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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, 08 Aug 2010 13:53:04 +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/Aug/08/t1281275568m51iu1mbxzk8how.htm/, Retrieved Sun, 08 Aug 2010 15:52:49 +0200

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/Aug/08/t1281275568m51iu1mbxzk8how.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:

Philippe De Vocht

Dataseries X:

» Textbox « » Textfile « » CSV «

31 30 29 27 25 24 25 27 28 28 29 31 31 27 25 16 20 21 25 24 28 27 23 36 37 30 27 22 22 25 33 35 35 29 25 34 31 29 21 19 18 25 23 22 20 15 17 25 26 26 23 24 24 42 40 45 47 40 39 49 55 54 48 44 48 62 57 60 56 57 54 62 65 68 69 67 72 82 72 77 79 78 76 79

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

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.520658832476646
beta	0.067876565022126
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	31	33.4532585470086	-2.45325854700855
14	27	27.9437063932419	-0.94370639324185
15	25	25.1867648143938	-0.186764814393758
16	16	15.733997852804	0.266002147196016
17	20	19.7763686665064	0.223631333493614
18	21	20.5545819923582	0.445418007641752
19	25	21.6306784855387	3.36932151446134
20	24	25.2648714500169	-1.26487145001688
21	28	25.6081963514623	2.39180364853766
22	27	27.2732623898035	-0.273262389803502
23	23	28.5827476842845	-5.58274768428446
24	36	27.5971719516474	8.40282804835264
25	37	30.8059890247365	6.19401097526351
26	30	30.9832039372543	-0.983203937254345
27	27	29.0280343300292	-2.02803433002919
28	22	19.2280559865027	2.77194401349728
29	22	25.0378508230883	-3.03785082308835
30	25	24.5919869542078	0.408013045792174
31	33	27.4165644467448	5.5834355532552
32	35	30.426852848416	4.57314715158404
33	35	36.2135641724589	-1.21356417245894
34	29	35.2475476858376	-6.2475476858376
35	25	31.2138392076751	-6.21383920767513
36	34	36.8936647030592	-2.89366470305916
37	31	33.0529844221037	-2.05298442210366
38	29	25.0954388777111	3.90456112228889
39	21	24.9564784361836	-3.95647843618357
40	19	16.1572949530762	2.8427050469238
41	18	18.9255881332673	-0.925588133267304
42	25	21.0124152164847	3.98758478351532
43	23	28.0892037074708	-5.08920370747081
44	22	24.588920918756	-2.588920918756
45	20	23.1502235058481	-3.15022350584807
46	15	17.9718243487919	-2.97182434879194
47	17	14.9845254806881	2.01547451931187
48	25	26.156057971405	-1.156057971405
49	26	23.3000043929845	2.69999560701545
50	26	20.5177633091302	5.48223669086979
51	23	17.3327961938787	5.66720380612129
52	24	17.0441849675901	6.95581503240989
53	24	20.5338551850987	3.46614481490132
54	42	27.8037170904305	14.1962829095695
55	40	36.7470111008003	3.25298889919974
56	45	39.9856056445657	5.01439435543433
57	47	43.7022438614477	3.29775613855232
58	40	43.6600891697468	-3.66008916974681
59	39	44.3742660117104	-5.37426601171036
60	49	51.5860705744426	-2.58607057444264
61	55	51.191347956425	3.80865204357505
62	54	51.7166762658176	2.28332373418243
63	48	48.2384728670048	-0.238472867004774
64	44	46.5676372155521	-2.56763721555208
65	48	44.1644653155488	3.83553468445121
66	62	57.5214746833759	4.47852531662414
67	57	56.5675547520897	0.432445247910273
68	60	59.4902366714991	0.509763328500867
69	56	60.1877617203679	-4.18776172036789
70	57	52.797600284894	4.20239971510598
71	54	56.9462163685593	-2.94621636855931
72	62	67.0069523359699	-5.00695233596994
73	65	68.5797238562198	-3.57972385621977
74	68	64.4286610041063	3.57133899589368
75	69	60.359377007645	8.64062299235505
76	67	62.4559524697232	4.54404753027679
77	72	67.3370724590954	4.66292754090463
78	82	81.9745501287929	0.0254498712070728
79	72	77.1467373538709	-5.14673735387088
80	77	77.3885519880273	-0.388551988027331
81	79	75.5218188247699	3.47818117523011
82	78	76.5708412871296	1.42915871287043
83	76	76.1770043950383	-0.177004395038267
84	79	87.1177103046535	-8.11771030465347

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	88.070982587435	79.9318722909182	96.2100928839519
86	89.6540577536913	80.3414952710334	98.9666202363492
87	86.4715524088726	75.9887759251451	96.9543288926002
88	82.1166010384526	70.458773669134	93.7744284077712
89	84.5391646783563	71.6963338922973	97.3819954644154
90	94.2114816823134	80.1703219083436	108.252641456283
91	86.5758442362144	71.320746443016	101.830942029413
92	91.6447039946236	75.158488560029	108.130919429218
93	91.7140466131453	73.9784464277438	109.449646798547
94	89.7273100976971	70.7233071895595	108.731313005835
95	87.5263293599868	67.2343947243994	107.818263995574
96	94.4660027198983	72.8662702628845	116.065735176912

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/08/t1281275568m51iu1mbxzk8how/16qn51281275579.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/08/t1281275568m51iu1mbxzk8how/16qn51281275579.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/08/t1281275568m51iu1mbxzk8how/2hz4q1281275579.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/08/t1281275568m51iu1mbxzk8how/2hz4q1281275579.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/08/t1281275568m51iu1mbxzk8how/3hz4q1281275579.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/08/t1281275568m51iu1mbxzk8how/3hz4q1281275579.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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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