Problem Set #3 Key. Forecasting

Transcription

1 Problem Set #3 Key Sonoma State University Business 581E Dr. Cuellar The data set bus581e_ps3.dta is a Stata data set containing annual sales (cases) and revenue from December 18, 2004 to April Use Stata and Excel to answer following questions. Your typed answers are due at the beginning of the next class. Answers must be presented in a professional manner for full credit. You may want to export your data into Excel to generate graphs for aesthetic purposes. Forecasting 1. Sales a. Show graphically sales for the entire time span. b. Construct a regression model of sales that accounts for a time trend in sales and seasonal variations. Show and explain your results. Cases = β 0 + β 1time 12 + DMonth k +u i k=2 β k c. Show graphically your predicted results along with your actual sales. Total Cases Sold jan jul jan jul jan2011 Date Actual Predicted

2 d. Re-run your regression on a sub-sample (hold-out sample) of your data. Hold out the last 13 periods. Show and explain your results. Compare with your regression results from the full sample. Full Sample Hold-Out Sample Cases Cases Time [28.66]** [21.39]** February -11, , [8.53]** [7.53]** March -11, , [8.88]** [7.46]** April -11, , [8.46]** [7.12]** May -14, , [11.30]** [9.47]** June -13, , [10.53]** [9.22]** July -14, , [11.68]** [9.99]** August -15, , [11.14]** [9.60]** September -13, , [10.19]** [9.13]** October -12, , [8.89]** [8.00]** November -7, , [5.42]** [4.58]** December [0.35] [0.59] Constant 35, , [34.45]** [31.27]** Observations Adjusted R Absolute value of t-statistics in brackets * significant at 5% level; ** significant at 1% level

3 e. Compare the predictions from your full sample regression with those of the hold-out sample regression. Specifically, compare the difference between actual and predicted results in units and percentage terms. Construct a table as follows: Full Sample Hold-Out Sample Forecast Difference %Difference Forecast Difference %Difference 1-May % % 29-May % % 26-Jun % % 24-Jul % % 21-Aug % % 18-Sep % % 16-Oct % % 13-Nov % % 11-Dec % % 8-Jan % % 5-Feb % % 5-Mar % % 2-Apr % % How well does the hold-out sample compare with the full sample results?

4 f. Use the full sample of data to forecast sales for 13 periods beyond the end of the data. g. Construct a margin of error for your forecast and a 95% confidence interval. Show your results for f & g in a table as follows: Period Forecasted Sales Margin of Error Lower CI Upper CI h. Show your results graphically. Be sure your graph clearly distinguishes between actual and predicted values. You may want to use Excel. Total Cases Sold Date Actual Lower 95% CI Predicted Upper 95% CI

5 30-Apr May Jun Jul Aug Sep Oct Nov Dec-11 7-Jan-12 4-Feb-12 3-Mar Mar-12 Sales (Cases) 70,000 65,000 Forecasted Sales Lower Confidence Interval Upper Confidence Interval Forecast 60,000 55,000 50,000 45,000

6 2. Revenue a. Show graphically revenue for the entire time span. b. Construct a regression model of revenue that accounts for a time trend in revenue and seasonal variations. Show and explain your results. Revenue = β 0 + β 1time 12 + DMonth k +u i k=2 β k c. Show graphically your predicted results along with your actual revenue. Revenue 2.0e e e e+06 01jan jul jan jul jan2011 Date Actual Predicted

7 d. Re-run your regression on a sub-sample (hold-out sample) of your data. Hold out the last 13 periods. Show and explain your results. Compare with your regression results from the full sample. Full Sample Hold-Out Sample Revenue Revenue Time 41, , [31.11]** [24.08]** February [8.55]** [7.48]** March [8.91]** [7.47]** April [8.85]** [7.40]** May [11.58]** [9.59]** June [11.01]** [9.45]** July [12.22]** [10.33]** August [11.52]** [9.82]** September [10.18]** [8.97]** October [8.66]** [7.68]** November -873, , [5.38]** [4.47]** December 2, , [0.02] [0.35] Constant [33.78]** [30.16]** Observations Adjusted R Absolute value of t-statistics in brackets * significant at 5% level; ** significant at 1% level

8 e. Compare the predictions from your full sample regression with those of the hold-out sample regression. Specifically, compare the difference between actual and predicted results in units and percentage terms. Construct a table as above. Full Sample Hold-Out Sample Forecast Difference %Diff Forecast Difference %Diff 1-May-10 $5,433,779 -$345, % $5,498,867 -$410, % 29-May-10 $5,475,671 -$2, % $5,541,220 -$68, % 26-Jun-10 $5,504,585 -$148, % $5,547,628 -$191, % 24-Jul-10 $5,415,987 -$463, % $5,502,856 -$550, % 21-Aug-10 $5,435,953 -$169, % $5,487,857 -$221, % 18-Sep-10 $5,694,820 $154, % $5,681,823 $167, % 16-Oct-10 $5,983,692 $239, % $5,953,824 $269, % 13-Nov-10 $6,556,705 $25, % $6,569,579 $12, % 11-Dec-10 $7,474,368 $157, % $7,469,108 $162, % 8-Jan-11 $7,513,829 $492, % $7,452,746 $553, % 5-Feb-11 $6,223,874 $135, % $6,222,239 $137, % 5-Mar-11 $6,209,375 -$214, % $6,266,118 -$271, % 2-Apr-11 $6,259,975 -$230, % $6,319,460 -$290, %

9 f. Use the full sample of data to forecast sales for 13 periods beyond the end of the data. g. Construct a margin of error for your forecast and a 95% confidence interval. Show your results for f & g in a table as above h. Show your results graphically. Be sure your graph clearly distinguishes between actual and predicted values. You may want to use Excel. Revenue 30-Apr e e e e May Jun Jul Aug Sep Oct Nov Dec-11 7-Jan-12 4-Feb-12 3-Mar Mar-12 Revenue Date Actual Lower 95% CI Predicted Upper 95% CI $9,000,000 $8,500,000 $8,000,000 Forecasted Revenue Lower Confidence Interval Upper Confidence Interval Forecast $7,500,000 $7,000,000 $6,500,000 $6,000,000 $5,500,000 $5,000,000

10 Period Forecasted Revenue Margin of Error Lower CI Upper CI 1 $5,978,371 $219,840 $5,758,530 $6,198,211 2 $6,007,285 $251,874 $5,755,411 $6,259,159 3 $5,918,687 $247,349 $5,671,338 $6,166,037 4 $5,938,653 $265,711 $5,672,941 $6,204,364 5 $6,197,520 $265,711 $5,931,809 $6,463,232 6 $6,486,392 $265,711 $6,220,680 $6,752,103 7 $7,059,404 $265,711 $6,793,693 $7,325,116 8 $7,977,068 $258,906 $7,718,162 $8,235,973 9 $8,016,529 $258,906 $7,757,623 $8,275, $6,726,574 $258,906 $6,467,668 $6,985, $6,712,075 $258,906 $6,453,170 $6,970, $6,762,675 $258,906 $6,503,769 $7,021, $6,481,071 $236,769 $6,244,302 $6,717,839 Use the data set bus581e_ps1 to answer the following questions. 3. Trend Analysis a. Show graphically total cases sold by period for the duration of the data set. b. Calculate the percentage growth rate of total sales using regression analysis. c. Show graphically total cases sold of chardonnay by period for the duration of the data set. d. Calculate the percentage growth rate of total chardonnay sales using regression analysis. Has the growth rate of chardonnay sales been above or below total sales? e. Show graphically total cases of merlot sold by period for the duration of the data set. f. Calculate the percentage growth rate of total merlot sales using regression analysis. Has the growth rate of merlot sales been above or below total sales? g. Show graphically total cases sold of cabernet sauvignon by period for the duration of the data set. h. Calculate the percentage growth rate of total cabernet sauvignon sales using regression analysis. Has the growth rate of merlot sales been above or below total sales? i. Show graphically total cases sold, chardonnay, merlot and cabernet sauvignon sales together. Describe your graph. Regression Results Total Chardonnay Merlot Cabernet Sauvignon time [13.31]** [18.59]** [5.11]** [22.18]** Constant [324.46]** [435.15]** [212.46]** [174.12]** Observations Adjusted R-squared Absolute value of t-statistics in brackets * significant at 5% level; ** significant at 1% level Annual Growth Rate 11.83% 10.65% 6.02% 28.82% Compounding Annual Growth Rate 11.23% 10.16% 5.86% 25.57% Not Compounding

11 Cases Sold Per 4-week ending period 70,000 Total 60,000 50,000 40,000 30,000 20,000 10, week ending period

12 Cases Sold Per 4-week ending period 16,000 Chardonnay 14,000 12,000 10,000 8,000 6,000 4,000 2, week ending period

13 Cases Sold Per 4-week ending period 18,000 16,000 Merlot 14,000 12,000 10,000 8,000 6,000 4,000 2, week ending period

14 Cases Sold Per 4-week ending period 12,000 Cabernet Sauvignon 10,000 8,000 6,000 4,000 2, week ending period

15 Cases Sold Per 4-week ending period 70,000 60,000 Chardonnay Merlot Total CB-S 50,000 40,000 30,000 20,000 10, week ending period

16 Indexed Cases Sold Per 4-week ending period 4. Indexing Trends a. Index total cases sold for the duration of the period and re-graph. Be sure that indexed cases sold are zero in the first period. Interpret your graph. b. Index total cases sold of chardonnay for the duration of the period and re-graph. Be sure that indexed cases sold are zero in the first period. Interpret your graph. c. Index total cases sold of merlot for the duration of the period and re-graph. Be sure that indexed cases sold are zero in the first period. Interpret your graph. d. Index total cases sold of cabernet sauvignon for the duration of the period and re-graph. Be sure that indexed cases sold are zero in the first period. Interpret your graph. e. Show graphically indexed total cases sold, indexed chardonnay, indexed merlot sales and indexed cabernet sauvignon sales together. Interpret your graph Chardonnay Merlot Total CB-S week ending period