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Exponential smoothing plat water

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 04 Jan 2011 13:44:50 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/04/t1294149041zd0krsvr1f67drl.htm/, Retrieved Tue, 04 Jan 2011 14:50:41 +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/2011/Jan/04/t1294149041zd0krsvr1f67drl.htm/},
    year = {2011},
}
@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 = {2011},
    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 - Kristina Henderickx

Dataseries X:

» Textbox « » Textfile « » CSV «

0.65 0.65 0.65 0.65 0.65 0.65 0.66 0.66 0.66 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.66 0.67 0.66 0.67 0.66 0.66 0.66 0.66 0.71 0.74 0.75 0.75 0.75 0.75 0.7 0.69 0.69 0.68 0.68 0.68 0.67 0.66 0.66 0.67 0.67 0.67 0.67 0.68 0.68 0.67 0.67 0.67 0.67 0.67 0.69 0.69 0.69 0.69 0.69 0.69 0.7 0.69 0.68 0.7 0.7 0.71 0.69 0.7 0.7 0.71 0.71 0.71 0.71 0.7 0.7 0.71 0.71 0.71 0.71 0.7 0.69 0.7 0.7 0.7 0.71 0.7 0.7 0.69

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	1
beta	0
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	0.65	0.65	0
4	0.65	0.65	0
5	0.65	0.65	0
6	0.65	0.65	0
7	0.66	0.65	0.01
8	0.66	0.66	0
9	0.66	0.66	0
10	0.65	0.66	-0.01
11	0.65	0.65	0
12	0.65	0.65	0
13	0.65	0.65	0
14	0.65	0.65	0
15	0.65	0.65	0
16	0.65	0.65	0
17	0.66	0.65	0.01
18	0.67	0.66	0.01
19	0.66	0.67	-0.01
20	0.67	0.66	0.01
21	0.66	0.67	-0.01
22	0.66	0.66	0
23	0.66	0.66	0
24	0.66	0.66	0
25	0.71	0.66	0.0499999999999999
26	0.74	0.71	0.03
27	0.75	0.74	0.01
28	0.75	0.75	0
29	0.75	0.75	0
30	0.75	0.75	0
31	0.7	0.75	-0.05
32	0.69	0.7	-0.01
33	0.69	0.69	0
34	0.68	0.69	-0.0099999999999999
35	0.68	0.68	0
36	0.68	0.68	0
37	0.67	0.68	-0.01
38	0.66	0.67	-0.01
39	0.66	0.66	0
40	0.67	0.66	0.01
41	0.67	0.67	0
42	0.67	0.67	0
43	0.67	0.67	0
44	0.68	0.67	0.01
45	0.68	0.68	0
46	0.67	0.68	-0.01
47	0.67	0.67	0
48	0.67	0.67	0
49	0.67	0.67	0
50	0.67	0.67	0
51	0.69	0.67	0.0199999999999999
52	0.69	0.69	0
53	0.69	0.69	0
54	0.69	0.69	0
55	0.69	0.69	0
56	0.69	0.69	0
57	0.7	0.69	0.01
58	0.69	0.7	-0.01
59	0.68	0.69	-0.0099999999999999
60	0.7	0.68	0.0199999999999999
61	0.7	0.7	0
62	0.71	0.7	0.01
63	0.69	0.71	-0.02
64	0.7	0.69	0.01
65	0.7	0.7	0
66	0.71	0.7	0.01
67	0.71	0.71	0
68	0.71	0.71	0
69	0.71	0.71	0
70	0.7	0.71	-0.01
71	0.7	0.7	0
72	0.71	0.7	0.01
73	0.71	0.71	0
74	0.71	0.71	0
75	0.71	0.71	0
76	0.7	0.71	-0.01
77	0.69	0.7	-0.01
78	0.7	0.69	0.01
79	0.7	0.7	0
80	0.7	0.7	0
81	0.71	0.7	0.01
82	0.7	0.71	-0.01
83	0.7	0.7	0
84	0.69	0.7	-0.01

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	0.69	0.668243878990188	0.711756121009812
86	0.69	0.659232198603294	0.720767801396706
87	0.69	0.65231729303539	0.72768270696461
88	0.69	0.646487757980377	0.733512242019623
89	0.69	0.64135183449535	0.73864816550465
90	0.69	0.636708604743717	0.743291395256283
91	0.69	0.632438714314611	0.747561285685389
92	0.69	0.628464397206588	0.751535602793412
93	0.69	0.624731636970565	0.755268363029435
94	0.69	0.621201104558753	0.758798895441247
95	0.69	0.617843109716887	0.762156890283113
96	0.69	0.614634586070779	0.76536541392922

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/04/t1294149041zd0krsvr1f67drl/1hsma1294148685.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/04/t1294149041zd0krsvr1f67drl/1hsma1294148685.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/04/t1294149041zd0krsvr1f67drl/2jl2q1294148685.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/04/t1294149041zd0krsvr1f67drl/2jl2q1294148685.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/04/t1294149041zd0krsvr1f67drl/3k9ns1294148685.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/04/t1294149041zd0krsvr1f67drl/3k9ns1294148685.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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