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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: Sun, 19 Dec 2010 13:58:47 +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/19/t1292767000xskov2vo9z0u3pi.htm/, Retrieved Sun, 19 Dec 2010 14:56:41 +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/19/t1292767000xskov2vo9z0u3pi.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 «

3.65 3.59 3.31 3.89 4.31 4.35 4.11 3.90 3.75 3.75 3.88 3.93 3.97 3.97 4.33 4.16 4.93 3.86 4.06 4.18 4.08 4.38 4.48 4.41 4.37 4.56 4.71 4.94 5.03 5.08 5.05 4.83 4.68 4.69 4.58 4.54 4.75 4.71 4.50 4.62 4.69 5.05 4.93 4.53 4.33 4.33 3.87 3.74 3.31 3.21 2.93 3.19 3.46 3.73 3.60 3.46 3.25 3.19 2.82 1.89 1.98 2.30 2.42 2.47 2.81 3.37 3.14 3.21 3.02 2.96 2.92 3.07

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	0.997151100012884
beta	0.00829700255916443
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	3.31	3.53	-0.22
4	3.89	3.24880661764686	0.641193382353144
5	4.31	3.83165799086539	0.478342009134614
6	4.35	4.25607943628624	0.0939205637137581
7	4.11	4.29795165366323	-0.187951653663235
8	3.9	4.0571996867436	-0.1571996867436
9	3.75	3.84581150704317	-0.0958115070431735
10	3.75	3.69484393466794	0.0551560653320622
11	3.88	3.69487016942601	0.185129830573988
12	3.93	3.82603153387095	0.103968466129049
13	3.97	3.87712292357362	0.092877076426376
14	3.97	3.91792292780825	0.052077072191747
15	4.33	3.91847001557807	0.411529984421926
16	4.16	4.28085070804473	-0.120850708044729
17	4.93	4.11136756534684	0.81863243465316
18	3.86	4.88546391695364	-1.02546391695364
19	4.06	3.81223352551218	0.247766474487817
20	4.18	4.01065608200127	0.16934391799873
21	4.08	4.1322805441043	-0.0522805441043008
22	4.38	4.0324793939958	0.347520606004198
23	4.48	4.33421556540237	0.145784434597627
24	4.41	4.43599641945058	-0.0259964194505775
25	4.37	4.36627072805071	0.00372927194929051
26	4.56	4.32621689615774	0.233783103842263
27	4.71	4.5174956688014	0.192504331198598
28	4.94	4.66920592653636	0.270794073463636
29	5.03	4.90122326516216	0.128776734837839
30	5.08	4.99269327531661	0.087306724683387
31	5.05	5.04353373964823	0.00646626035176734
32	4.83	5.01381754377958	-0.183817543779579
33	4.68	4.79283885363159	-0.11283885363159
34	4.69	4.64170308539406	0.0482969146059382
35	4.58	4.65164360371996	-0.0716436037199601
36	4.54	4.5413925685612	-0.00139256856119907
37	4.75	4.50118090915973	0.248819090840272
38	4.71	4.71252665238087	-0.00252665238087246
39	4.5	4.67322180734754	-0.173221807347544
40	4.62	4.46227497349457	0.157725026505429
41	4.69	4.58263705581385	0.107362944186146
42	5.05	4.6536687851988	0.396331214801197
43	4.93	5.01612453638795	-0.0861245363879473
44	4.53	4.89678646482661	-0.366786464826605
45	4.33	4.49455148420647	-0.164551484206472
46	4.33	4.29261394244503	0.0373860575549729
47	3.87	4.29234795109352	-0.422347951093518
48	3.74	3.83016344845185	-0.0901634484518512
49	3.31	3.69847113288724	-0.388471132887236
50	3.21	3.2661070180824	-0.0561070180824048
51	2.93	3.16469595210753	-0.234695952107532
52	3.19	2.8832630087899	0.306736991210103
53	3.46	3.14425826764208	0.315741732357917
54	3.73	3.41684486070488	0.313155139295124
55	3.6	3.68944307649045	-0.0894430764904457
56	3.46	3.55985004330323	-0.099850043303228
57	3.25	3.4190535958345	-0.169053595834499
58	3.19	3.20785210769285	-0.0178521076928542
59	2.82	3.14727365276819	-0.327273652768191
60	1.89	2.77544750934489	-0.885447509344893
61	1.98	1.83971206020207	0.140287939797933
62	2.3	1.92795049585735	0.372049504142652
63	2.42	2.25036833177059	0.169631668229406
64	2.47	2.37234842468633	0.097651575313669
65	2.81	2.42336139591984	0.386638604080162
66	3.37	2.76573690316037	0.60426309683963
67	3.14	3.33011620204012	-0.190116202040119
68	3.21	3.1008064084391	0.109193591560904
69	3.02	3.17085710323558	-0.150857103235576
70	2.96	2.98034986574422	-0.0203498657442234
71	2.92	2.91980970180536	0.000190298194640892
72	3.07	2.87975275933904	0.190247240660955

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	3.03078529102384	2.45209257671315	3.60947800533453
74	2.99211257740914	2.17149481254445	3.81273034227383
75	2.95343986379445	1.94470996372845	3.96216976386044
76	2.91476715017976	1.74545171444026	4.08408258591925
77	2.87609443656506	1.56355983063596	4.18862904249417
78	2.83742172295037	1.39384028547235	4.28100316042838
79	2.79874900933567	1.23321866542566	4.36427935324568
80	2.76007629572098	1.07969937079829	4.44045322064367
81	2.72140358210628	0.931901621281566	4.510905542931
82	2.68273086849159	0.788824039609276	4.5766376973739
83	2.6440581548769	0.649713680939965	4.63840262881383
84	2.6053854412622	0.51398793592322	4.69678294660118

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767000xskov2vo9z0u3pi/1etcv1292767123.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767000xskov2vo9z0u3pi/1etcv1292767123.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767000xskov2vo9z0u3pi/273bg1292767123.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767000xskov2vo9z0u3pi/273bg1292767123.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767000xskov2vo9z0u3pi/373bg1292767123.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292767000xskov2vo9z0u3pi/373bg1292767123.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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