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Tijdreeks 1 stap 32

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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: Wed, 11 Aug 2010 13:42:05 +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/11/t1281534099ljrobcmcg3dd1aq.htm/, Retrieved Wed, 11 Aug 2010 15:41:43 +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/11/t1281534099ljrobcmcg3dd1aq.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:

Marianne Nykjaer

Dataseries X:

» Textbox « » Textfile « » CSV «

268 267 266 264 284 283 268 258 259 259 260 262 255 259 258 258 288 289 271 268 274 284 284 279 273 280 276 271 298 297 278 270 280 289 288 293 285 283 275 268 295 290 267 252 268 278 280 278 261 263 259 265 294 285 255 231 246 258 265 260 238 241 239 233 265 255 224 194 210 222 230 225 206 204 207 195 230 221 195 162 182 203 211 206 187 181 189 174 213 201 177 140 165 192 197 196 176 164 177 165 208 195 164 123 147 173 176 170 157 145 148 135 175 168 140 109 129 150 150 152

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	4 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.131066859076249
beta	0.192073350226661
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	266	266	0
4	264	265	-1
5	284	263.843758690197	20.1562413098027
6	283	265.967821782414	17.0321782175861
7	268	268.111199468881	-0.111199468880557
8	258	268.004849102474	-10.0048491024741
9	259	266.349902573036	-7.34990257303565
10	259	264.857901786057	-5.85790178605691
11	260	263.413983396093	-3.41398339609327
12	262	262.204436556555	-0.204436556554924
13	255	261.410408362313	-6.41040836231332
14	259	259.641604426522	-0.64160442652161
15	258	258.612747464200	-0.612747464199515
16	258	257.572247112446	0.427752887553822
17	288	256.678890317656	31.3211096823442
18	289	260.623120496677	28.3768795033234
19	271	264.895832028563	6.10416797143716
20	268	266.402998292676	1.59700170732361
21	274	267.359628072009	6.64037192799077
22	284	269.14444426123	14.8555557387699
23	284	272.379979245224	11.6200207547762
24	279	275.483970461366	3.51602953863431
25	273	277.614311115199	-4.61431111519943
26	280	278.562870808509	1.43712919149090
27	276	280.340752713723	-4.34075271372285
28	271	281.252069720199	-10.2520697201994
29	298	281.130518749618	16.8694812503824
30	297	284.988384202545	12.0116157974549
31	278	288.511930318781	-10.5119303187805
32	270	288.818753918452	-18.8187539184518
33	280	287.563076446760	-7.56307644676025
34	289	287.592248972709	1.40775102729083
35	288	288.832639037869	-0.832639037868546
36	293	289.75842698365	3.24157301634989
37	285	291.299813926765	-6.29981392676501
38	283	291.432046896729	-8.43204689672945
39	275	291.072542639377	-16.0725426393769
40	268	289.307005170526	-21.3070051705262
41	295	286.319010986972	8.68098901302847
42	290	287.479988141218	2.52001185878237
43	267	287.896905285385	-20.8969052853852
44	252	284.718572537776	-32.7185725377756
45	268	279.167138902158	-11.1671389021582
46	278	276.159257393703	1.84074260629654
47	280	274.90261774184	5.09738225815977
48	278	274.201139418782	3.79886058121815
49	261	273.425102166603	-12.4251021666029
50	263	270.209845953033	-7.20984595303258
51	259	267.496633078963	-8.49663307896282
52	265	264.400866987210	0.599133012789537
53	294	262.512337232505	31.4876627674946
54	285	265.464954669064	19.5350453309355
55	255	267.342764116597	-12.3427641165966
56	231	264.731726898528	-33.7317268985279
57	246	258.468127813007	-12.4681278130072
58	258	254.677603603003	3.32239639699739
59	265	253.040333308761	11.9596666912393
60	260	252.836200942801	7.16379905719879
61	238	252.183833975882	-14.1838339758823
62	241	248.376429569067	-7.37642956906689
63	239	245.275552713591	-6.27555271359094
64	233	242.160980737222	-9.16098073722236
65	265	238.437602114531	26.5623978854694
66	255	240.065068300251	14.9349316997490
67	224	240.544537716172	-16.5445377161721
68	194	236.481592300834	-42.4815923008337
69	210	227.949707855236	-17.9497078552356
70	222	222.181266415188	-0.181266415187537
71	230	218.737115502929	11.2628844970706
72	225	217.076450436345	7.92354956365526
73	206	215.177580236703	-9.17758023670271
74	204	210.806278126015	-6.80627812601548
75	207	206.574430821583	0.425569178417078
76	195	203.301152498974	-8.30115249897415
77	230	198.675113221519	31.3248867784812
78	221	200.031321268509	20.9686787314915
79	195	200.558048624364	-5.55804862436398
80	162	197.468080322886	-35.4680803228862
81	182	189.565008671361	-7.56500867136131
82	203	185.128660041739	17.8713399582611
83	211	184.476074900565	26.5239250994354
84	206	185.625282162222	20.3747178377780
85	187	186.481454472558	0.518545527442285
86	181	184.748194743731	-3.74819474373098
87	189	182.361348025178	6.63865197482184
88	174	181.502997098763	-7.50299709876276
89	213	178.602260815351	34.3977391846495
90	201	182.059266619793	18.9407333802070
91	177	183.967193781927	-6.96719378192682
92	140	182.304055029179	-42.3040550291788
93	165	174.944443514279	-9.94444351427862
94	192	171.575758738312	20.4242412616883
95	197	172.701571145475	24.2984288545247
96	196	174.946860751833	21.0531392481673
97	176	177.296801659332	-1.29680165933232
98	164	176.684759742071	-12.6847597420713
99	177	174.26080206851	2.73919793148994
100	165	173.927371885104	-8.92737188510375
101	208	171.840099356004	36.1599006439956
102	195	176.572579658645	18.4274203413551
103	164	179.444819649786	-15.4448196497861
104	123	177.488716684159	-54.4887166841589
105	147	169.043529254827	-22.0435292548266
106	173	164.295896892934	8.70410310706595
107	176	163.797381143533	12.2026188564671
108	170	164.064599091970	5.93540090802958
109	157	163.659812926461	-6.65981292646097
110	145	161.436554511906	-16.4365545119065
111	148	157.518108054075	-9.51810805407467
112	135	154.266827500942	-19.2668275009417
113	175	149.252781110315	25.7472188896854
114	168	150.786756487701	17.2132435122986
115	140	151.635544467583	-11.6355444675829
116	109	148.41029397791	-39.4102939779101
117	129	140.552561804427	-11.5525618044268
118	150	136.055225689999	13.9447743100006
119	150	135.250797368660	14.7492026313398
120	152	134.923106015648	17.0768939843519

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	135.330399283344	102.105376737128	168.555421829561
122	133.499477693733	99.8713665238017	167.127588863665
123	131.668556104123	97.5045233757499	165.832588832495
124	129.837634514512	94.9908966482832	164.68437238074
125	128.006712924901	92.3193049731988	163.694120876603
126	126.17579133529	89.4815387343311	162.870043936249
127	124.344869745679	86.4723783395158	162.217361151842
128	122.513948156068	83.2894330805575	161.738463231579
129	120.683026566457	79.9328325885497	161.433220544365
130	118.852104976846	76.4048201780365	161.299389775656
131	117.021183387236	72.7093021580612	161.33306461641
132	115.190261797625	68.8514011559819	161.529122439267

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/11/t1281534099ljrobcmcg3dd1aq/1raxl1281534121.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/11/t1281534099ljrobcmcg3dd1aq/1raxl1281534121.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/11/t1281534099ljrobcmcg3dd1aq/2raxl1281534121.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/11/t1281534099ljrobcmcg3dd1aq/2raxl1281534121.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/11/t1281534099ljrobcmcg3dd1aq/321f61281534121.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/11/t1281534099ljrobcmcg3dd1aq/321f61281534121.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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