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Exponential Smoothing Kwartz Uurwerken Danielle Versmissen

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 28 May 2008 11:53:44 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/28/t121199729318sslpgerfot80t.htm/, Retrieved Wed, 28 May 2008 19:54:56 +0200

User-defined keywords:

Dataseries X:

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120,05 120,05 120,08 120,12 120,18 120,2 120,25 120,25 120,24 120,29 120,25 120,26 120,32 120,31 120,36 120,4 120,4 120,39 120,44 120,5 120,53 120,64 120,78 120,94 121 121,05 121,15 121,07 121,18 121,46 121,71 121,71 121,74 121,76 121,76 121,82 121,82 121,82 121,94 121,99 122,18 122,41 122,48 122,52 122,62 122,63 122,74 122,58 122,59 122,61 122,63 122,37 122,36 122,47 122,46 122,45 122,49 122,5 122,37 122,37 122,51 122,51 122,55 122,56 122,72 122,97 123,03 123,05 123,08 123,08 123,12 123,07 123,04 123,06 123,39 124,02 124,05 123,99 124,46 124,46 124,6 124,84 124,84 124,99

Text written by user:

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	6 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.109959999025065
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	120.08	120.05	0.0300000000000011
4	120.12	120.083298799971	0.0367012000292561
5	120.18	120.127334463890	0.0526655361098136
6	120.2	120.193125566189	0.00687443381052333
7	120.25	120.213881478925	0.0361185210754229
8	120.25	120.267853071467	-0.0178530714668170
9	120.24	120.265889947746	-0.0258899477457391
10	120.29	120.253043089117	0.0369569108831627
11	120.25	120.307106871002	-0.0571068710015368
12	120.26	120.260827399522	-0.000827399521881489
13	120.32	120.270736418671	0.0492635813287308
14	120.31	120.336153442026	-0.0261534420261285
15	120.36	120.323277609566	0.0367223904335532
16	120.4	120.377315603583	0.0226843964172900
17	120.4	120.419809979791	-0.0198099797906508
18	120.39	120.417631674432	-0.0276316744321861
19	120.44	120.404593295539	0.0354067044614368
20	120.5	120.458486616727	0.0415133832733829
21	120.53	120.523051428311	0.00694857168912222
22	120.64	120.553815493247	0.0861845067529572
23	120.78	120.673292341526	0.10670765847442
24	120.94	120.825025915547	0.114974084452612
25	121	120.997668465762	0.00233153423829435
26	121.05	121.057924841264	-0.00792484126428405
27	121.15	121.107053425727	0.0429465742734294
28	121.07	121.211775830992	-0.141775830991833
29	121.18	121.116186160754	0.0638138392458387
30	121.46	121.233203130455	0.226796869544543
31	121.71	121.538141714009	0.171858285990552
32	121.71	121.807039250969	-0.0970392509694165
33	121.74	121.796368815027	-0.056368815027426
34	121.76	121.820170500182	-0.0601705001819539
35	121.76	121.833554152041	-0.0735541520406144
36	121.82	121.825466137554	-0.00546613755395242
37	121.82	121.884865081074	-0.0648650810738332
38	121.82	121.877732516822	-0.0577325168221989
39	121.94	121.871384249329	0.0686157506712846
40	121.99	121.998929237206	-0.00892923720563488
41	122.18	122.047947378291	0.132052621708809
42	122.41	122.252467884446	0.157532115554417
43	122.48	122.499790115718	-0.0197901157183367
44	122.52	122.567613994613	-0.0476139946132577
45	122.62	122.602378359812	0.0176216401880112
46	122.63	122.70431603535	-0.0743160353498951
47	122.74	122.706144244175	0.0338557558247317
48	122.58	122.819867023053	-0.239867023052753
49	122.59	122.633491245432	-0.0434912454317242
50	122.61	122.638708948126	-0.0287089481264644
51	122.63	122.655552112218	-0.0255521122184632
52	122.37	122.672742401984	-0.302742401983821
53	122.36	122.379452847757	-0.0194528477568525
54	122.47	122.367313812636	0.102686187363531
55	122.46	122.488605185699	-0.0286051856988507
56	122.45	122.475459759507	-0.0254597595072852
57	122.49	122.462660204377	0.0273397956233055
58	122.5	122.505666488277	-0.00566648827677341
59	122.37	122.515043401231	-0.145043401231376
60	122.37	122.369094428973	0.000905571026606822
61	122.51	122.369194005563	0.140805994437414
62	122.51	122.524677032574	-0.0146770325736583
63	122.55	122.523063146086	0.0269368539138242
64	122.56	122.566025122516	-0.00602512251626308
65	122.72	122.575362600050	0.144637399949744
66	122.97	122.751266928408	0.218733071592283
67	123.03	123.025318816747	0.00468118325325406
68	123.05	123.085833559653	-0.0358335596527155
69	123.08	123.101893301468	-0.0218933014682392
70	123.08	123.12948591406	-0.0494859140601278
71	123.12	123.124044442998	-0.00404444299832107
72	123.07	123.163599716050	-0.0935997160501927
73	123.04	123.103307491365	-0.0633074913645402
74	123.06	123.066346199676	-0.00634619967583205
75	123.39	123.085648371566	0.304351628434333
76	124.02	123.449114876332	0.570885123668418
77	124.05	124.141889403974	-0.0918894039735818
78	123.99	124.161785245202	-0.17178524520223
79	124.46	124.082895739807	0.377104260192723
80	124.46	124.594362123890	-0.134362123890412
81	124.6	124.579587664878	0.0204123351215770
82	124.84	124.721832205228	0.118167794771523
83	124.84	124.974825935826	-0.134825935826356
84	124.99	124.960000476054	0.0299995239456479

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	125.113299223678	124.877300129219	125.349298318137
86	125.236598447356	124.884017759046	125.589179135667
87	125.359897671034	124.904705886924	125.815089455145
88	125.483196894713	124.930293936672	126.036099852753
89	125.606496118391	124.957522808768	126.255469428014
90	125.729795342069	124.984852095995	126.474738588143
91	125.853094565747	125.011446905748	126.694742225746
92	125.976393789425	125.036817161095	126.915970417755
93	126.099693013103	125.060660933037	127.138725093170
94	126.222992236782	125.082787033733	127.363197439830
95	126.346291460460	125.103073129582	127.589509791337
96	126.469590684138	125.121441487762	127.817739880513

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t121199729318sslpgerfot80t/1hqtp1211997218.png (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t121199729318sslpgerfot80t/39s8x1211997218.png (open in new window)

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Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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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