsa Pornchaiwiseskul) Answer the following questions: 2 1.1) Estimate equation (1.2). That is, estimate 1,2, and their variances. 1.2) Show that that the price spread follow an AR(1) process as follows:
St = + St-1 + ’t ------(1.3)
where ’t = IID normal noise in period t 1.3) Estimate equation (1.1). That is, estimate ,2 and their variances. Hint: to get 2, try to estimate var(Vt) from the given printouts.
1.4) Estimate Var(’t). 1.5) Discuss how to estimate and its variance. What additional information or regression runs are needed? TEST#2 (20 points) Foreign direct investment and stock market return have been postulated to have lagged own and cross effects. Their rate of change can be expressed in VAR(1) as follows:
FDIt = 1 FDIt-1 + 2 RMt-1 + u1t ------(2.1)
RMt = 1 FDIt-1+ 2 RMt-1 + u2t ------(2.2) where FDIt = rate of change of foreign direct investment in period t RMt = rate of change of stock market return in period t u1t,u2t = error terms or shocks for FDI and RM in period t, respectively Given the following printouts,
Page 2/6 Final Exam (0900-1200hr, January 26, 2004) 2940603 Advanced Econometrics (Assoc. Prof. Pongsa Pornchaiwiseskul)
Page 3/6 Final Exam (0900-1200hr, January 26, 2004) 2940603 Advanced Econometrics (Assoc. Prof. Pongsa Pornchaiwiseskul)
answer the following questions.
2.1) Estimate equations (2.1) and (2.2). That is, estimate 1,2,1,2,var(u1t) and var(u2t) 2.2) Assume simultaneous shocks, determine the weight of shock series (u1t and u1,t+1) in total variation of FDIt+1 and RMt+1 Hint: Sources of total variation of FDIt+1 and RMt+1 are (u1t ,u2t) and (u1,t+1, u2,t+1)
Page 4/6 Final Exam (0900-1200hr, January 26, 2004) 2940603 Advanced Econometrics (Assoc. Prof. Pongsa Pornchaiwiseskul) 2.3) Check the validity of your estimates in 2.1). Is there any long-term relationship
between FDIt and RMt? Explain. 2.4) Given that FDIt and RMt have a long-term relationship (regardless of your answer in question 2.3), what will be your answer to question 2.2? TEST#3 (20 points) Return of food sector during period t has been postulated to follow equations (3.1) and (3.2)below:
RFD t – RGOV t = 1 +2(RSET t – RGOV t) + 3t + ut ------(3.1) 2 Var(ut) = 0 + 1(ut-1) ------(3.2) where RFDt = return of food sector in period t RGOVt = interest rate of government bond in period t RSETt = average return of stock market in period t ut = independent error term in period t 2 [t] = Var(u t)
Estimation of Equations (3.1) and (3.2) based on 80 periods of time series data is shown below:
Page 5/6 Final Exam (0900-1200hr, January 26, 2004) 2940603 Advanced Econometrics (Assoc. Prof. Pongsa Pornchaiwiseskul)
Based on the above EViews printout, answer the following questions: 3.1) Estimate equations (3.1) and (3.2).
3.2) Given RFD80 =0.02, RGOV80 =0.01 and RSET80 =0.15 and RSET81 =0.18 and RGOV81=0.011, predict the return of food sector in period t=81. 3.3) Provide the prediction interval for the answer in question 3.2 TEST#4 (20 points) A financial analyst believed that excess return of a particular stock for week t is determined by the following model :
ERAt = 1 2ERMt t ------(4.1) where ERAt = excess return of stock A in week t ERM t = excess return of stock market in week t
t = IID error term in week t 2 Var(t) = [1] for all t The second analyst argued that the excess return should follow the following model:
ERAt = 1 2ERAt-1 3ERMt-1 4FXDt-1 t ------(4.2) where FXDt = exchange rate depreciation in week t FXDt ~ IID Normal
t = IID error term in week t 2 Var(t) = [2] for all t Which analyst should you trust or they are both correct? Discuss in details the situations under which one is more appropriate than the other.
End of Exam. Good luck.
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