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Tijreeks A Stap 32

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 20 Aug 2010 06:21:42 +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/20/t12822853966mnppip8nv9ozjy.htm/, Retrieved Fri, 20 Aug 2010 08:23:16 +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/20/t12822853966mnppip8nv9ozjy.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 Tendeloo Willem MAR 201 A

Dataseries X:

» Textbox « » Textfile « » CSV «

252 251 250 248 268 267 252 242 243 243 244 246 236 241 240 239 253 249 232 229 221 222 224 224 215 225 225 221 238 234 228 227 216 219 225 227 205 215 214 209 222 216 206 199 189 198 203 211 199 211 210 203 214 202 193 193 176 192 200 195 180 197 194 194 212 202 195 198 170 187 190 189 176 188 195 194 211 203 194 194 163 183 181 184 171 178 179 186 205 204 195 186 156 167 164 165 153 160 154 169 186 188 187 169 131 146 145 137 119 118 113 123 142 141 138 124 83 100 96 98

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	0.738004770331473
beta	0.00040330803731264
gamma	0.993056849962919

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	236	242.919871794872	-6.91987179487191
14	241	242.844421905514	-1.84442190551403
15	240	240.597462599674	-0.597462599673577
16	239	239.603920712573	-0.603920712572801
17	253	253.522099621085	-0.522099621084777
18	249	249.542174152664	-0.542174152664415
19	232	236.047272209696	-4.0472722096963
20	229	222.797719870216	6.20228012978382
21	221	227.864232117884	-6.86423211788363
22	222	222.243886236117	-0.243886236117390
23	224	222.717647938579	1.28235206142091
24	224	225.693162468729	-1.69316246872879
25	215	212.880176802538	2.11982319746204
26	225	220.794387068484	4.20561293151567
27	225	223.336423244760	1.66357675523960
28	221	224.010143754598	-3.01014375459798
29	238	236.173375094842	1.82662490515762
30	234	233.921864316552	0.0781356834476696
31	228	219.973263378747	8.026736621253
32	227	218.305122375500	8.6948776245005
33	216	221.816376499747	-5.81637649974658
34	219	218.696909085873	0.303090914127239
35	225	219.976696024572	5.02330397542829
36	227	224.945269119408	2.05473088059222
37	205	215.897786261591	-10.8977862615910
38	215	214.751228481830	0.248771518170344
39	214	213.714158963002	0.285841036997965
40	209	212.157142571301	-3.15714257130097
41	222	225.472285489058	-3.47228548905818
42	216	218.855646691196	-2.85564669119628
43	206	204.809471930610	1.19052806938979
44	199	198.267511128100	0.732488871900472
45	189	192.122132444236	-3.12213244423609
46	198	192.579101849707	5.42089815029325
47	203	198.861397456291	4.13860254370923
48	211	202.401897024954	8.59810297504623
49	199	194.812657729491	4.18734227050911
50	211	207.702695208854	3.2973047911463
51	210	208.929639637437	1.07036036256309
52	203	207.060590756305	-4.06059075630466
53	214	219.631493776482	-5.63149377648202
54	202	211.585642847658	-9.58564284765825
55	193	193.627273055343	-0.627273055342613
56	193	185.625910450993	7.37408954900675
57	176	183.382475992651	-7.38247599265094
58	192	182.920008152688	9.07999184731176
59	200	191.572222466877	8.42777753312319
60	195	199.442798816816	-4.4427988168157
61	180	181.082244973198	-1.08224497319770
62	197	189.850674895864	7.14932510413558
63	194	193.341116872594	0.658883127405545
64	194	189.833408235382	4.16659176461792
65	212	208.069712008887	3.93028799111335
66	202	206.056984643891	-4.05698464389053
67	195	194.516449095078	0.483550904921998
68	198	189.423878164407	8.57612183559323
69	170	184.235835039232	-14.2358350392324
70	187	183.004249591043	3.99575040895664
71	190	187.738618001623	2.26138199837669
72	189	187.711951691381	1.28804830861864
73	176	174.459035857898	1.54096414210173
74	188	187.309755181968	0.690244818031886
75	195	184.347474628052	10.6525253719483
76	194	189.133486121603	4.86651387839723
77	211	207.830805799761	3.16919420023930
78	203	203.184013802688	-0.184013802688412
79	194	195.689965184857	-1.68996518485685
80	194	191.105052970836	2.89494702916429
81	163	175.793687440199	-12.7936874401987
82	183	180.374805878861	2.62519412113912
83	181	183.651016198034	-2.6510161980344
84	184	179.748836519265	4.25116348073493
85	171	168.752496592352	2.24750340764831
86	178	181.907498781423	-3.90749878142293
87	179	178.146831306662	0.853168693337778
88	186	174.195393789328	11.8046062106716
89	205	197.573426871851	7.42657312814865
90	204	195.199413517400	8.80058648259953
91	195	193.950141789495	1.04985821050511
92	186	192.586844307124	-6.58684430712441
93	156	166.199967869213	-10.1999678692126
94	167	176.711566047109	-9.71156604710868
95	164	169.511449397	-5.51144939700015
96	165	165.294192582807	-0.294192582807284
97	153	150.420854348426	2.57914565157353
98	160	162.218124716795	-2.21812471679536
99	154	160.942237802094	-6.9422378020939
100	169	154.0841380573	14.9158619426998
101	186	178.617240952035	7.38275904796515
102	188	176.566373136307	11.4336268636928
103	187	175.242521801349	11.7574781986509
104	169	179.796576813874	-10.7965768138739
105	131	149.363561882391	-18.3635618823906
106	146	153.975742189308	-7.97574218930825
107	145	149.148241638383	-4.1482416383835
108	137	147.293649833780	-10.2936498337796
109	119	125.784467627682	-6.7844676276823
110	118	129.416653420513	-11.4166534205128
111	113	120.113811035301	-7.1138110353006
112	123	118.806698942634	4.19330105736555
113	142	133.454028606123	8.54597139387727
114	141	133.303364113004	7.6966358869957
115	138	129.292549555985	8.70745044401522
116	124	125.713429896508	-1.71342989650771
117	83	100.003562887558	-17.0035628875582
118	100	108.310988013908	-8.3109880139077
119	96	104.220695108887	-8.22069510888707
120	98	97.7493086649663	0.250691335033650

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	84.9256286750589	72.0975511862882	97.7537061638295
122	92.3523415833215	76.4068273587536	108.297855807889
123	92.5906809139406	74.0425916736461	111.138770154235
124	99.4736936871483	78.6439991873445	120.303388186952
125	112.155817512138	89.2692902851702	135.042344739106
126	105.471674166226	80.6970397533869	130.246308579066
127	96.0358702563044	69.5058052837184	122.565935228890
128	83.3089291131015	55.1313020102517	111.486556215951
129	54.8755465692248	25.1402896418012	84.6108034966483
130	77.9884370210588	46.7720169382773	109.204857103840
131	80.0528127596765	47.4212814894648	112.684344029888
132	81.852465911647	47.8636238534155	115.841307969879

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/20/t12822853966mnppip8nv9ozjy/1r3lq1282285296.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t12822853966mnppip8nv9ozjy/1r3lq1282285296.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t12822853966mnppip8nv9ozjy/2r3lq1282285296.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t12822853966mnppip8nv9ozjy/2r3lq1282285296.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t12822853966mnppip8nv9ozjy/3kckb1282285296.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t12822853966mnppip8nv9ozjy/3kckb1282285296.ps (open in new window)

Parameters (Session):

par1 = 12 ;

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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