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*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 07 Dec 2010 09:58:27 +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/07/t1291715832kj14sro727vjbq6.htm/, Retrieved Tue, 07 Dec 2010 10:57:13 +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/07/t1291715832kj14sro727vjbq6.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

46 62 66 59 58 61 41 27 58 70 49 59 44 36 72 45 56 54 53 35 61 52 47 51 52 63 74 45 51 64 36 30 55 64 39 40 63 45 59 55 40 64 27 28 45 57 45 69 60 56 58 50 51 53 37 22 55 70 62 58 39 49 58 47 42 62 39 40 72 70 54 65

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.0052078015322195
beta	0.748150948749452
gamma	0.25528536166977

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	44	46.6829275162342	-2.68292751623424
14	36	37.4190430644953	-1.41904306449529
15	72	73.8530991176902	-1.85309911769019
16	45	46.4992868689191	-1.49928686891911
17	56	58.5280218489155	-2.52802184891554
18	54	56.6166500130302	-2.61665001303023
19	53	39.8250398059739	13.1749601940261
20	35	26.7460174628003	8.25398253719967
21	61	58.3124366705048	2.68756332949519
22	52	70.6780753105334	-18.6780753105334
23	47	49.8765178806111	-2.8765178806111
24	51	60.2589543160451	-9.2589543160451
25	52	43.8820727191788	8.11792728082122
26	63	35.4182662438474	27.5817337561526
27	74	70.7026877438139	3.2973122561861
28	45	44.6347207925172	0.365279207482814
29	51	56.2770561007029	-5.27705610070291
30	64	54.6076354785841	9.39236452141591
31	36	42.3875265574203	-6.38752655742034
32	30	28.3372481923372	1.66275180766281
33	55	58.0193961688328	-3.01939616883282
34	64	64.9214476290073	-0.921447629007304
35	39	48.5935132205767	-9.5935132205767
36	40	57.3421270504528	-17.3421270504528
37	63	45.5357064917938	17.4642935082062
38	45	42.1670454537912	2.83295454620884
39	59	70.871765996104	-11.8717659961041
40	55	44.2098670646111	10.7901329353889
41	40	54.3550646421634	-14.3550646421634
42	64	56.2876626193856	7.71233738061445
43	27	40.2125612602168	-13.2125612602168
44	28	28.295078420808	-0.295078420808014
45	45	56.1952612606278	-11.1952612606278
46	57	63.2805438281635	-6.28054382816352
47	45	44.9988779073651	0.00112209263485852
48	69	51.5467253028107	17.4532746971893
49	60	48.8342287943918	11.1657712056082
50	56	41.8730315777751	14.1269684222249
51	58	66.3961330276469	-8.3961330276469
52	50	45.9909501814054	4.00904981859455
53	51	49.6482746531891	1.35172534681087
54	53	57.2022581602745	-4.20225816027445
55	37	36.1756493264523	0.824350673547698
56	22	27.8097452358259	-5.80974523582585
57	55	52.5850986283772	2.41490137162282
58	70	61.0143960970928	8.98560390290722
59	62	44.7099668281243	17.2900331718757
60	58	55.9867291513162	2.01327084868375
61	39	51.7821660569171	-12.7821660569171
62	49	45.5200718147799	3.47992818522015
63	58	64.3110080261975	-6.31100802619751
64	47	47.0876940994298	-0.0876940994297968
65	42	50.0740054724618	-8.07400547246176
66	62	56.1550961322957	5.84490386770427
67	39	36.4460517136148	2.55394828638519
68	40	26.3985372376223	13.6014627623777
69	72	53.7141715402752	18.2858284597248
70	70	64.2963957269039	5.70360427309613
71	54	50.0674692452199	3.9325307547801
72	65	57.7044727938858	7.29552720611421

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	49.7600979167729	44.93399307301	54.5862027605359
74	47.8458222112158	43.0169907886171	52.6746536338144
75	64.890662188957	60.049021466264	69.73230291165
76	48.9424610210496	44.098824891789	53.7860971503103
77	50.1556222804349	45.2968040011599	55.0144405597099
78	60.5502489705729	55.6477129204628	65.452785020683
79	39.1243020066996	34.2506060901198	43.9979979232794
80	31.5989563297198	26.7279081957863	36.4700044636533
81	61.7540626591045	56.6889789637508	66.8191463544582
82	69.5189743771737	64.2907325284064	74.747216225941
83	54.0022555840128	48.8562735881468	59.1482375798789
84	62.9699373692392	38.8679760125794	87.071898725899

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715832kj14sro727vjbq6/1tjuo1291715903.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715832kj14sro727vjbq6/1tjuo1291715903.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715832kj14sro727vjbq6/2mtts1291715903.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715832kj14sro727vjbq6/2mtts1291715903.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715832kj14sro727vjbq6/3mtts1291715903.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715832kj14sro727vjbq6/3mtts1291715903.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 1 ; par3 = 1 ; par4 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;

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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