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tijdreeks 2 - stap 27

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 06 Aug 2010 07:52:42 +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/06/t1281081221vp8qubzqqu2f4ez.htm/, Retrieved Fri, 06 Aug 2010 09:53:42 +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/06/t1281081221vp8qubzqqu2f4ez.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:

Van de Walle Mathias

Dataseries X:

» Textbox « » Textfile « » CSV «

239 238 237 235 233 232 233 235 236 236 237 239 238 237 244 230 237 244 239 240 230 228 231 228 225 227 238 214 222 233 228 218 203 209 207 203 195 199 207 182 181 189 186 174 153 158 153 147 143 156 168 142 146 150 145 133 111 115 109 105 96 112 127 107 116 125 120 107 86 87 79 83 75 89 104 86 98 98 85 74 49 54 47 56

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	0.346185870041599
beta	0.111603919487912
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	238	235.941239316239	2.0587606837606
14	237	235.3969563733	1.60304362670033
15	244	243.256845337065	0.74315466293453
16	230	230.389431859024	-0.389431859024484
17	237	238.114886958018	-1.11488695801847
18	244	245.671125314383	-1.67112531438292
19	239	234.428570048477	4.57142995152327
20	240	238.440386271279	1.55961372872056
21	230	240.136477709341	-10.1364777093412
22	228	236.558584311988	-8.55858431198797
23	231	234.321268417602	-3.32126841760171
24	228	234.060384419367	-6.06038441936744
25	225	230.879823462712	-5.87982346271187
26	227	226.182264653014	0.81773534698624
27	238	232.070646540989	5.92935345901117
28	214	219.321056263557	-5.3210562635569
29	222	223.737338651766	-1.73733865176635
30	233	229.562766441861	3.43723355813876
31	228	223.215838609252	4.78416139074776
32	218	224.386065407814	-6.38606540781421
33	203	214.431352238965	-11.4313522389646
34	209	210.133759276445	-1.1337592764454
35	207	212.874826045797	-5.87482604579728
36	203	208.824187260518	-5.82418726051802
37	195	204.737696897866	-9.73769689786576
38	199	201.828752932247	-2.82875293224694
39	207	208.40113315391	-1.40113315390957
40	182	184.07924956736	-2.07924956736014
41	181	190.407228731678	-9.4072287316782
42	189	195.110669698856	-6.11066969885616
43	186	184.12015551378	1.87984448622038
44	174	174.65060880023	-0.650608800230458
45	153	161.273255306033	-8.27325530603287
46	158	162.814183405711	-4.81418340571108
47	153	159.051687882799	-6.05168788279883
48	147	152.836422182996	-5.83642218299565
49	143	144.050007460696	-1.05000746069641
50	156	146.864458068119	9.13554193188074
51	168	157.17302906551	10.8269709344904
52	142	135.774344565098	6.22565543490157
53	146	139.640458315702	6.35954168429771
54	150	152.020859648375	-2.02085964837457
55	145	147.891894023194	-2.89189402319386
56	133	135.153036320324	-2.15303632032445
57	111	116.250765887901	-5.2507658879006
58	115	121.195399428938	-6.1953994289378
59	109	116.188056501917	-7.1880565019172
60	105	109.718643381837	-4.71864338183654
61	96	104.490303212596	-8.49030321259619
62	112	111.142713390679	0.857286609321037
63	127	119.125742074271	7.87425792572856
64	107	93.0167773537544	13.9832226462456
65	116	99.276019411588	16.7239805884119
66	125	109.785687020689	15.2143129793113
67	120	111.740161786482	8.25983821351832
68	107	104.462168538912	2.53783146108769
69	86	86.4569225710658	-0.456922571065846
70	87	93.9271673493949	-6.92716734939488
71	79	89.4728762963973	-10.4728762963973
72	83	84.8093236651718	-1.80932366517177
73	75	79.5630694829347	-4.56306948293468
74	89	95.2792353176928	-6.27923531769282
75	104	106.696387949595	-2.69638794959508
76	86	81.8306301455162	4.16936985448385
77	98	87.0137239355625	10.9862760644375
78	98	94.8576796971306	3.14232030286936
79	85	87.9272998192283	-2.92729981922825
80	74	72.4443581959761	1.55564180402391
81	49	51.5121415641949	-2.51214156419486
82	54	53.332218301527	0.667781698472979
83	47	48.7740500496292	-1.77405004962918
84	56	52.7074398851711	3.29256011482893

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	47.5452413114487	35.3596142377337	59.7308683851638
86	64.0136146958272	50.9568552213931	77.0703741702614
87	80.4842595986172	66.4448322143786	94.5236869828558
88	61.682252998325	46.555704389738	76.8088016069121
89	70.3592432679948	54.048414708992	86.6700718269975
90	69.3272377217598	51.7419940949844	86.9124813485352
91	57.2750431538902	38.3317389563754	76.2183473514051
92	45.7840158173614	25.4048505862527	66.1631810484702
93	21.6410942953023	-0.246548426581541	43.5287370171862
94	26.4943866196423	3.03020828654	49.9585649527446
95	20.1672063788479	-4.93757332568744	45.2719860833833
96	28.1545789555547	1.34862612537637	54.9605317857329

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/06/t1281081221vp8qubzqqu2f4ez/1hrfd1281081158.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/06/t1281081221vp8qubzqqu2f4ez/1hrfd1281081158.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/06/t1281081221vp8qubzqqu2f4ez/2siwy1281081158.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/06/t1281081221vp8qubzqqu2f4ez/2siwy1281081158.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/06/t1281081221vp8qubzqqu2f4ez/3siwy1281081158.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/06/t1281081221vp8qubzqqu2f4ez/3siwy1281081158.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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