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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: Wed, 22 Dec 2010 06:49:03 +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/t1293000529fn6i2deyn9pasje.htm/, Retrieved Wed, 22 Dec 2010 07:48:49 +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/t1293000529fn6i2deyn9pasje.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 «

100,4 97,7 97 96,5 98,4 106,3 103,1 102,4 95 98,1 106,1 99,1 101,2 95,5 99,8 97,1 97,5 96,8 97,7 100,9 94,3 99,5 100,8 97 99,2 101 102,3 97 91,2 97,6 95,7 100,5 94,4 102,9 105,1 98,8 100,7 99,6 107,7 102,9 101,6 102,7 110,5 109,8 94,3 102,5 105 102,3 107,7 100,3 99,5 95 97,7 96,3 97,8 106,4 96,1 106,2 114,7 111,9 121 117,7 115,4 114,3 109,5 108,1 108,2 99,1 101,2 98,1 95,5 97,9 98,2 98,7 95,6 95,8 94,4 96,5 103,3 104,3 104,5 102,3 103,8 103,1 102,2 106,3 102,1 94 102,6 102,6 106,7 107,9 109,3 105,9 109,1 108,5 111,7 109,8 109,1 108,5 108,5 106,2 117,1 109,8 115,2 115,9 119,2 121 118,6 117,6 114,6 110,6 102,5 101,6 107,4 105,8 102,8 104 100,4 100,6

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

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.632771665684048
beta	-6.91178884959509e-18
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	97	97.7	-0.700000000000003
4	96.5	97.2570598340212	-0.757059834021163
5	98.4	96.7780138218251	1.62198617817491
6	106.3	97.8043607175053	8.49563928249466
7	103.1	103.180160537340	-0.0801605373403191
8	102.4	103.129437220605	-0.729437220605348
9	95	102.667870015511	-7.66787001551097
10	98.1	97.8158591335473	0.284140866452660
11	106.1	97.9956554229015	8.1043445770985
12	99.1	103.123855040230	-4.02385504022959
13	101.2	100.577673583952	0.622326416047642
14	95.5	100.971464106834	-5.47146410683401
15	99.8	97.5092766502222	2.29072334977782
16	97.1	98.9587814798824	-1.85878147988244
17	97.5	97.7825972267146	-0.282597226714557
18	96.8	97.6037777088487	-0.803777708848699
19	97.7	97.0951699491808	0.604830050819203
20	100.9	97.4778892678934	3.42211073210657
21	94.3	99.6433039760038	-5.34330397600377
22	99.5	96.2622126188517	3.23778738114834
23	100.8	98.3109927331517	2.48900726684830
24	97	99.885966007295	-2.88596600729500
25	99.2	98.0598084897514	1.14019151024860
26	101	98.7812893708902	2.21871062910978
27	102.3	100.185226591343	2.11477340865709
28	97	101.523395283683	-4.52339528368319
29	91.2	98.6611189154796	-7.4611189154796
30	97.6	93.9399342714648	3.66006572853517
31	95.7	96.2559201590231	-0.555920159023117
32	100.5	95.9041496340107	4.59585036598928
33	94.4	98.8122735253324	-4.41227352533240
34	102.9	96.0203118572542	6.8796881427458
35	105.1	100.373583582726	4.72641641727374
36	98.8	103.364325971801	-4.564325971801
37	100.7	100.476149823900	0.223850176100484
38	99.6	100.617795872694	-1.01779587269429
39	107.7	99.9737634830032	7.72623651699683
40	102.9	104.862707033332	-1.96270703333217
41	101.6	103.620761634601	-2.02076163460079
42	102.7	102.342080929124	0.357919070875980
43	110.5	102.568561975782	7.9314380242177
44	109.8	107.587351225636	2.21264877436367
45	94.3	108.987452676164	-14.6874526761642
46	102.5	99.6936487816122	2.80635121838785
47	105	101.469428316566	3.53057168343412
48	102.3	103.703474041509	-1.40347404150943
49	107.7	102.815395434519	4.88460456548083
50	100.3	105.906234801626	-5.60623480162639
51	99.5	102.358768267985	-2.85876826798538
52	95	100.549820709248	-5.54982070924757
53	97.7	97.0380514148092	0.661948585190842
54	96.3	97.4569137236576	-1.15691372365757
55	97.8	96.724851499686	1.07514850031397
56	106.4	97.4051750070874	8.9948249929126
57	96.1	103.096845400389	-6.99684540038922
58	106.2	98.6694398818512	7.53056011814884
59	114.7	103.434564951346	11.2654350486539
60	111.9	110.563013051738	1.33698694826174
61	121	111.409020509988	9.59097949001232
62	117.7	117.477920577424	0.222079422575689
63	115.4	117.618446143562	-2.21844614356168
64	114.3	116.214676282070	-1.91467628206981
65	109.5	115.003123381819	-5.50312338181875
66	108.1	111.520902833040	-3.42090283304047
67	108.2	109.356252449234	-1.15625244923416
68	99.1	108.624608660981	-9.524608660981
69	101.2	102.597706173583	-1.39770617358333
70	98.1	101.713277309988	-3.61327730998813
71	95.5	99.4268978079686	-3.92689780796856
72	97.9	96.9420681410493	0.957931858950744
73	98.2	97.5482202790493	0.651779720950657
74	98.7	97.9606480187344	0.739351981265628
75	95.6	98.4284890034466	-2.82848900344663
76	95.8	96.6387013053667	-0.838701305366698
77	94.4	96.1079948833584	-1.70799488335842
78	96.5	95.0272241160359	1.47277588396412
79	103.3	95.9591549653112	7.34084503468884
80	104.3	100.604233705440	3.69576629456031
81	104.5	102.942809899628	1.55719010037242
82	102.3	103.928155673227	-1.62815567322694
83	103.8	102.897904895886	0.902095104113798
84	103.1	103.468725117522	-0.36872511752172
85	102.2	103.235406310728	-1.03540631072795
86	106.3	102.580230534829	3.71976946517114
87	102.1	104.933995255266	-2.83399525526586
88	94	103.140723357051	-9.14072335705059
89	102.6	97.3567326128526	5.24326738714738
90	102.6	100.674523651045	1.92547634895529
91	106.7	101.892910527608	4.80708947239162
92	107.9	104.934700540146	2.96529945985412
93	109.3	106.811058018610	2.48894198139021
94	105.9	108.385989981965	-2.48598998196502
95	109.1	106.812925960203	2.28707403979683
96	108.5	108.260121609908	0.239878390091846
97	111.7	108.411909858368	3.28809014163183
98	109.8	110.492520134208	-0.692520134207854
99	109.1	110.054313015365	-0.954313015365415
100	108.5	109.450450779049	-0.950450779048666
101	108.5	108.849032456439	-0.349032456439346
102	106.2	108.628174607600	-2.42817460760043
103	117.1	107.091694516577	10.0083054834226
104	109.8	113.424666647997	-3.6246666479975
105	115.2	111.131080295595	4.0689197044053
106	115.9	113.705777394486	2.19422260551411
107	119.2	115.094219287459	4.10578071254136
108	121	117.692240987867	3.30775901213312
109	118.6	119.785297167656	-1.18529716765578
110	117.6	119.035274704548	-1.43527470454765
111	114.6	118.127073539037	-3.52707353903685
112	110.6	115.895241340750	-5.29524134075037
113	102.5	112.544562657365	-10.0445626573647
114	101.6	106.188648013596	-4.58864801359627
115	107.4	103.285081566795	4.11491843320485
116	105.8	105.888885357928	-0.0888853579281772
117	102.8	105.832641221937	-3.03264122193704
118	104	103.913671784510	0.0863282154901697
119	100.4	103.968297833221	-3.56829783322107
120	100.6	101.710380069637	-1.11038006963700

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	101.007763023430	92.3740976712982	109.641428375563
122	101.007763023430	90.790813232796	111.224712814065
123	101.007763023430	89.4219117972113	112.593614249650
124	101.007763023430	88.1984759922245	113.817050054636
125	101.007763023430	87.0821133129301	114.933412733931
126	101.007763023430	86.0488323975035	115.966693649357
127	101.007763023430	85.082453259315	116.933072787546
128	101.007763023430	84.1714517678505	117.844074279010
129	101.007763023430	83.3072753943704	118.708250652490
130	101.007763023430	82.4833697022379	119.532156344623
131	101.007763023430	81.694580128579	120.320945918282
132	101.007763023430	80.936766059111	121.078759987750

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293000529fn6i2deyn9pasje/18kim1293000538.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293000529fn6i2deyn9pasje/18kim1293000538.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293000529fn6i2deyn9pasje/20th71293000538.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293000529fn6i2deyn9pasje/20th71293000538.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293000529fn6i2deyn9pasje/30th71293000538.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293000529fn6i2deyn9pasje/30th71293000538.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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