Economic Forecasting

Question 1. The following table shows quarterly data of sales in billion dollars for five years 2016-2020 for a company.

Yr\Qtr Q1 Q2 Q3 Q4
2016 10 14 8 25
2017 16 22 14 35
2018 20 30 19 42
2019 26 34 24 50
2020 34 40 30 55

 

Plot the data and comment on its time series features like trend, seasonality, etc. Apply the double moving average with four periods (DMA-4). Calculate the MPE and comment about systematic bias in forecasting. Also calculate the RMSE of in-sample forecasts. Forecast for the first two quarters of 2021 using DMA-4. Plot the DMA-4 forecast vs actual values and comment on the pattern of the forecasted time series plots. Also plot the errors of DMA-4 and comment.

Question 2. For the data in question 1 apply the Holt-Winters’ triple smoothing (three parameter model) with alpha = 0.2, beta = 0.4 and gamma = 0.4. Calculate MPE and RMSE and compare with the results in Part (A). Forecast for the first two quarters of 2021. Plot the forecasted values vs. actual values as well as the errors and comment.

Question 3. For the data in question 1 perform the Decomposition using Ratio-to-Moving average. Estimate the seasonal coefficients and the de-seasonalized series. Then estimate the Trend using Linear Regression. Finally Forecast for in-sample periods and the first two quarters of 2021. Calculate errors in forecast. Compare its RMSE with the results above. Plot the errors and comment.

Question 4. It was felt by the local utility company that fuel consumption (natural gas) in their small town would be affected by temperature and chill index. The following data was collected for 10 weeks during the winter.

Week Fuel Consumption Y(MMcf) Average Temp

X1 (0F)

Chill Index

X2

1 15.4 30.0 18
2 11.7 28.0 15
3 12.4 32.5 25
4 10.8 39.0 20
5 9.4 40.9 10
6 6.5 50.8 16
7 10.0 40.1 5
8

9

10

9.5

9.0

8.3

50.5

45.0

48.0

0

10

8

 

Conduct a Multiple Regression among Fuel consumption (Y), temperature (X1), and chill index (X2). Solve using excel. What is the multiple regression equation? Interpret the coefficients and predict the fuel consumption when temperature is 35 degrees, and the chill index is 12. Are the coefficients of the multiple regression model statistically significant at alpha = 0.05 and 0.01? How do you know? Discuss indicating the individual test statistics and p-values. What are R2, adjusted R2 and se? Interpret R2 and Adjusted R2 and compare these values. Perform F-test, show the ANOVA table and conclude about the overall statistical significance of the model.