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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: Tue, 21 Dec 2010 23:55:40 +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/Dec/22/t12929756396m121aanlku5qny.htm/, Retrieved Wed, 22 Dec 2010 00:53:59 +0100

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/Dec/22/t12929756396m121aanlku5qny.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:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

97 100.7 101.4 101.5 101.8 101.5 102.2 101.8 98.5 98.4 97.5 97.7 98.3 99.6 99.4 96.7 96.9 96.1 97.9 99.2 97.8 94.9 93.3 91.5 89.1 92.3 91.8 92.1 94.4 92.8 92.6 92.3 92.1 89.8 87.4 87.7 86.3 89.1 90.4 87.1 86.7 84.4 88.4 88.9 88.5 87.2 86.2 83.4 87.5 85.7 87.4 86.8 87.9 85.9 87.7 87 86.8 86.2 86.1 87.5 85.7 88.9 89.8 91.4 95.2 94.1 96.8 96.1 96.6 94.2 93.9 96.5 93.4 95 95.2 94 97 96.9 96.3 96.3 97.3 95.7 96.4 95.1 94.6 95.9 96.2 94.3 98.3 95.9 92.1 94.6 94.7 96.7 97.5 96.2 97.1 95.9 94.5 99.4 101.3 101.4 100.9 101.4 103.1 102.4 101.1 102 103.9 101.7 101.2 101.9 101.1 103.1 103.3 101.4 102.8 103 102.6 102.2

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	16 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.840013960810943
beta	0.212264917034862
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	101.4	104.4	-3
4	101.5	105.045041636468	-3.54504163646818
5	101.8	104.600140289904	-2.80014028990354
6	101.5	104.281686077061	-2.78168607706051
7	102.2	103.482743751354	-1.28274375135366
8	101.8	103.714213647816	-1.91421364781573
9	98.5	103.073925205897	-4.5739252058974
10	98.4	99.3838859314774	-0.983885931477374
11	97.5	98.5340975006736	-1.03409750067355
12	97.7	97.4577453853595	0.242254614640473
13	98.3	97.4967421944844	0.803257805515642
14	99.6	98.1502147955844	1.44978520441560
15	99.4	99.605284104439	-0.205284104438945
16	96.7	99.6334688041553	-2.93346880415530
17	96.9	96.8468866650616	0.0531133349383737
18	96.1	96.5785456173235	-0.478545617323505
19	97.9	95.7782763147406	2.12172368525943
20	99.2	97.5405845173899	1.6594154826101
21	97.8	99.210430272496	-1.41043027249603
22	94.9	98.0500752697104	-3.15007526971044
23	93.3	94.866718456253	-1.56671845625304
24	91.5	92.7340489632144	-1.23404896321439
25	89.1	90.6607887790286	-1.56078877902863
26	92.3	88.0347653742005	4.26523462579949
27	91.8	91.0631977311374	0.736802268862618
28	92.1	91.2590735407788	0.840926459221194
29	94.4	91.6923569314561	2.7076430685439
30	92.8	94.1764959689413	-1.37649596894133
31	92.6	92.9844644037283	-0.384464403728316
32	92.3	92.5572010875426	-0.25720108754264
33	92.1	92.1909803667577	-0.0909803667576625
34	89.8	91.9481650727964	-2.14816507279642
35	87.4	89.5942562719425	-2.19425627194252
36	87.7	86.8103822724631	0.889617727536887
37	86.3	86.7756292140407	-0.475629214040708
38	89.1	85.5092423629112	3.59075763708883
39	90.4	88.2989290500254	2.10107094997457
40	87.1	90.2118906157628	-3.11189061576276
41	86.7	87.191024496527	-0.491024496526919
42	84.4	86.2841701415937	-1.88417014159373
43	88.4	83.8710961080504	4.52890389194957
44	88.9	87.65262223877	1.24737776122997
45	88.5	88.9000349144654	-0.400034914465351
46	87.2	88.6922695204388	-1.49226952043884
47	86.2	87.300931955339	-1.10093195533895
48	83.4	86.0420211924863	-2.64202119248627
49	87.5	83.0174870624831	4.48251293751686
50	85.7	86.7769177482957	-1.07691774829574
51	87.4	85.6743286930812	1.72567130691880
52	86.8	87.2336502450063	-0.433650245006334
53	87.9	86.9017893264056	0.998210673594443
54	85.9	87.9506980163406	-2.05069801634055
55	87.7	86.0728301192598	1.62716988074017
56	87	87.5745559306639	-0.574555930663905
57	86.8	87.1243548437356	-0.324354843735634
58	86.2	86.826491912291	-0.62649191229103
59	86.1	86.1631226754615	-0.0631226754615142
60	87.5	85.9617363428484	1.53826365715162
61	85.7	87.3798177471108	-1.67981774711079
62	88.9	85.7951451120427	3.10485488795734
63	89.8	88.7832769720049	1.01672302799513
64	91.4	90.1986362190472	1.20136378095282
65	95.2	91.9833060383843	3.21669396161570
66	94.1	96.0344355500285	-1.93443555002848
67	96.8	95.4136238721683	1.38637612783172
68	96.1	97.8295388448611	-1.72953884486112
69	96.6	97.3196554621864	-0.719655462186424
70	94.2	97.5297696972706	-3.32976969727063
71	93.9	94.9536353057947	-1.05363530579473
72	96.5	94.1016166164614	2.3983833835386
73	93.4	96.5769867524313	-3.17698675243125
74	95	93.8024939461285	1.19750605387151
75	95.2	94.916158076731	0.283841923269023
76	94	95.3129421563963	-1.31294215639633
77	97	94.1343005173468	2.86569948265321
78	96.9	96.9767461533741	-0.076746153374117
79	96.3	97.3338121154443	-1.03381211544435
80	96.3	96.7025949283216	-0.402594928321633
81	97.3	96.5298241032304	0.770175896769558
82	95.7	97.4795237375567	-1.77952373755669
83	96.4	95.970141224599	0.429858775400987
84	95.1	96.3933170484664	-1.29331704846638
85	94.6	95.1383955885162	-0.538395588516252
86	95.9	94.421619803024	1.47838019697609
87	96.2	95.6625671440682	0.537432855931783
88	94.3	96.2089328129547	-1.90893281295470
89	98.3	94.3599439590746	3.94005604092544
90	95.9	98.1267210366629	-2.22672103666287
91	92.1	96.3162826820945	-4.21628268209452
92	94.6	92.0827984042614	2.51720159573861
93	94.7	93.9543657979788	0.745634202021193
94	96.7	94.4707425229669	2.22925747703312
95	97.5	96.630872366575	0.86912763342491
96	96.2	97.8034443848026	-1.60344438480264
97	97.1	96.6131184459564	0.48688155404362
98	95.9	97.2655091342532	-1.36550913425320
99	94.5	96.1183880031701	-1.61838800317011
100	99.4	94.4702776198999	4.92972238010013
101	101.3	99.2016679582938	2.09833204170624
102	101.4	101.928795014574	-0.528795014573788
103	100.9	102.354811610615	-1.45481161061495
104	101.4	101.743560435568	-0.343560435568207
105	103.1	102.004517048449	1.09548295155136
106	102.4	103.669620825238	-1.26962082523809
107	101.1	103.121624042702	-2.02162404270229
108	102	101.581467385913	0.41853261408734
109	103.9	102.165703051776	1.73429694822367
110	101.7	104.164433801026	-2.46443380102647
111	101.2	102.196750017638	-0.99675001763815
112	101.9	101.284215098362	0.615784901638278
113	101.1	101.836029854472	-0.736029854472065
114	103.1	101.121063176440	1.97893682355986
115	103.3	103.039561718417	0.260438281583177
116	101.4	103.560935069876	-2.16093506987580
117	102.8	101.663014407287	1.13698559271344
118	103	102.738123920357	0.261876079642676
119	102.6	103.124823168879	-0.524823168878996
120	102.2	102.757105211451	-0.557105211450988

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	102.262934967809	98.4513573182622	106.074512617355
122	102.236740879426	96.7967575475938	107.676724211257
123	102.210546791043	95.1115043664934	109.309589215592
124	102.184352702660	93.3604726500812	111.008232755238
125	102.158158614277	91.532220204904	112.784097023649
126	102.131964525893	89.6231952835992	114.640733768188
127	102.105770437510	87.6330076489895	116.578533226031
128	102.079576349127	85.5626452683782	118.596507429877
129	102.053382260744	83.4137058242774	120.693058697211
130	102.027188172361	81.1880370466166	122.866339298106
131	102.000994083978	78.8875599124513	125.114428255505
132	101.974799995595	76.514179868529	127.435420122662

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t12929756396m121aanlku5qny/1avub1292975722.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t12929756396m121aanlku5qny/1avub1292975722.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t12929756396m121aanlku5qny/2lmtw1292975722.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t12929756396m121aanlku5qny/2lmtw1292975722.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t12929756396m121aanlku5qny/3lmtw1292975722.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t12929756396m121aanlku5qny/3lmtw1292975722.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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')

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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