Holt-WintersQuarterly data on Intel sales ($ millions)M:==>4alpha0.2Change values of alpha, beta and gamma and see the effects. Also notice that in this case MAD and MAPE results for Holt-Winters method is far superior to simple exponential smoothingbeta0.2QuarterSalesLtTtStFtExponentialgamma0.1Q1-86280.05280.05Holt-wintersExponentialQ2-86305.18305.1825.121330.3019990921285.0787998199MAD291.084217216652.7483399417Q3-86324.14325.27719917323.89099960330.9964946819347.944253181292.890439682MAPE8.18%21.70%Q4-86355.64350.462958869924.1499516221.0147777111380.148831876305.4407515945Q1-87394.53378.59692839224.9467552021.0420924482420.5298251957323.2592012741Q2-87438.96410.626146750126.36324783321.0689918381467.1380961332346.3985608942Q3-87501.13450.169673963228.99930370921.0081650179483.0814009378377.3444485765Q4-87572.49496.165409422632.39859005931.028682429543.7244988886416.3731586537Q1-88635.81544.876265653235.66104329351.0545715305612.2181184067460.2599267642Q2-88726.68600.386544444939.63089039321.0831285111693.2211313018513.5445411428Q3-88784.94667.730320738545.17346757321.0249018119730.6563843488567.8234327495Q4-88727.34711.734991758944.93970826271.0280067166777.8666738983599.7267458486Q1-89713.08740.576294980441.72002725441.0454019582817.8141071794622.3979963341Q2-89747.34763.833055899738.02737398741.0726560185860.1204161028647.3857970459Q3-89771.44792.027252275536.06073846511.0198120671844.4941255421672.1962375818Q4-89894.97836.588904471537.76092121131.0321851112902.4908720484716.7519897602Q1-90894.46870.601980948737.01135226451.0436018225947.1869287101752.2929915732Q2-90968.30906.633353508736.81535632361.07219224511011.5583902979795.4945929961Q3-901012.44953.313394252738.78829320771.02403318651015.9450523213838.8838743938Q4-901046.07996.3727055439.64249682361.03395492331071.1930191352880.3220989047Q1-911132.781045.902238853841.61990412161.04754793871139.2315791667930.8132790994Q2-911252.691103.685884016244.85265232981.07847324881238.6680866205995.1878226813Q3-911187.701150.796553390645.30425573871.02483690261225.80824843971033.6908579681Q4-911205.451190.053094242944.09471276141.03185314671273.45929810571068.042485874Q1-921241.291224.308067394342.12676483941.04418028991322.386290281102.6921880095Q2-921319.691257.881427513140.41608389531.07553986631396.37073188641146.0923498033Q3-921426.171316.958783131344.14833823991.03064566751402.81915767151202.107279806Q4-921856.831448.78826702661.68456737081.05683238431596.31660700871333.0524231185Q1-932023.561595.966314840878.78326345961.06655434791786.2114443881471.1537381164Q2-932129.561735.798000630490.99294792561.0906706621992.42729313211602.8349900048Q3-932239.851896.0822354128104.8512052971.04571142012092.39894981861730.2375919184Q4-932389.032052.8587492483115.23626700471.06752505332314.4957477421861.996672961Q1-942660.002233.2785363291128.27297101991.07900631312548.12898523982021.5973383688Q2-942770.002397.1855554616135.39978064241.09715576882778.64061138472171.277870695Q3-942863.002573.6380754202143.61032850571.0523835812859.58760579532309.622296556Q4-943228.002778.5620474451155.87305720951.07694774743160.2332758072493.2978372448Q1-953557.003006.8584059482170.35771746821.08940190733461.26530480412706.0382697959Q2-953894.003251.6082951052185.2361518061.1071963143805.26150334752943.6306158367Q3-954171.003542.1523106248206.29772454871.0648984883991.71877474543189.1044926694Q4-954580.003849.3119720226226.47011191851.08823527484435.40983599823467.2835941355Q1-964644.004113.2035759694233.95441032421.09336641274753.03653311743702.6268753084Q2-964621.004312.4473760265227.01228827081.10363161335009.89119303153886.3015002467Q3-965142.004597.2935838103238.57907217341.0702570545175.62682254424137.4412001974Q4-966440.005052.265713403281.85768365721.10687931075904.2308287194597.9529601579Q1-976448.005446.7752270465304.38804965451.10241174496340.14994286594967.9623681263Q2-975960.005681.0011680762290.35562792951.09817953766557.62184532565166.369894501Q3-976155.005927.2764076037281.53955024911.06707330876625.26178729295364.0959156008Q4-976507.006142.7907057897268.33449983651.10212043227065.83208270575592.6767324807Q1-986001.006217.6040953068229.63027777261.08868684757019.01926482535674.3413859845Q2-985927.006237.2102698499187.62545712671.08338804196960.59019789125724.8731087876Q3-986731.006401.4501327424182.94833827991.0655140287015.76893714155926.0984870301Q4-987614.006649.2189571863195.91243551271.10641807887573.57712448626263.6787896241Q1-997103.006780.9798843846183.08213384981.08456703577552.9920992526431.5430316993Q2-996746.006816.6021086135153.59015192561.07401350027486.08058654376494.4344253594Q3-997328.006951.6401571967149.87973125711.06437659717558.69157323276661.1475402875Q4-998212.007165.6457402317162.70490161271.11037864318137.24404166786971.31803223Q1-007993.007336.6327427453164.36132179291.08505676958139.00438781467175.654425784Q2-008300.007546.3996595357173.44244079241.07659837378311.16945045147400.5235406272Q3-008731.007816.4584175908192.76570424491.06963914148566.9796132077666.6188325018Q4-008702.007974.7725563848185.87539115471.10845987839045.75083044077873.6950660014Q1-016677.007759.2373743257105.5932765121.06260336398357.19550618147634.3560528011

Holt-Winters

SalesFtHolt-Winters

Regression

SalesExponentialExponential smoothing

QuarterSaleslog sales)tQ1Q2Q3Q4predicted value of Log(sales)predicted salesQ1-86280.052.4472417799110002.5415322623347.9623556932MAD557.9330975753Q2-86305.182.4845532218201002.5779557929378.404064801MAPE13.37%Q3-86324.142.5107286071300102.6046599952402.4018745959Q4-86355.642.551013043400012.6452566355441.8314595629Q1-87394.532.5960833348510002.6436173242440.1668424014Q2-87438.962.6424209891601002.6800408548478.6751199666Q3-87501.132.6999486686700102.7067450571509.0319674507Q4-87572.492.757766387800012.7473416974558.9097649428Q1-88635.812.8033253045910002.7457023861556.8040507245Q2-88726.682.86134499961001002.7821259167605.5164090152Q3-88784.942.89483590731100102.808830119643.917337977Q4-88727.342.86173747121200012.8494267593707.011958038Q1-89713.082.85314008191310002.847787448704.3482630626Q2-89747.342.87351648431401002.8842109785765.9686210811Q3-89771.442.88730102771500102.9109151808814.5451850968Q4-89894.972.95181090331600012.9515118212894.3588753722Q1-90894.462.95155946661710002.9498725098890.989343619Q2-90968.302.98601037981801002.9862960404968.9381158722Q3-901012.443.00536972411900103.01300024271030.3866962938Q4-901046.073.01956282182000013.0535968831131.3497443193Q1-911132.783.05414480582110003.05195757171127.0873402749Q2-911252.693.09784222272201003.08838110231225.6912966811Q3-911187.703.07470785312300103.11508530461303.422773008Q4-911205.453.08114884012400013.15568194491431.1394220118Q1-921241.293.09387360532510003.15404263361425.7475487286Q2-921319.693.12047291212601003.19046616421550.4799843771Q3-921426.173.15417038312700103.21717036651648.8090648945Q4-921856.833.2687728452800013.25776700681810.3685933732Q1-932023.563.3061158712910003.25612769551803.5479594773Q2-932129.563.32828988033001003.2925512261961.3325055529Q3-932239.853.35021854733100103.31925542832085.7172275766Q4-932389.033.37822214823200013.35985206872290.0874600076Q1-942660.003.42488163663310003.35821275732281.4594666745Q2-942770.003.44247976913401003.39463628792481.0544064416Q3-942863.003.4568213483500103.42134049022638.3991003154Q4-943228.003.50893352613600013.46193713052896.9241919473Q1-953557.003.55108386523710003.46029781922886.0099176887Q2-953894.003.59039594723801003.49672134983138.4943400957Q3-954171.003.62024018983900103.52342555213337.5328738275Q4-954580.003.6608654784000013.56402219243664.5630005159Q1-964644.003.66689221114110003.56238288113650.7566172709Q2-964621.003.66473596854201003.59880641173970.1453935225Q3-965142.003.71113207234300103.6255106144221.9259711496Q4-966440.003.80888586744400013.66610725434635.61387698Q1-976448.003.80942502884510003.66446794294618.149021893Q2-975960.003.77524625974601003.70089147355022.1707410271Q3-976155.003.78922805734700103.72759567585340.6691648331Q4-976507.003.81338080674800013.76819231625863.9777821871Q1-986001.003.77822362684910003.76655300485841.8850184416Q2-985927.003.77283492725001003.80297653546352.9660634544Q3-986731.003.82807959065100103.82968073776755.8615009141Q4-987614.003.88161287255200013.8702773787417.8385738169Q1-997103.003.85144181475310003.86863806677389.8915792681Q2-996746.003.82904633695401003.90506159738036.4009677516Q3-997328.003.86498546075500103.93176579968546.0572843703Q4-998212.003.91444894075600013.97236243999383.4477467416Q1-007993.003.9027098135710003.97072312869348.095243392Q2-008300.003.91907809245801004.007146659210165.9193311292Q3-008731.003.94106398825900104.033850861410810.6264608676Q4-008702.003.9396190796000014.074447501811869.9120693488Q1-016677.003.82458137626110004.072808190411825.1917152192SUMMARY OUTPUTRegression StatisticsMultiple R0.9872616176R Square0.9746855015Adjusted R Square0.9728773231Standard Error0.0756357636Observations61ANOVAdfSSMSFSignificance FRegression412.33495579013.0837389475539.0427560590Residual560.32036304940.0057207687Total6012.6553188395CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%Intercept2.54317157370.026299497496.700386788802.49048738452.59585576282.49048738452.5958557628t0.02552126550.000550460646.363477633700.02441856120.02662396970.02441856120.0266239697Q1-0.02716057680.0271888881-0.99895871840.3221117802-0.08162642830.0273052747-0.08162642830.0273052747Q2-0.01625831170.0276402097-0.5882123130.5587546941-0.07162826840.0391116451-0.07162826840.0391116451Q3-0.01507537490.027623761-0.54573940370.587412543-0.07041238090.0402616312-0.07041238090.0402616312RESIDUAL OUTPUTObservationPredicted log sales)Residuals12.5415322623-0.094290482422.5779557929-0.093402571132.6046599952-0.093931388142.6452566355-0.094243592652.6436173242-0.047533989462.6800408548-0.037619865772.7067450571-0.006796388582.74734169740.010424689692.74570238610.0576229184102.78212591670.079219083112.8088301190.0860057883122.84942675930.0123107119132.8477874480.0053526339142.8842109785-0.0106944943152.9109151808-0.0236141532162.95151182120.0002990821172.94987250980.0016869568182.9862960404-0.0002856606193.0130002427-0.0076305186203.053596883-0.0340340612213.05195757170.0021872341223.08838110230.0094611204233.1150853046-0.0403774515243.1556819449-0.0745331048253.1540426336-0.0601690282263.1904661642-0.0699932521273.2171703665-0.0629999834283.25776700680.0110058382293.25612769550.0499881756303.2925512260.0357386542313.31925542830.0309631189323.35985206870.0183700796333.35821275730.0666688793343.39463628790.0478434811353.42134049020.0354808578363.46193713050.0469963955373.46029781920.090786046383.49672134980.0936745974393.52342555210.0968146378403.56402219240.0968432856413.56238288110.10450933423.59880641170.0659295569433.6255106140.0856214584443.66610725430.1427786131453.66446794290.1449570859463.70089147350.0743547862473.72759567580.0616323814483.76819231620.0451884906493.76655300480.0116706219503.8029765354-0.0301416082513.8296807377-0.0016011471523.8702773780.0113354945533.8686380667-0.017196252543.9050615973-0.0760152604553.9317657996-0.0667803389563.9723624399-0.0579134992573.9707231286-0.0680133156584.0071466592-0.0880685668594.0338508614-0.0927868732604.0744475018-0.1348284228614.0728081904-0.2482268142

Farid Alizadeh:For Holt-Winters method the formulas are different for the first cycle (bordered red) and the rest of the cycles.

salespredicted salesSales

Log(sales)predicted Log(sales)Log of sales

Farid Alizadeh:Here we assume that sales are exponential growth with respect to time. Thus we take log (base 10 here, but any other bases will do) We then create four columns representing the dummy that is 0-1) variables for each quarter. Then we use multiple regression with log sales) as dependent variable, and time and three of the four dummy variables (in this case Q1-Q3) as independent variables. The regression produces coefficients of the equation we then use these variables to get predicted values of log sales) and then raise 10 to these values to get the predicted sales.