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Sukkur Institute of Business Administration, Sukkur *

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Economics

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Nov 24, 2024

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Question 1 This data house.xlsx . was taken from the Economic Report of the President, 2015 . It ranges from 1974-2014. You are asked to develop a suitable regression model to explain new housing starts, which is a key economic indicator. The data file contains the following variables: • Hstart : New housing starts (thousands) • UN : seasonally adjusted civilian unemployment rate (%) • DM2 : Percentage changes in (Seasonally adjusted) M2 money supply • Mgrate : New home mortgage yield (%) • DGDP : Percentage changes in real gross domestic product Note that home mortgage yield is the effective rate (in the primary market) on conventional mortgages, reflecting fees and charges as well as contract rate and assuming, on the average, repayment at end of 10 years. Import the data to Eviews and look at above variables. （1） [3 marks] Plot the data series using a line chart with Hstart on the right axis and all other variables on the left axis. Briefly comment on the dynamics (peaks and troughs) of the new housing starts. Hint: For plotting multiple data series, select all the data series/ right click/open/as Group. Then click view/Graph. Hint: For plotting data series on different axes, double click the graph, in the Graph Options window, click Axes & Scaling in the Option Pages box, assign left or right axis to each variable in the Series axis assignment box . （2） [3 marks] Estimate the regression model Hstart t =β +β 1 2 UN t +β 3 DM 2 t +β 4 Mgrate t +β 5 DGDP t +ε t (1) by OLS and write down the fitted equation (with the corresponding tstatistic underneath each estimated coefficient, R 2 , and sample size T). （3） [3 marks] Plot the residuals from part (2) vs. time (i.e., line chart). Comment on the dynamics of the residual (i.e., showing pattern of serial correlation or not).

（4） [3 marks] Test that the errors in model (1) are not serially correlated against the alternative that they are autoregressive of order 2 using the BreuschGodfrey test at the 5% significance level. Report the Eviews output and comment on the result. （5） [2 marks] How do serial correlated errors affect OLS estimation results? （6） [3 marks] Estimate model (1) using Newey-West error correction method. Comment on the estimation results in relation to your answer in part (5). （7） [3 marks] What does economic theory suggest about the impact of unemployment rate on new housing starts (positive, negative, or no relationship)? Carefully interpret the OLS estimate of 𝛽𝛽 2 in equation (1). Question 2 The Eviews file btcusd_monthly.wf1 contains the monthly data for the Bitcoin (USD) price from September 2018 to September 2023. (1) [3 marks] Plot the data series and comment on the dynamics (e.g., peak, trough, time series properties) of the data series. (2) [3 marks] Compute the sample ACF and the sample PACF for this series for the first 12 lags using Eviews. Provide the Eviews outputs and comment on the pattern of the correlogram. (3) [4 marks] Consider two models: AR(2): y t = + α α α 01 y t − 1 + 2 y t − 2 + ε t ARMA(1,1): y t = + α α 01 y t − 1 + βε ε 1 t − 1 + t Select the best model out of these two using AIC and SBIC. Provide all the Eviews outputs. Hint: AIC and SBIC of each model are provided as parts of the model estimation output. To estimate the model with the maximum likelihood method : Quick/Estimate Equation/Method: LS-Least Squares (NLS and ARMA) /Options: ARMA → Method: ML

Compare the forecasting performance of the AR(2) and ARMA(1,1) models, with the in-sample period 2018M09 to 2023M03 and out-of-sample period 2023M04 to 2023M09. (4) [2 marks] What are the similarities and differences between a one-step-ahead static and a dynamic forecast? (5) [2 marks] Estimate the AR(2) and ARMA(1,1) models over the period from 2018M09 to 2023M03 using the maximum likelihood method . Hint: To estimate the model with the maximum likelihood method : Quick/Estimate Equation/Method: LS-Least Squares (NLS and ARMA) /Options: ARMA → Method: ML (6) [5 marks] Use the estimation results of each model in (5) to provide a dynamic forecast for the rest of the sample period. Plot the forecasted values, the prediction intervals, and the original time series for the whole sample period in a single graph ( see week 9 tutorial for an example ). Comments on the prediction output. (7) [3 marks] Select a suitable model based on the forecasting exercise conducted in part (6), using root mean square errors. Provide Eviews forecast evaluation results for each model.

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