Create an exceptional smoothing forecast with alpha =0.2 and find the MSE & MAD.

Question

Create an exceptional smoothing forecast with alpha =0.2 and find the MSE & MAD.

Area State_income 2004Q1 25739844 2004Q2 26051804 2004Q3 26148468 2004Q4 26662680 2005Q1 27072828 2005Q2 27434924 2005Q3 27912832 2005Q4 28478792 2006Q1 29361392 2006Q2 29762808 2006Q3 30188004 2006Q4 30586372 2007Q1 31473828 2007Q2 32084344 2007Q3 32364432 2007Q4 32807044 2008Q1 33793200 2008Q2 34006456 2008Q3 33957960 2008Q4 33766452 2009Q1 33015220 2009Q2 33088744 2009Q3 33162128 2009Q4 33182296 2010Q1 33756764 2010Q2 34022020 2010Q3 34267116 2010Q4 35029332 2011Q1 35854088 2011Q2 36437464 2011Q3 36904828 2011Q4 37325484 2012Q1 38325008 2012Q2 38525916 2012Q3 38576316 2012Q4 39584120 2013Q1 39304143 2013Q2 39848594 2013Q3 39978331 2013Q4 40044614

Explanation / Answer

Area State_income Forecast               Ft=Ft-1 +?(At-1 -Ft-1) prediction errors (e) e2 2004Q1 25739844 25739844 0 0 2004Q2 26051804 25739844 311960 9.732E+10 2004Q3 26148468 25802236 346232 1.199E+11 2004Q4 26662680 25871482.4 791197.6 6.26E+11 2005Q1 27072828 26029721.92 1043106.1 1.088E+12 2005Q2 27434924 26238343.14 1196580.9 1.432E+12 2005Q3 27912832 26477659.31 1435172.7 2.06E+12 2005Q4 28478792 26764693.85 1714098.2 2.938E+12 2006Q1 29361392 27107513.48 2253878.5 5.08E+12 2006Q2 29762808 27558289.18 2204518.8 4.86E+12 2006Q3 30188004 27999192.95 2188811.1 4.791E+12 2006Q4 30586372 28436955.16 2149416.8 4.62E+12 2007Q1 31473828 28866838.53 2606989.5 6.796E+12 2007Q2 32084344 29388236.42 2696107.6 7.269E+12 2007Q3 32364432 29927457.94 2436974.1 5.939E+12 2007Q4 32807044 30414852.75 2392191.3 5.723E+12 2008Q1 33793200 30893291 2899909 8.409E+12 2008Q2 34006456 31473272.8 2533183.2 6.417E+12 2008Q3 33957960 31979909.44 1978050.6 3.913E+12 2008Q4 33766452 32375519.55 1390932.4 1.935E+12 2009Q1 33015220 32653706.04 361513.96 1.307E+11 2009Q2 33088744 32726008.83 362735.17 1.316E+11 2009Q3 33162128 32798555.87 363572.13 1.322E+11 2009Q4 33182296 32871270.29 311025.71 9.674E+10 2010Q1 33756764 32933475.43 823288.57 6.778E+11 2010Q2 34022020 33098133.15 923886.85 8.536E+11 2010Q3 34267116 33282910.52 984205.48 9.687E+11 2010Q4 35029332 33479751.61 1549580.4 2.401E+12 2011Q1 35854088 33789667.69 2064420.3 4.262E+12 2011Q2 36437464 34202551.75 2234912.2 4.995E+12 2011Q3 36904828 34649534.2 2255293.8 5.086E+12 2011Q4 37325484 35100592.96 2224891 4.95E+12 2012Q1 38325008 35545571.17 2779436.8 7.725E+12 2012Q2 38525916 36101458.54 2424457.5 5.878E+12 2012Q3 38576316 36586350.03 1989966 3.96E+12 2012Q4 39584120 36984343.22 2599776.8 6.759E+12 2013Q1 39304143 37504298.58 1799844.4 3.239E+12 2013Q2 39848594 37864267.46 1984326.5 3.938E+12 2013Q3 39978331 38261132.77 1717198.2 2.949E+12 2013Q4 40044614 38604572.42 1440041.6 2.074E+12 65763684 1.353E+14 MSE 1.84748E-16 MAD 3.80149E-10

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