FIN7028 Exam Time Table Code FIN7028 Normal answer book EXAMINATION FOR THE DEGREE OF MASTER OF SCIENCE (FINANCE) AND OTHER DEGREES TIME-SERIES FINANCIAL ECONOMETRICS Monday, 29th May 2017 9:30 AM – 11:30 AM Examiners: Professor Gerhard Kling and the internal examiners Write on both sides of the answer paper Answer THREE from the available five questions All questions carry equal marks Allocation of marks within each question is shown in brackets You have TWO HOURS to complete the paper FIN7028/MAY2017 Answer THREE (3) from the available FIVE (5) questions. Explicitly state any assumptions you make and any formulas you use in each of your answers. Question 1 A) How would you test if a process follows a White Noise Suggest a test statistic and explain it. (25 marks) B) Write an ARMA(p,q) model using three representations. Discuss their importance and interpretation. (50 marks) C) Is there a special characteristic of the process illustrated in the following figure How would you model it (10 marks) 0 1 0 2 0 3 0 4 0 s 4 0 100 200 300 400 500 t D) You are given the following Autocorrelation and Partial Autocorrelation STATA output for the first 12 lags. Write the equation of the model (or models) you would fit to the underlying time series and explain your reasoning. -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ——————————————————————————- 1 0.7084 0.7086 252.41 0.0000 |—– |—– 2 0.7353 0.4694 524.95 0.0000 |—– |— 3 0.6991 0.2347 771.76 0.0000 |—– |- 4 0.6152 -0.0446 963.26 0.0000 |—- | 5 0.6014 0.0112 1146.6 0.0000 |—- | 6 0.5361 -0.0401 1292.6 0.0000 |—- | 7 0.4963 -0.0228 1418.1 0.0000 |– | 8 0.4476 -0.0412 1520.3 0.0000 |- | 9 0.3978 -0.0411 1601.2 0.0000 | | 10 0.3836 0.0481 1676.5 0.0000 | | (15 marks) End of Question 1 Page 2 of 7 FIN7028/MAY2017 Question 2 A) What is an Impulse Response Function (IRF) and how is it used (25 marks) B) Assuming you fit a model of your choice. What two residual diagnostics would you use (40 marks) C) Discuss the following Impulse Response Function (IRF) figures. (35 marks) Figure 1 0 .5 1 0 50 asymp, rt, rt 95% CI impulse response function (irf) step Graphs by irfname, impulse variable, and response variable Figure 2 -.5 0 .5 1 0 50 asymp, rt, rt 95% CI impulse response function (irf) step Graphs by irfname, impulse variable, and response variable Figure 3 -.5 0 .5 1 0 50 asymp, rt, rt 95% CI impulse response function (irf) step Graphs by irfname, impulse variable, and response variable Figure 4 -1 -.5 0 .5 1 0 50 asymp, rt, rt 95% CI impulse response function (irf) step Graphs by irfname, impulse variable, and response variable End of Question 2 Page 3 of 7 FIN7028/MAY2017 Question 3 A) Answer the following questions. i. Write the equation to describe an AR(1) process. Explicitly state any assumptions you might make. ii. What is the mean of this process iii. What is the variance of this process iv. When is such a process stationary (40 marks) B) Answer the following questions. i. What is a nonstationary process ii. Fully discuss a statistic to test if a series has a unit root. (30 marks) C) You are given the following STATA output for a time series Yt. —————————————————————————— | OPG x | Coef. Std. Err. z P>|z| [95% Conf. Interval] ————-+—————————————————————- x | _cons | .0638859 .0809849 0.79 0.430 -.0948416 .2226134 ————-+—————————————————————- ARMA | ar | L1. | -.2984583 .0933253 -3.20 0.001 -.4813725 -.1155441 L2. | -.0926419 .0794731 -1.17 0.244 -.2484063 .0631225 L3. | -1.073482 .0699466 -15.35 0.000 -1.210575 -.9363896 L4. | .1343098 .0923316 1.45 0.146 -.0466569 .3152765 L5. | -.0441516 .0494018 -0.89 0.371 -.1409774 .0526743 L6. | -.5001629 .0449697 -11.12 0.000 -.5883018 -.412024 | ma | L1. | 1.172461 .1059787 11.06 0.000 .9647467 1.380176 L2. | 1.37105 .1556337 8.81 0.000 1.066014 1.676087 L3. | 1.224464 .1945243 6.29 0.000 .8432031 1.605724 L4. | .6371695 .1930177 3.30 0.001 .2588618 1.015477 L5. | .2859264 .1483375 1.93 0.054 -.0048098 .5766626 L6. | -.2640845 .0946195 -2.79 0.005 -.4495354 -.0786337 ————-+—————————————————————- /sigma | .9416276 .0319045 29.51 0.000 .879096 1.004159 —————————————————————————— Write the model which is suggested by the above output. Explicitly state any assumptions you might make. (30 marks) End of Question 3 Page 4 of 7 FIN7028/MAY2017 Question 4 A) Consider you have a time series, rt. Answer the following questions. i. Write the equatio
ns to describe a random walk with and without drift. Explicitly state any assumptions you might make. ii. What is the importance of the drift parameter iii. What is the 5-steps ahead and 105-steps ahead forecasts implied by the model without the drift iv. Is drift an important factor in financial time series (i.e. stock prices) (40 marks) B) You have a time series, yt, which you need to model. Answer the following questions. i. First, you perform an Augmented Dickey-Fuller test which yields the output below. ———- Interpolated Dickey-Fuller ——— Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value —————————————————————————— Z(t) -12.278 -3.440 -2.870 -2.570 —————————————————————————— MacKinnon approximate p-value for Z(t) = 0.0000 Which transformation will you take for your series ii. Then, you specify a model, estimate it and obtain the residuals. You examine the autocorrelation function (ACF) of the residuals and you find the following estimates. How do you proceed (20 marks) Page 5 of 7 FIN7028/MAY2017 C) You are provided with the following STATA output. What model is employed Comment on the relationships between the variables. (40 marks) —————————————————————————— | Coef. Std. Err. z P>|z| [95% Conf. Interval] ————-+—————————————————————- uk | uk | L1. | .3891385 .0906135 4.29 0.000 .2115393 .5667378 L2. | .0592089 .0896294 0.66 0.509 -.1164616 .2348793 | us | L1. | .049665 .0883177 0.56 0.574 -.1234344 .2227645 L2. | .0160367 .0909355 0.18 0.860 -.1621937 .1942671 | ca | L1. | .1042349 .0952222 1.09 0.274 -.0823972 .2908669 L2. | .1100174 .0848875 1.30 0.195 -.0563591 .2763939 | _cons | .0012729 .0007097 1.79 0.073 -.000118 .0026638 ————-+—————————————————————- us | uk | L1. | .490393 .1020039 4.81 0.000 .290469 .6903169 L2. | -.3115908 .1008961 -3.09 0.002 -.5093435 -.1138381 | us | L1. | .2348676 .0994194 2.36 0.018 .0400091 .4297261 L2. | .0873776 .1023664 0.85 0.393 -.1132568 .288012 | ca | L1. | .2398951 .1071919 2.24 0.025 .0298028 .4499873 L2. | -.1317754 .0955581 -1.38 0.168 -.3190658 .0555151 | _cons | .0029139 .0007989 3.65 0.000 .0013481 .0044796 ————-+—————————————————————- ca | uk | L1. | .3534272 .0924013 3.82 0.000 .1723239 .5345304 L2. | -.1913663 .0913978 -2.09 0.036 -.3705027 -.0122299 | us | L1. | .4682664 .0900601 5.20 0.000 .2917517 .644781 L2. | -.0082187 .0927297 -0.09 0.929 -.1899655 .1735282 | ca | L1. | .3378001 .0971009 3.48 0.001 .1474858 .5281144 L2. | -.1758988 .0865623 -2.03 0.042 -.3455579 -.0062397 | _cons | .0012444 .0007237 1.72 0.086 -.000174 .0026628 —————————————————————————— End of Question 4 Page 6 of 7 FIN7028/MAY2017 Question 5 A) Answer the following questions. i. What is the order of integration of a stationary long memory process ii. What is the order of integration of a nonstationary long memory process iii. Write the general equations which could describe an ARCH(m) model. Explicitly state any assumptions you would make. (40 marks) B) Consider an ARMA(1,3) process. What are the stationarity conditions (15 marks) C) Answer the following questions. I. What is the i.i.d. bootstrap II. When should we use block bootstrap (15 marks) D) Based on the following STATA output, write the equation for and explain the fitted model. (30 marks) Sample: 1957m2 – 2013m12 Number of obs = 683 Distribution: Gaussian Wald chi2(.) = . Log likelihood = -1934.459 Prob > chi2 = . —————————————————————————— | OPG sp | Coef. Std. Err. z P>|z| [95% Conf. Interval] ————-+—————————————————————- sp | _cons | .6096803 .1566118 3.89 0.000 .3027269 .9166337 ————-+—————————————————————- ARCH | arch | L1. | .1213892 .0267218 4.54 0.000 .0690154 .173763 | garch | L1. | .8361481 .0286658 29.17 0.000 .7799641 .892332 | _cons | .9092731 .3228682 2.82 0.005 .2764631 1.542083 —————————————————————————— END OF EXAMINATION Page 7 of 7