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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: Thu, 16 Dec 2010 17:57:57 +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/16/t1292522276xq272htw26ihuw9.htm/, Retrieved Thu, 16 Dec 2010 18:57:56 +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/16/t1292522276xq272htw26ihuw9.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 «

98.6 100.1 98.8 98.3 102.8 103.6 105.2 100.1 98.2 98.4 97.4 98.4 100.3 101.1 104.1 107.3 110.1 112.6 114.3 115.3 109.9 108.2 103.2 101.8 105.6 108.2 109.8 114.6 117.2 116.5 116.1 112.1 106.8 106.9 104.5 103 105.9 107.7 107.1 112.5 114.5 114.6 113.1 112.8 111.9 112 112.4 110 112.3 109.6 111.9 110.8 110.4 110.8 114 108.4 110.5 105.1 102.3 104.3 103.4 102.4 104.5 107.3 110.1 111.8 111.8 105.7 106 106.4 107.1 111.5 109.6 109.9 109.3 111.4 112.9 115.5 118.4 116.2 113.3 113.8 114.1 117.1 115.5 115.2 114.2 115.3 118.8 118 118.1 111.8 112 114.3 115 118.5 117.6 119.1 120.6 123.6 122.7 123.8 123.1 124.5 120.7 118.7 119 122.3 118.6 118.1 118.2 120.8 119.7 119.7 117.1 114.5 116.5 116.4 114.9 115.5

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

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999933893038648
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	100.1	98.6	1.5
3	98.8	100.099900839558	-1.29990083955796
4	98.3	98.8000859324946	-0.500085932494557
5	102.8	98.3000330591614	4.49996694083859
6	103.6	102.799702520859	0.800297479140639
7	105.2	103.599947094765	1.60005290523453
8	100.1	105.199894225364	-5.09989422536444
9	98.2	100.100337138510	-1.90033713851045
10	98.4	98.2001256255138	0.199874374486228
11	97.4	98.3999867869125	-0.999986786912444
12	98.4	97.4000661060879	0.999933893912129
13	100.3	98.3999338974087	1.90006610259127
14	101.1	100.299874392404	0.800125607596414
15	104.1	101.099947106127	3.00005289387262
16	107.3	104.099801675619	3.20019832438071
17	110.1	107.299788444613	2.80021155538695
18	112.6	110.099814886523	2.50018511347707
19	114.3	112.599834720359	1.70016527964067
20	115.3	114.299887607240	1.00011239276043
21	109.9	115.299933885609	-5.39993388560869
22	108.2	109.900356973221	-1.70035697322068
23	103.2	108.200112405433	-5.00011240543272
24	101.8	103.200330542238	-1.40033054223754
25	105.6	101.800092571597	3.79990742840296
26	108.2	105.599748799666	2.60025120033352
27	109.8	108.199828105294	1.60017189470560
28	114.6	109.799894217498	4.8001057825016
29	117.2	114.599682679593	2.60031732040746
30	116.5	117.199828100923	-0.699828100923398
31	116.1	116.500046263509	-0.400046263509225
32	112.1	116.100026445843	-4.00002644584288
33	106.8	112.100264429594	-5.30026442959365
34	106.9	106.800350384376	0.0996496156242017
35	104.5	106.899993412467	-2.39999341246671
36	103	104.500158656272	-1.50015865627176
37	105.9	103.000099170930	2.89990082906969
38	107.7	105.899808296368	1.80019170363202
39	107.1	107.699880994797	-0.599880994796635
40	112.5	107.100039656310	5.39996034369027
41	114.5	112.499643025030	2.00035697496975
42	114.6	114.499867762479	0.100132237521223
43	113.1	114.599993380562	-1.49999338056205
44	112.8	113.100099160004	-0.300099160004436
45	111.9	112.800019838644	-0.900019838643559
46	112	111.900059497577	0.0999405024233084
47	112.4	111.999993393237	0.400006606762943
48	110	112.399973556779	-2.39997355677872
49	112.3	110.000158654959	2.29984134504083
50	109.6	112.299847964477	-2.69984796447709
51	111.9	109.600178478745	2.29982152125497
52	110.8	111.899847965788	-1.09984796578759
53	110.4	110.800072707607	-0.400072707606952
54	110.8	110.400026447591	0.399973552408966
55	114	110.799973558964	3.20002644103617
56	108.4	113.999788455976	-5.59978845597573
57	110.5	108.400370184999	2.09962981500095
58	105.1	110.499861199853	-5.39986119985298
59	102.3	105.100356968416	-2.80035696841564
60	104.3	102.300185123090	1.99981487691012
61	103.4	104.299867798315	-0.899867798315213
62	102.4	103.400059487526	-1.00005948752576
63	104.5	102.400066110894	2.09993388910610
64	107.3	104.499861179752	2.80013882024845
65	110.1	107.299814891331	2.80018510866877
66	111.8	110.099814888271	1.70018511172876
67	111.8	111.799887605929	0.000112394071479116
68	105.7	111.79999999257	-6.09999999256996
69	106	105.700403252464	0.299596747536242
70	106.4	105.999980194569	0.400019805430617
71	107.1	106.399973555906	0.700026444093808
72	111.5	107.099953723379	4.4000462766211
73	109.6	111.499709126311	-1.89970912631085
74	109.9	109.600125583998	0.299874416002226
75	109.3	109.899980176214	-0.599980176213577
76	111.4	109.300039662866	2.09996033713369
77	112.9	111.399861178003	1.50013882199684
78	115.5	112.899900830381	2.60009916961913
79	118.4	115.499828115345	2.90017188465532
80	116.2	118.399808278449	-2.19980827844931
81	113.3	116.200145422641	-2.90014542264085
82	113.8	113.300191719801	0.499808280198636
83	114.1	113.799966959193	0.300033040806653
84	117.1	114.099980165727	3.00001983427263
85	115.5	117.099801677805	-1.59980167780475
86	115.2	115.500105758028	-0.300105758027684
87	114.2	115.200019839080	-1.00001983907974
88	115.3	114.200066108273	1.09993389172715
89	118.8	115.299927286713	3.50007271328727
90	118	118.799768620828	-0.799768620828416
91	118.1	118.000052870273	0.0999471297266865
92	111.8	118.099993392799	-6.29999339279895
93	112	111.800416473420	0.199583526580270
94	114.3	111.999986806140	2.30001319386048
95	115	114.299847953117	0.700152046883318
96	118.5	114.999953715076	3.50004628492431
97	117.6	118.499768622576	-0.899768622575522
98	119.1	117.600059480970	1.49994051903045
99	120.6	119.09990084349	1.50009915650992
100	123.6	120.599900833003	3.00009916699696
101	122.7	123.599801672560	-0.8998016725603
102	123.8	122.700059483154	1.09994051684561
103	123.1	123.799927286275	-0.699927286274772
104	124.5	123.100046270066	1.39995372993394
105	120.7	124.499907453313	-3.79990745331288
106	118.7	120.700251200335	-2.00025120033516
107	119	118.700132230529	0.299867769471206
108	122.3	118.999980176653	3.30001982334704
109	118.6	122.299781845717	-3.69978184571708
110	118.1	118.600244581335	-0.50024458133548
111	118.2	118.100033069649	0.0999669303508028
112	120.8	118.19999339149	2.60000660851
113	119.7	120.799828121464	-1.09982812146362
114	119.7	119.700072706295	-7.27062951142443e-05
115	117.1	119.700000004806	-2.60000000480640
116	114.5	117.100171878100	-2.60017187809983
117	116.5	114.500171889462	1.99982811053815
118	116.4	116.499867797440	-0.0998677974403819
119	114.9	116.400006601957	-1.50000660195663
120	115.5	114.900099160878	0.599900839121531

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	115.499960342378	110.656048602652	120.343872082105
122	115.499960342378	108.649861088484	122.350059596272
123	115.499960342378	107.110428851637	123.889491833120
124	115.499960342378	105.812617183386	125.187303501371
125	115.499960342378	104.669217231861	126.330703452896
126	115.499960342378	103.635501856128	127.364418828629
127	115.499960342378	102.684900685166	128.315019999591
128	115.499960342378	101.800101479461	129.199819205295
129	115.499960342378	100.969079030160	130.030841654597
130	115.499960342378	100.183077808529	130.816842876227
131	115.499960342378	99.4354880696372	131.564432615120
132	115.499960342378	98.7211746816814	132.278746003075

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292522276xq272htw26ihuw9/15ibf1292522270.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292522276xq272htw26ihuw9/15ibf1292522270.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292522276xq272htw26ihuw9/25ibf1292522270.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292522276xq272htw26ihuw9/25ibf1292522270.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292522276xq272htw26ihuw9/3y9si1292522270.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292522276xq272htw26ihuw9/3y9si1292522270.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')

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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