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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: Tue, 21 Dec 2010 19:55:16 +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/21/t1292961198l6y8u634igjwzqs.htm/, Retrieved Tue, 21 Dec 2010 20:53:22 +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/21/t1292961198l6y8u634igjwzqs.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 «

13,2 13,8 16,2 14,7 13,9 16,0 14,4 12,3 15,9 15,9 15,5 15,1 14,5 15,1 17,4 16,2 15,6 17,2 14,9 13,8 17,5 16,2 17,5 16,6 16,2 16,6 19,6 15,9 18,0 18,3 16,3 14,9 18,2 18,4 18,5 16,0 17,4 17,2 19,6 17,2 18,3 19,3 18,1 16,2 18,4 20,5 19,0 16,5 18,7 19,0 19,2 20,5 19,3 20,6 20,1 16,1 20,4 19,7 15,6 14,4 13,9 14,3 15,3 14,4 13,8 15,7 14,7 12,5 16,2 16,1 16 15,8 15,2

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	0.357744444336104
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	13.8	13.2	0.600000000000001
3	16.2	13.4146466666017	2.78535333339834
4	14.7	14.4110913471380	0.288908652862034
5	13.9	14.51444681262	-0.614446812619986
6	16	14.2946318790652	1.70536812093484
7	14.4	14.9047178498775	-0.504717849877499
8	12.3	14.7241578431266	-2.42415784312656
9	15.9	13.8569288425542	2.04307115744576
10	15.9	14.5878261985138	1.31217380148620
11	15.5	15.0572490859989	0.442750914001129
12	15.1	15.2156407657075	-0.115640765707505
13	14.5	15.1742709242369	-0.674270924236872
14	15.1	14.9330542471138	0.166945752886239
15	17.4	14.9927781627143	2.40722183728568
16	16.2	15.8539484012878	0.346051598712179
17	15.6	15.9777464381807	-0.377746438180731
18	17.2	15.8426097485538	1.35739025144618
19	14.9	16.3282085698047	-1.42820856980468
20	13.8	15.8172748886038	-2.01727488860384
21	17.5	15.0956060045071	2.40439399549291
22	16.2	15.9557645983898	0.244235401610236
23	17.5	16.0431384564260	1.45686154357398
24	16.6	16.5643225798065	0.0356774201934691
25	16.2	16.577085978669	-0.377085978668990
26	16.6	16.4421855647631	0.157814435236887
27	19.6	16.4986428022052	3.10135719779485
28	15.9	17.6081361096180	-1.70813610961804
29	18	16.9970599062323	1.00294009376770
30	18.3	17.3558561527796	0.944143847220374
31	16.3	17.6936183687768	-1.39361836877683
32	14.9	17.1950591398222	-2.29505913982218
33	18.2	16.374014483128	1.82598551687200
34	18.4	17.0272506572271	1.37274934277286
35	18.5	17.5183441080702	0.981655891929833
36	16	17.8695260496579	-1.86952604965787
37	17.4	17.2007134918511	0.199286508148855
38	17.2	17.2720071329725	-0.0720071329725371
39	19.6	17.2462469811990	2.35375301880096
40	17.2	18.0882890470144	-0.888289047014418
41	18.3	17.7705085754804	0.529491424519602
42	19.3	17.9599311909259	1.34006880907410
43	18.1	18.4393333624003	-0.339333362400254
44	16.2	18.3179387372237	-2.11793873722367
45	18.4	17.5602579205377	0.839742079462319
46	20.5	17.8606709841406	2.63932901585943
47	19	18.8048762763394	0.195123723660643
48	16.5	18.8746807044371	-2.37468070443713
49	18.7	18.0251518753526	0.6748481246474
50	19	18.2665750427158	0.733424957284157
51	19.2	18.5289537465217	0.671046253478305
52	20.5	18.7690168155961	1.73098318440389
53	19.3	19.3882664330558	-0.0882664330558178
54	20.6	19.3566896070087	1.24331039299127
55	20.1	19.8014769926867	0.298523007313307
56	16.1	19.9082719400595	-3.80827194005953
57	20.4	18.5458838109822	1.85411618901784
58	19.7	19.2091835767569	0.490816423243079
59	15.6	19.3847704253611	-3.78477042536105
60	14.4	18.0307898326005	-3.63078983260054
61	13.9	16.7318949414357	-2.83189494143569
62	14.3	15.7188002591936	-1.41880025919355
63	15.3	15.2112323488444	0.088767651155564
64	14.4	15.2429884828821	-0.842988482882104
65	13.8	14.9414140364917	-1.14141403649171
66	15.7	14.5330795062496	1.16692049375044
67	14.7	14.9505388298707	-0.250538829870720
68	12.5	14.860909955394	-2.360909955394
69	16.2	14.016307535274	2.183692464726
70	16.1	14.7975113826683	1.30248861733166
71	16	15.2634694493298	0.736530550670246
72	15.8	15.5269591619158	0.273040838084155
73	15.2	15.6246380048173	-0.424638004817325

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
74	15.4727261177400	12.3382302998620	18.6072219356179
75	15.4727261177400	12.1436892583095	18.8017629771704
76	15.4727261177400	11.9599054860256	18.9855467494543
77	15.4727261177400	11.7852701966814	19.1601820387985
78	15.4727261177400	11.6185396213569	19.3269126141231
79	15.4727261177400	11.4587286179832	19.4867236174967
80	15.4727261177400	11.3050411119837	19.6404111234962
81	15.4727261177400	11.1568228882459	19.7886293472340
82	15.4727261177400	11.0135285368394	19.9319236986405
83	15.4727261177400	10.8746976875689	20.070754547911
84	15.4727261177400	10.7399375292001	20.2055147062798
85	15.4727261177400	10.6089096940903	20.3365425413897

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292961198l6y8u634igjwzqs/10ecb1292961309.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292961198l6y8u634igjwzqs/10ecb1292961309.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292961198l6y8u634igjwzqs/20ecb1292961309.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292961198l6y8u634igjwzqs/20ecb1292961309.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292961198l6y8u634igjwzqs/30ecb1292961309.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292961198l6y8u634igjwzqs/30ecb1292961309.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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