25573 Fitting And Forecasting Time Series Econometrics Assignment

Question 1.

Your employer, a food retailer, needs forecasts of expected restaurant and food sales for the next 12 months. Your employer understands the food and restaurant market, but does not have technical expertise in time series forecasting. You are given the task of constructing these forecasts and reporting the results to your employer. To build your forecasts you have 21 years of monthly observations on the natural log of café and restaurant sales in millions of dollars running from January 1993 to December 2014, lsales, in data file lsales_resid.xls. Café and restaurant sales are highly seasonal, rising strongly around Christmas/New Year. They also trend upwards over time with the growth of the economy. Choose your series based on the group member with the lowest student number.

(a) Graph the lsales series and notice the seasonal pattern and trend in the log of café and restaurant sales. You ask your assistant to remove the time-trend and seasonal influences from the data.  How do you think the assistant could achieve this? What regression would she run? (You do not need to run this regression but just state it)

Your assistant completes this task, and gives you the cleaned data as lsales_resid in file_lsales resid.xls. Notice that these cleaned data are deviations from the trend, which explains the negative figures. (Use the series with the same number as the number allocated to the lowest student number of your group members.) 

(b) You decide to reserve the last 12 months of data to use to evaluate and justify your forecasting model. Using the lsales_resid data to December 2013 only, find a parsimonious AR, MA or ARMA(p,q) model that fits well. Write a brief report on this part of the project, explaining to your employer what you have done, why you have selected the model you have, and what are its strengths and weaknesses as a model. (You can assume that your data is stationary)

(c) Use your preferred estimated model to make point and interval forecasts for each month of the final year of the dataset (January-December 2014). 

• Report the numerical values and plot your forecasts. Compare your forecasts to the actual outcomes for lsales_resid in 2014 and compute the RMSFE. Does the forecasting model perform well? Why or why not? 
• Compare your forecasting model to one that would assume that the trend continued with no deviations ie lsales_resid=0 for each monthly observation in 2014.  Does your time series model improve on this naïve model. 

Write a brief report to your employer on this part of the project, explaining the performance of the forecasting model compared with the actual outcomes for 2014. 

(d) Update the estimation of your fitted model using all the data. Use the updated model to forecast cafe and restaurant sales for the year ahead (2015). Make point forecasts of the level of cafe and restaurant sales for each month in 2015 with 95% confidence intervals. To help you, your assistant gives you the underlying trend projections for the log of cafe and restaurant sales in each month for the coming year. These are given in Table 2.1. Adjust these underlying trend projections with your lsales_resid model forecasts then translate them into millions of dollars. 

• Graph your forecasts with confidence intervals assuming that the projections made by your assistant are correct. Explain your projections to your employer. 
• What is the outlook for restaurant and cafe sales in 2015? How confident can you be in your forecasts? 

Table 2.1

Question 2. 

Use the data on exchange rates (t1 – t8), over a span of 1000 days from DailyExchangeRates_2017.xls Choose the series that matches the student number of the member of your group with the lowest student number. Use the tab ‘series_alocation’ to determine what series this relates to.

(a) What are the conditions for covariance stationarity in a time series?

(b) Are these conditions met in your allocated exchange rate series? Justify your answer using unit root tests.

(c) Given your conclusion for (b), construct a stationary ARMA model of your exchange rate series. Is this model likely to forecast well? Why or why not?