Zhenhao Gong Homework 3 Econ 3313 Spring 2021
Question 1 (Calculating forecasts from trend models) (1 point)
You work for the International Monetary Fund in Washington DC, monitoring Singapore’s real consumption expenditures. Using a sample of real consumption data (measured in bil- lions of 2005 Singapore dollars), yt, t = 1990 : Q1, · · · , 2006 : Q4, (where Q1 is the first quarter and there are four quarters in a year), you estimate the linear consumption trend model, yt = β0 + β1TIMEt + εt, where εt ∼ N(0,σ2). By the OLS method, you obtain the estimates βˆ0 = 0.51, βˆ1 = 2.30, and σˆ2 = 16. Based upon your estimated trend model, construct feasible point, interval and density forecasts for 2010:Q1.
Question 2 (Understanding model selection criteria) (1 point)
You are tracking and forecasting the earnings of a new company developing and applying proprietary nano-technology. The earnings are trending upward. You fit linear, quadratic, and exponential trend models, yielding sums of squared residuals of 4352, 2791, and 2749, respectively. Which trend model would you select, and why?
Question 3 (Outliers) (1 point)
Recall the lower-left panel of the multiple comparison plot of the Anscombe data in our lecture note 8, which made clear that dataset number three contained a severely anomalous observation. We call such data points “outliers.”
1. Outliers require special attention because they can have substantial influence on the fitted regression line. Regression parameter estimates obtained by least squares are particularly susceptible to such distortions. Why?
2. Outliers can arise for a number of reasons. Perhaps the outlier is simply a mistake due to a clerical recording error, in which case you’d want to replace the incorrect data with the correct data. We’ll call such outliers measurement outliers, because they simply reflect measurement errors. If a particular value of a recorded series is plagued by a measurement outlier, there’s no reason why observations at other times should necessarily be affected. But they might be affected. Why?
3. How to identify and treat outliers is a time-honored problem in data analysis, and there’s no easy answer. What factors would you, as a forecaster, examine when deciding what to do with an outlier?
1
Zhenhao Gong Homework 3 Econ 3313 Spring 2021
Question 4 (Graphical analysis of foreign exchange rate data) (1 point)
Magyar Select, a marketing firm representing a group of Hungarian wineries, is considering entering into a contract to sell 8,000 cases of premium Hungarian dessert wine to AMI Imports, a worldwide distributor based in New York and London. The contract must be signed now, but payment and delivery is 90 days hence. Payment is to be in U.S. Dollars; Magyar is therefore concerned about U.S. Dollar / Hungarian Forint ($/Ft) exchange rate volatility over the next 90 days. Magyar has hired you to analyze and forecast the exchange rate, on which it has collected data for the last 502 days. Naturally, you suggest that Magyar begin with a graphical examination of the data.
1. Why might we be interested in examining data on the log rather than the level of the $/Ft exchange rate?
2. Take logs and produce a time series plot of the log of the $/Ft exchange rate. Discuss.
3. Produce a time series plot of the change in the log $/Ft exchange rate, and also pro- duce a histogram, normality test, and other descriptive statistics. Discuss. Do the log exchange rate changes appear normally distributed? If not, what is the nature of the deviation from normality?
(Please attach the graphs generated by R with your answers.)
2
Zhenhao Gong Homework 3 Econ 3313 Spring 2021
Question 5 (Empirical Exercises) (1 point)
The data set ”DataLiquor” contains the volume of U.S. liquor sales from 1987.01-2014.12. We use this data set to do the following tasks. (You may want to answer this question after the R Lab session 5 in Next Tuesday.)
1. Produce a time series plot of it. Discuss.
2. Fit log linear, log quadratic trend models to your series. Discuss the associated diag- nostic statistics and residual plots.
Hint: you can generate the regressor TIMEt in the trend model by the following code: TIME=data.frame(c(1:336))
3. Select a trend model using the AIC and using the SIC. Do the selected models agree? If not, which do you prefer?
4. Use your preferred model to forecast the liquor sales on 2015.01 and construct a 95% forecasting interval for the estimation.
(Please attach the R codes and graphs for this question.)
3