Forecasting Homework Problems 1) The following data are US exports to Mexico. Complete the missing values. (24) Month DATE Ratio of Adjusted Seasonally Trend Original 12-month Original to Seasonal Seasonal Adjusted Projection Forecast Series MA MA Index Index Series 13356.8 97.6 13685.3 12253.7 11959.6 112.7 13768.7 12322.1 13892.7 13368.6 12390.5 13349.2 12458.8 13800.3 12527.2 13690.3 VALUE 1 Feb-01 2 Mar-01 15523.7 3 Apr-01 14403.0 4 May-01 15108.0 110.8 5 Jun-01 15051.0 109.3 13772.3 6 Jul-01 11700.0 89.2 13110.5 7 Aug-01 13764.0 101.9 13503.0 12664.0 8 Sep-01 12423.0 104.6 11873.1 12732.4 9 Oct-01 13895.0 110.6 12567.2 12800.8 14153.2 10 Nov-01 13214.0 105.1 12567.9 12869.1 13530.7 11 Dec-01 11319.0 12 Jan-02 12061.5 13 Feb-02 12368.2 14 Mar-02 15 Apr-02 16 May-02 14586.0 13204.1 110.5 17 Jun-02 14214.0 13134.3 18 Jul-02 11607.0 19 Aug-02 20 21 11240.5 12908.8 96.4 11740.1 12937.5 12473.5 94.0 12837.8 13005.9 12219.4 97.6 12672.4 13074.3 12760.4 112.7 12376.4 13142.7 14817.9 13099.4 13211.0 14233.3 110.8 13168.1 13279.4 14709.3 109.3 13006.4 13347.8 14587.1 89.2 13006.3 13416.2 11972.8 101.9 101.9 13649.2 13484.6 13745.2 100.9 104.6 104.6 12743.8 13552.9 14180.7 110.7 110.6 110.6 13297.1 13621.3 15060.4 13340.0 104.3 105.1 105.1 13228.0 13689.7 14393.5 13410.1 90.7 96.4 96.4 12613.4 13758.1 13264.6 13484.9 89.4 94.0 92.3 97.6 13954.0 13271.7 105.1 112.7 14113.0 13247.6 107.7 107.7 108.2 109.3 13126.6 88.4 89.2 13913.0 13139.0 105.9 Sep-02 13334.0 13214.9 Oct-02 14702.0 13282.1 22 Nov-02 13908.0 23 Dec-02 12161.0 24 Jan-03 12889.7 13479.2 95.6 94.0 13719.3 13826.5 12990.4 25 Feb-03 13292.6 13556.2 98.1 97.6 13619.5 13894.8 13561.3 26 Mar-03 15359.6 13673.3 112.3 112.7 13623.1 13963.2 15743.1 27 Apr-03 14646.4 13717.8 106.8 107.7 13594.5 14031.6 15117.3 28 May-03 15208.0 13769.6 110.4 110.8 13729.7 14100.0 15618.2 29 Jun-03 15003.2 13835.4 108.4 109.3 13728.6 14168.4 15483.8 30 Jul-03 12029.5 13870.6 86.7 89.2 13479.7 14236.7 12705.1 31 Aug-03 12989.7 13793.6 94.2 101.9 12743.4 14305.1 14581.6 32 Sep-03 14518.1 13892.3 104.5 104.6 13875.4 14373.5 15039.2 33 Oct-03 15554.6 13963.4 111.4 110.6 14068.3 14441.9 15967.7 34 Nov-03 14598.2 14020.9 104.1 105.1 13884.4 14510.3 15256.2 35 Dec-03 13834.0 14160.3 97.7 96.4 14348.6 14578.6 14055.7 36 Jan-04 13290.8 14193.7 93.6 94.0 14146.2 14647.0 13761.3 37 Feb-04 14341.7 14281.2 100.4 97.6 14694.4 14715.4 14362.2 38 Mar-04 17458.0 14456.0 120.8 112.7 15484.3 14783.8 16668.2 39 Apr-04 16014.0 14570.0 109.9 107.7 14863.9 14852.2 16001.4 40 May-04 16334.0 14663.8 111.4 110.8 14746.2 14920.5 16527.1 41 Jun-04 16438.0 14783.4 111.2 109.3 15041.5 14988.9 16380.6 42 Jul-04 13824.0 14932.9 92.6 89.2 15490.6 15057.3 13437.4 Forecasting Homework Problems 1 43 Aug-04 16060.0 15188.8 105.7 101.9 15755.5 15125.7 15418.1 44 Sep-04 16673.0 15368.4 108.5 104.6 15934.9 15194.1 15897.8 16875.0 45 Oct-04 16975.0 15486.7 109.6 110.6 15352.9 15262.5 46 Nov-04 16772.0 15667.9 107.0 105.1 15951.9 15330.8 16119.0 47 Dec-04 15983.1 15847.0 100.9 96.4 16577.7 15399.2 14846.9 48 Jan-05 15572.3 16037.1 97.1 94.0 16574.6 15467.6 14532.3 49 Feb-05 16127.0 16185.9 99.6 97.6 16523.6 15536.0 15163.0 a) Note that the Adjusted Seasonal Index for March is 112.7. What does this number mean? (10) To estimate the Trend, a regression of the Seasonally Adjusted Series on a trend yielded the following results. SUMMARY OUTPUT Regression Statistics Multiple R 0.803 R Square 0.645 Adjusted R Square 0.638 Standard Error 732 Observations 49 ANOVA Regression Residual Total Intercept Trend df SS MS F 1 47 48 45823881 25186924 71010805 45823881 535892 86 Coefficients 12185.3 68.4 Standard Error 212.4 7.4 t Stat 57.4 9.2 Pvalue 0.0 0.0 Significance F 3.76219E12 Lower 95% 11758.0 53.5 Upper 95% 12612.6 83.3 YOU MAY NEED TO USE THESE REGRESSION RESULTS TO HELP COMPLETE THE TABLE ABOVE Forecasting Homework Problems 2 b) What is your forecast of US Exports to Mexico for March 2005 (which would be the 50th observations)? (10) 2) The following results are an autoregression for US Exports to Mexico where the dependent variable is the lagged value of US Exports. SUMMARY OUTPUT Regression Statistics Multiple R 0.558 R Square 0.311 Adjusted R Square 0.296 Standard Error 1299 Observations 48 ANOVA Regression Residual Total Intercept Lagged Exports df 1 46 47 Coefficients 6300 0.563 SS MS 35017027 35017027 77583215 1686592 112600242 Standard Error 1778 0.124 t Stat 3.54 4.56 F 21 Significance F 3.827E-05 P-value 0.0009192 3.827E-05 Lower 95% 2721 0.315 3) Based on these regression results, what is your forecast of US Exports to Mexico for March 2005? (10) Forecasting Homework Problems 3 Upper 95% 9879 0.812