Exponential Smoothing USD/CAD FX

*Unverified author*

R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Wed, 18 May 2011 19:09:54 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/18/t130574565177wg2hhp773c9um.htm/, Retrieved Wed, 18 May 2011 21:07:35 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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1.0086 1.0126 1.0158 1.0026 1.0030 0.9880 0.9831 0.9890 0.9972 1.0000 1.0039 0.9999 0.9800 0.9654 0.9809 0.9862 0.9986 1.0220 1.0309 1.0176 0.9953 0.9791 0.9776 0.9923 1.0298 1.0526 1.0698 1.1018 1.1133 1.1274 1.1438 1.1786 1.1865 1.1581 1.1666 1.1750 1.1642 1.1706 1.1587 1.1841 1.1936 1.1987 1.2116 1.1917 1.2090 1.2448 1.2500 1.2316 1.2276 1.2313 1.2329 1.2385 1.2554 1.2927 1.3139 1.3186 1.3542 1.3697 1.3601 1.3796 1.4041 1.3845 1.3855 1.3850 1.3380 1.3330 1.3224 1.3113 1.2676 1.2301 1.2193 1.2068 1.1919 1.1933 1.1826 1.1686 1.1828 1.1706 1.1534 1.1613 1.1560 1.1491 1.1438 1.1349 1.1775 1.1942 1.2019 1.2617 1.2617 1.2703 1.3038 1.3248 1.3414 1.3825 1.3716 1.3681 1.4071 1.3715 1.3558 1.3562 1.3692 1.3648 1.3704 1.3504 1.3592 1.3863 1.3851 1.4089 1.4303 1.4468 1.5144 1.5430 1.5116 1.4729 1.4864 1.4724 1.4535 1.4805 1.4823 1.5257 1.5278 1.5411 1.5462 1.5809 1.5946 1.5545 1.5637 1.5696 etc...

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Herman Ole Andreas Wold' @ www.yougetit.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.999926986355262 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 1.0126 1.0086 0.004 3 1.0158 1.01259970794542 0.00320029205457906 4 1.0026 1.01579976633501 -0.013199766335013 5 1.003 1.00260096376305 0.000399036236950145 6 0.988 1.00299997086491 -0.01499997086491 7 0.9831 0.988001095202544 -0.00490109520254389 8 0.989 0.983100357846824 0.00589964215317607 9 0.9972 0.988999569245624 0.00820043075437626 10 1 0.997199401256662 0.00280059874333782 11 1.0039 0.999999795518078 0.00390020448192174 12 0.9999 1.00389971523186 -0.00399971523185561 13 0.98 0.999900292033787 -0.0199002920337871 14 0.9654 0.980001452992853 -0.0146014529928526 15 0.9809 0.965401066105302 0.0154989338946985 16 0.9862 0.980898868366347 0.00530113163365309 17 0.9986 0.986199612945058 0.012400387054942 18 1.022 0.998599094602545 0.023400905397455 19 1.0309 1.02199829141461 0.0089017085853933 20 1.0176 1.03089935005381 -0.0132993500538117 21 0.9953 1.01760097103402 -0.0223009710340202 22 0.9791 0.995301628275176 -0.0162016282751763 23 0.9776 0.97910118293993 -0.00150118293993096 24 0.9923 0.977600109606838 0.0146998903931621 25 1.0298 0.992298926707425 0.0375010732925749 26 1.0526 1.02979726190996 0.0228027380900426 27 1.0698 1.05259833508898 0.017201664911018 28 1.1018 1.06979874404375 0.0320012559562504 29 1.1133 1.10179766347167 0.0115023365283338 30 1.1274 1.11329916017249 0.0141008398275129 31 1.1438 1.12739897044629 0.0164010295537098 32 1.1786 1.14379880250105 0.0348011974989453 33 1.1865 1.17859745903773 0.00790254096227061 34 1.1581 1.18649942300668 -0.0283994230066817 35 1.1666 1.15810207354538 0.00849792645461789 36 1.175 1.16659937953542 0.00840062046458323 37 1.1642 1.17499938664008 -0.010799386640082 38 1.1706 1.16420078850258 0.00639921149742073 39 1.1587 1.17059953277025 -0.0118995327702454 40 1.1841 1.15870086882826 0.0253991311717416 41 1.1936 1.18409814551686 0.00950185448314 42 1.1987 1.19359930623497 0.00510069376502775 43 1.2116 1.19869962757976 0.0129003724202423 44 1.1917 1.21159905809679 -0.0198990580967913 45 1.209 1.19170145290276 0.0172985470972415 46 1.2448 1.20899873697003 0.0358012630299722 47 1.25 1.2447973860193 0.00520261398070021 48 1.2316 1.24999962013819 -0.0183996201381911 49 1.2276 1.23160134342333 -0.00400134342332814 50 1.2313 1.22760029215267 0.00369970784733287 51 1.2329 1.23129972987085 0.00160027012915442 52 1.2385 1.23289988315845 0.00560011684155448 53 1.2554 1.23849959111506 0.0169004088849416 54 1.2927 1.25539876603955 0.0373012339604502 55 1.3139 1.29269727650096 0.0212027234990448 56 1.3186 1.31389845191188 0.00470154808812095 57 1.3542 1.31859965672284 0.0356003432771619 58 1.3697 1.35419740068918 0.0155025993108167 59 1.3601 1.36969886809872 -0.00959886809872113 60 1.3796 1.36010070084835 0.0194992991516547 61 1.4041 1.3795985762851 0.0245014237149008 62 1.3845 1.40409821106175 -0.0195982110617532 63 1.3855 1.38450143093682 0.000998569063179966 64 1.385 1.38549992709083 -0.000499927090833019 65 1.338 1.3850000365015 -0.0470000365014989 66 1.333 1.33800343164397 -0.00500343164396799 67 1.3224 1.33300036531878 -0.0106003653187805 68 1.3113 1.32240077397131 -0.0111007739713076 69 1.2676 1.31130081050797 -0.0437008105079668 70 1.2301 1.26760319075545 -0.0375031907554533 71 1.2193 1.23010273824465 -0.0108027382446463 72 1.2068 1.21930078874729 -0.0125007887472923 73 1.1919 1.20680091272815 -0.0149009127281485 74 1.1933 1.19190108796995 0.00139891203005171 75 1.1826 1.19329989786033 -0.0106998978603339 76 1.1686 1.18260078123854 -0.0140007812385412 77 1.1828 1.16860102224807 0.0141989777519327 78 1.1706 1.18279896328088 -0.0121989632808828 79 1.1534 1.17060089069077 -0.0172008906907715 80 1.1613 1.15340125589972 0.00789874410027802 81 1.156 1.1612994232839 -0.00529942328390454 82 1.1491 1.15600038693021 -0.00690038693020889 83 1.1438 1.1491005038224 -0.00530050382239988 84 1.1349 1.1438003870091 -0.0089003870091029 85 1.1775 1.1349006498497 0.0425993501503048 86 1.1942 1.17749688966618 0.016703110333818 87 1.2019 1.19419878044504 0.00770121955496395 88 1.2617 1.20189943770589 0.0598005622941087 89 1.2617 1.26169563374299 4.36625701039084e-06 90 1.2703 1.2616999996812 0.00860000031879626 91 1.3038 1.27029937208263 0.0335006279173682 92 1.3248 1.30379755399705 0.021002446002945 93 1.3414 1.32479846653487 0.016601533465131 94 1.3825 1.34139878786153 0.0411012121384666 95 1.3716 1.3824969990507 -0.0108969990506989 96 1.3681 1.37160079562962 -0.00350079562961714 97 1.4071 1.36810025560585 0.0389997443941514 98 1.3715 1.40709715248652 -0.035597152486518 99 1.3558 1.37150259907785 -0.0157025990778454 100 1.3562 1.35580114650399 0.000398853496009766 101 1.3692 1.35619997087825 0.0130000291217474 102 1.3648 1.36919905082049 -0.00439905082049208 103 1.3704 1.36480032119073 0.00559967880926626 104 1.3504 1.37039959114704 -0.0199995911470408 105 1.3592 1.35040146024304 0.008798539756957 106 1.3863 1.35919935758654 0.0271006424134561 107 1.3851 1.38629802128332 -0.00119802128332291 108 1.4089 1.3851000874719 0.0237999125280997 109 1.4303 1.40889826228164 0.021401737718358 110 1.4468 1.43029843738113 0.0165015626188747 111 1.5144 1.44679879516077 0.0676012048392305 112 1.543 1.51439506418965 0.0286049358103539 113 1.5116 1.54299791144938 -0.031397911449379 114 1.4729 1.51160229247595 -0.0387022924759519 115 1.4864 1.47290282579543 0.0134971742045666 116 1.4724 1.48639901452212 -0.0139990145221178 117 1.4535 1.47240102211907 -0.0189010221190729 118 1.4805 1.45350138003251 0.0269986199674859 119 1.4823 1.48049802873235 0.0018019712676467 120 1.5257 1.48229986843151 0.04340013156849 121 1.5278 1.52569683119821 0.00210316880178785 122 1.5411 1.52779984643998 0.0133001535600195 123 1.5462 1.54109902890731 0.00510097109268703 124 1.5809 1.54619962755951 0.0347003724404913 125 1.5946 1.58089746639933 0.0137025336006658 126 1.5545 1.59459899952808 -0.0400989995280798 127 1.5637 1.55450292777411 0.00919707222589428 128 1.5696 1.56369932848824 0.00590067151176399 129 1.5099 1.56959956917047 -0.0596995691704667 130 1.3982 1.50990435888313 -0.111704358883134 131 1.3806 1.39820815594238 -0.0176081559423753 132 1.316 1.38060128563564 -0.0646012856356424 133 1.3181 1.31600471677532 0.002095283224681 134 1.3596 1.31809984701574 0.0415001529842649 135 1.3078 1.35959696992257 -0.0517969699225733 136 1.2209 1.30780378188556 -0.0869037818855605 137 1.227 1.22090634516186 0.00609365483814295 138 1.2439 1.22699955508005 0.0169004449199495 139 1.2016 1.24389876603692 -0.0422987660369187 140 1.1735 1.20160308838708 -0.0281030883870763 141 1.1545 1.17350205190891 -0.0190020519089114 142 1.1226 1.15450138740907 -0.0319013874090674 143 1.1212 1.12260232923657 -0.00140232923656702 144 1.1392 1.12120010238917 0.0179998976108313 145 1.1718 1.13919868576187 0.0326013142381294 146 1.0984 1.17179761965922 -0.0733976196592243 147 1.0449 1.09840535902773 -0.0535053590277266 148 0.9816 1.04490390662128 -0.0633039066212755 149 1.0038 0.981604622048949 0.0221953779510514 150 1.0099 1.00379837943456 0.0061016205654405 151 1.0416 1.00989955449844 0.0317004455015564 152 1.2118 1.04159768543493 0.170202314565066 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 153 1.21178757290867 1.15274384915061 1.27083129666673 154 1.21178757290867 1.12829018627691 1.29528495954043 155 1.21178757290867 1.10952582134216 1.31404932447518 156 1.21178757290867 1.09370659182973 1.32986855398761 157 1.21178757290867 1.07976950463133 1.34380564118601 158 1.21178757290867 1.06716937692076 1.35640576889658 159 1.21178757290867 1.05558233973797 1.36799280607937 160 1.21178757290867 1.04479737221106 1.37877777360628 161 1.21178757290867 1.0346678975811 1.38890724823624 162 1.21178757290867 1.02508719356449 1.39848795225285 163 1.21178757290867 1.01597469308108 1.40760045273626 164 1.21178757290867 1.00726780328849 1.41630734252885

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/18/t130574565177wg2hhp773c9um/1uiv31305745792.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t130574565177wg2hhp773c9um/1uiv31305745792.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t130574565177wg2hhp773c9um/29h641305745792.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t130574565177wg2hhp773c9um/29h641305745792.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t130574565177wg2hhp773c9um/34sgn1305745792.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t130574565177wg2hhp773c9um/34sgn1305745792.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) if (par2 == 'Single') K <- 1 if (par2 == 'Double') K <- 2 if (par2 == 'Triple') K <- par1 nx <- length(x) nxmK <- nx - K x <- ts(x, frequency = par1) if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) fit myresid <- x - fit$fitted[,'xhat'] bitmap(file='test1.png') op <- par(mfrow=c(2,1)) plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') par(op) dev.off() bitmap(file='test2.png') p <- predict(fit, par1, prediction.interval=TRUE) np <- length(p[,1]) plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') spectrum(myresid,main='Residals Periodogram') cpgram(myresid,main='Residal Cumulative Periodogram') qqnorm(myresid,main='Residual Normal QQ Plot') qqline(myresid) par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'alpha',header=TRUE) a<-table.element(a,fit$alpha) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'beta',header=TRUE) a<-table.element(a,fit$beta) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'gamma',header=TRUE) a<-table.element(a,fit$gamma) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Observed',header=TRUE) a<-table.element(a,'Fitted',header=TRUE) a<-table.element(a,'Residuals',header=TRUE) a<-table.row.end(a) for (i in 1:nxmK) { a<-table.row.start(a) a<-table.element(a,i+K,header=TRUE) a<-table.element(a,x[i+K]) a<-table.element(a,fit$fitted[i,'xhat']) a<-table.element(a,myresid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Forecast',header=TRUE) a<-table.element(a,'95% Lower Bound',header=TRUE) a<-table.element(a,'95% Upper Bound',header=TRUE) a<-table.row.end(a) for (i in 1:np) { a<-table.row.start(a) a<-table.element(a,nx+i,header=TRUE) a<-table.element(a,p[i,'fit']) a<-table.element(a,p[i,'lwr']) a<-table.element(a,p[i,'upr']) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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