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College of Business City University of Hong Kong EF3451 Economic and Business Forecasting Semester A 2017-18 Homework 1 Due week 6 (13th October 2017) in class Write down your full name and student ID number Question 1: Using 30 annual observations on time series data, a forecaster obtained the following regression using the ordinary least squares method: ln Yt 1.31 0.27 ln X 1t 0.53ln X 2t 0.82 ln X 3t (0.17) (0.21) (0.30) R 2 0.615 , DW 0.496 , where figures in brackets below parameter estimates are the corresponding estimated standard errors; Yt= number of business failures; X1t = volume of industrial production; X2t = short term interest rate; X3t = value of new business orders placed. Which of the following statements is true, which is false, and why? (a) The estimated partial regression coefficient on ln X 2t , 0.53, is interpreted as: all else remaining the same, one unit change in the short term interest rate leads to an expected 0.53 increase in business failures. (3 marks) (b) The value of R 2 will decline considerably if X 2t or X 3t is dropped. (3 marks) (c) There appears to be some problem with serial correlation in the error term. (4 marks) Question 2: Suppose that the annual revenues of world's two top oil producers have a covariance of 1,735,492. (a) Based on the covariance, the claim is made that the revenues are \"very strongly positively related.\" Evaluate the claim. (3 marks) (b) Suppose instead that, again based on the covariance, the claim is made that the revenues are \"positively related.\" Evaluate the claim. (3 marks) (c) Suppose you learn that the revenues have a correlation of 0.93. In light of that new information, re-evaluate the claims in parts a and b above. (4 marks) 1 Question 3: Given the regression model, yt 0 1 xt 2 xt 2 3 zt t iid t (0, 2 ) Find the mean and variance of yt conditional on xt xt * , zt zt * . Does the conditional mean adapt to the conditioning information? Does the conditional variance adapt to the conditioning information? (10 marks) 4. Computer Application The file HKGDP contains Hong Kong nominal GDP (hkgdp) and Hong Kong real GDP (hkrgdp) data from 1973Q1 to 2016Q2. This problem deals with the Hong Kong nominal GDP (hkgdp) data. a. Plot hkgdp and its log. What are the key features of the data? (3 marks) b. Model the log hkgdp with trend (Linear or Quadratic trend) and seasonality models. Use the data from 1973Q1 to 2014Q4 used for model selection and estimation, and the data from 2015Q01 to 2016Q2 reserved for forecast evaluation. In the model selection part, you should try to extend the lecture notes example by adding more lagged dependent variables to the regression, i.e. loghkgdp(-1), loghkgdp (-2), loghkgdp (-3), ... , and make use of the Schwarz model selection criterion to choose the best model. (4 marks) c. Now re-estimate your best model again with all data up to 2016Q2. This time you will make a true out-of-sample forecast of log hkgdp for 2016Q3 - 2017Q2, a real application of forecasting. (3 marks) Note: To make true out-of-sample forecast in E-Views, you need to ensure the data range specified in the workfile does cover the forecast period, even though your data ends earlier. You have to reset the data range to 2017Q2 so as to make out-ofsample forecast for 2016Q3 - 2017Q2. 2