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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 29 May 2010 13:30:09 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/May/29/t1275139928htg26hdca04i4f3.htm/, Retrieved Sat, 29 May 2010 15:32:12 +0200

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/May/29/t1275139928htg26hdca04i4f3.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

589 561 640 656 727 697 640 599 568 577 553 582 600 566 653 673 742 716 660 617 583 587 565 598 628 618 688 705 770 736 678 639 604 611 594 634 658 622 709 722 782 756 702 653 615 621 602 635 677 635 736 755 811 798 735 697 661 667 645 688 713 667 762 784 837 817 767 722 681 687 660 698 717 696 775 796 858 826 783 740 701 706 677 711 734 690 785 805 871 845 801 764 725 723 690 734 750 707 807 824 886 859 819 783 740 747 711 751 804 756 860 878 942 913 869 834 790 800 763 800 826 799 890 900 961 935 894 855 809 810 766 805 821 773 883 898 957 924 881 837 784 791 760 802 828 778 889 902 969 947 908 867 815 812 773 813 834 782 892 903 966 937 896 858 817 827 797 843

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	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.543073214984479
beta	0
gamma	0.942604207416955

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	600	592.908070200467	7.09192979953343
14	566	562.675109199843	3.32489080015671
15	653	651.15087957216	1.84912042784015
16	673	672.385187611159	0.614812388841187
17	742	742.118596249891	-0.118596249891425
18	716	716.179878460986	-0.179878460985719
19	660	655.035058916818	4.96494108318177
20	617	616.172022332151	0.827977667849382
21	583	585.175810628719	-2.17581062871932
22	587	593.241738957405	-6.24173895740535
23	565	565.242426375484	-0.242426375484001
24	598	594.587838567348	3.41216143265228
25	628	617.660894167636	10.3391058323645
26	618	586.12205365317	31.8779463468305
27	688	695.083053932834	-7.08305393283376
28	705	712.00928700475	-7.00928700475049
29	770	780.822628390711	-10.8226283907111
30	736	747.829951993133	-11.8299519931327
31	678	680.4307426735	-2.43074267349982
32	639	634.469247222763	4.53075277723656
33	604	603.09153433594	0.908465664059918
34	611	611.287395187533	-0.287395187532752
35	594	588.160001045539	5.83999895446141
36	634	623.768701257599	10.231298742401
37	658	654.692445184553	3.30755481544702
38	622	626.86819115501	-4.86819115500964
39	709	699.916926839331	9.08307316066873
40	722	726.108374499949	-4.10837449994870
41	782	796.660131966902	-14.660131966902
42	756	760.41120544434	-4.41120544433943
43	702	699.369743321413	2.63025667858676
44	653	657.709257002431	-4.70925700243072
45	615	618.821664359513	-3.82166435951342
46	621	624.06050307681	-3.06050307681016
47	602	601.652046878822	0.347953121177738
48	635	636.575918895763	-1.57591889576349
49	677	658.167822388423	18.8321776115770
50	635	634.697377200639	0.302622799361302
51	736	718.180077266758	17.8199227332416
52	755	743.812051181113	11.1879488188871
53	811	820.627879480584	-9.62787948058406
54	798	790.451592607766	7.54840739223368
55	735	736.040719264392	-1.04071926439156
56	697	686.947574728143	10.0524252718571
57	661	654.220440285998	6.77955971400172
58	667	665.98996645336	1.01003354664010
59	645	645.765238012644	-0.765238012643636
60	688	681.610128646281	6.38987135371906
61	713	718.54573242353	-5.54573242353035
62	667	671.382809275995	-4.38280927599465
63	762	764.55251513966	-2.55251513965936
64	784	776.664387935416	7.3356120645841
65	837	844.467654597554	-7.46765459755409
66	817	822.162171354625	-5.16217135462534
67	767	755.431926651043	11.5680733489567
68	722	716.294885326516	5.7051146734841
69	681	678.4544662217	2.54553377830007
70	687	685.566416832414	1.43358316758554
71	660	664.148090676016	-4.14809067601630
72	698	702.220824469723	-4.22082446972263
73	717	728.719095313762	-11.7190953137621
74	696	678.118719898638	17.8812801013617
75	775	787.115225888424	-12.115225888424
76	796	798.673109592635	-2.67310959263477
77	858	855.607145487772	2.39285451222838
78	826	839.201553386458	-13.2015533864578
79	783	774.21073743258	8.78926256742068
80	740	730.240182737651	9.75981726234852
81	701	692.414074678258	8.58592532174225
82	706	702.423128848135	3.57687115186491
83	677	679.106348228755	-2.10634822875500
84	711	719.307570259149	-8.30757025914886
85	734	740.89241068307	-6.89241068307058
86	690	704.646437861595	-14.6464378615949
87	785	783.156389344274	1.84361065572625
88	805	806.597028246051	-1.59702824605085
89	871	867.012791603072	3.98720839692839
90	845	844.368127824755	0.63187217524478
91	801	795.233144593094	5.76685540690562
92	764	749.020372554303	14.9796274456974
93	725	712.443225189428	12.5567748105716
94	723	722.499745711662	0.500254288338169
95	690	694.373597821263	-4.37359782126293
96	734	731.476601492216	2.52339850778390
97	750	760.311698581786	-10.3116985817862
98	707	717.75969675123	-10.7596967512300
99	807	808.358064246905	-1.35806424690509
100	824	829.142850633479	-5.14285063347859
101	886	891.680234931396	-5.6802349313956
102	859	861.777433184102	-2.77743318410239
103	819	812.113180557159	6.88681944284099
104	783	769.53196049704	13.4680395029595
105	740	730.22423410209	9.77576589790942
106	747	733.530490323992	13.4695096760082
107	711	709.560407516763	1.43959248323665
108	751	753.997723643214	-2.99772364321382
109	804	774.792489545268	29.2075104547318
110	756	751.406648923372	4.59335107662798
111	860	860.92687768821	-0.926877688210311
112	878	881.53297202236	-3.53297202236070
113	942	948.987056508297	-6.98705650829743
114	913	917.823590153726	-4.82359015372572
115	869	868.232926442888	0.767073557111758
116	834	822.380390954156	11.6196090458437
117	790	777.539364537388	12.4606354626115
118	800	783.736877327323	16.2631226726775
119	763	753.78907557948	9.2109244205193
120	800	803.260033992059	-3.26003399205877
121	826	839.865356207762	-13.8653562077620
122	799	780.630921106658	18.3690788933424
123	890	900.000836757672	-10.0008367576717
124	900	915.30106789176	-15.30106789176
125	961	977.049767831213	-16.0497678312128
126	935	941.116867018099	-6.11686701809879
127	894	891.991057625785	2.00894237421505
128	855	850.258525809465	4.74147419053497
129	809	800.803363932153	8.19663606784673
130	810	806.24057709271	3.75942290729017
131	766	765.97060307373	0.0293969262697829
132	805	805.241335560175	-0.241335560175344
133	821	839.068420765764	-18.0684207657645
134	773	791.198102094539	-18.1981020945386
135	883	876.400024648074	6.59997535192565
136	898	898.175914936503	-0.175914936502636
137	957	967.578166740362	-10.5781667403616
138	924	938.875067244273	-14.8750672442733
139	881	888.695391228737	-7.69539122873698
140	837	843.316507441881	-6.3165074418813
141	784	790.232524074934	-6.23252407493419
142	791	785.976506509112	5.02349349088797
143	760	745.96585423561	14.0341457643897
144	802	792.110850113679	9.8891498863212
145	828	823.43607447443	4.56392552557088
146	778	787.488837287769	-9.48883728776889
147	889	889.285364221146	-0.285364221145642
148	902	904.502971731331	-2.50297173133129
149	969	968.497587179644	0.502412820355744
150	947	943.590261965579	3.40973803442125
151	908	905.497653209536	2.50234679046389
152	867	865.019649353961	1.98035064603869
153	815	814.709263500261	0.290736499738955
154	812	818.94420448093	-6.9442044809307
155	773	775.022497769282	-2.02249776928250
156	813	811.301589630045	1.69841036995535
157	834	836.172248665732	-2.17224866573179
158	782	790.094904179485	-8.0949041794845
159	892	897.661302294342	-5.66130229434202
160	903	909.08458954487	-6.08458954486991
161	966	972.696941830527	-6.69694183052695
162	937	945.12723725248	-8.12723725248054
163	896	900.649624293677	-4.64962429367711
164	858	856.530100380542	1.46989961945769
165	817	805.806446754375	11.1935532456254
166	827	812.833484526553	14.1665154734470
167	797	782.092396791722	14.9076032082784
168	843	830.004766984475	12.9952330155248

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
169	859.965927621504	843.238841266743	876.693013976266
170	810.98708162045	792.09352128844	829.880641952461
171	928.097269904348	905.8662452846	950.328294524096
172	942.925120844953	918.633977747132	967.216263942775
173	1012.43762506758	985.298948759301	1039.57630137586
174	986.628582685448	958.438389422891	1014.81877594800
175	945.95184357546	917.115705019858	974.787982131064
176	904.754344682149	875.386750698343	934.121938665954
177	854.73436119912	825.140830834817	884.327891563422
178	856.950066463488	825.895357093098	888.004775833877
179	817.325811868334	786.025358698467	848.6262650382
180	857.252613110201	825.341492581997	889.163733638406

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/29/t1275139928htg26hdca04i4f3/10xcf1275139806.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/29/t1275139928htg26hdca04i4f3/10xcf1275139806.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/29/t1275139928htg26hdca04i4f3/20xcf1275139806.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/29/t1275139928htg26hdca04i4f3/20xcf1275139806.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/29/t1275139928htg26hdca04i4f3/3a6ti1275139806.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/29/t1275139928htg26hdca04i4f3/3a6ti1275139806.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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')

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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