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Tijdreeks 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, 13 Aug 2010 14:29:10 +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/13/t1281709825bvw77wtm0kcscyd.htm/, Retrieved Fri, 13 Aug 2010 16:30:29 +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/13/t1281709825bvw77wtm0kcscyd.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:

Cols Julien

Dataseries X:

» Textbox « » Textfile « » CSV «

356 355 354 352 372 371 356 346 347 347 348 350 353 351 348 351 370 370 351 335 330 328 332 334 343 334 336 343 365 364 351 326 320 312 315 316 319 311 315 322 336 339 317 295 291 283 285 289 296 283 285 289 306 306 283 258 255 248 244 249 258 252 246 249 267 284 261 235 229 218 218 229 237 231 229 233 245 256 224 194 192 178 170 187 192 182 178 186 204 224 194 173 178 168 152 163 172 170 156 155 178 194 164 135 139 135 109 121 131 135 119 121 151 169 135 105 112 105 82 81

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0011609542690148
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	354	354	0
4	352	353	-1
5	372	350.998839045731	21.0011609542690
6	371	371.023220433195	-0.0232204331950925
7	356	370.023193475334	-14.0231934753340
8	346	355.006913189004	-9.00691318900368
9	347	344.996456574686	2.00354342531375
10	347	345.998782596979	1.00121740302097
11	348	345.999944964597	2.00005503540274
12	350	347.002266937029	2.99773306297112
13	353	349.005747168026	3.99425283197428
14	351	352.010384312902	-1.01038431290249
15	348	350.009211302921	-2.00921130292107
16	351	347.006878700482	3.99312129951841
17	370	350.011514531701	19.988485468299
18	370	369.034720249237	0.965279750763443
19	351	369.035840894884	-18.0358408948840
20	335	350.014902108402	-15.0149021084018
21	330	333.9974704937	-3.99747049370023
22	328	328.992829613265	-0.992829613265314
23	332	326.991676983487	5.00832301651263
24	334	330.997491417474	3.00250858252599
25	343	333.000977192631	9.99902280736939
26	334	342.012585600845	-8.01258560084483
27	336	333.003283355386	2.99671664461431
28	343	335.006762406367	7.99323759363273
29	365	342.016042189675	22.9839578103251
30	364	364.042725513614	-0.0427255136136182
31	351	363.042675911246	-12.0426759112462
32	326	350.028694915237	-24.0286949152367
33	320	325.000798699296	-5.00079869929596
34	312	318.994993000697	-6.99499300069749
35	315	310.986872133712	4.01312786628836
36	316	313.99153119164	2.00846880835991
37	319	314.993862932077	4.00613706792268
38	311	317.998513874009	-6.99851387400861
39	315	309.99038891945	5.0096110805502
40	322	313.99620484882	8.0037951511801
41	336	321.005496888969	14.994503111031
42	339	335.022904821367	3.97709517863251
43	317	338.027522046993	-21.0275220469934
44	295	316.003110055506	-21.0031100555061
45	291	293.978726405225	-2.97872640522462
46	283	289.975268240088	-6.97526824008821
47	285	281.967170272647	3.03282972735263
48	289	283.970691249267	5.02930875073343
49	296	287.976530046731	8.02346995326911
50	283	294.985844928425	-11.9858449284255
51	285	281.971929910588	3.02807008941193
52	289	283.975445361485	5.02455463851476
53	306	287.981278639643	18.0187213603573
54	306	305.002197551128	0.997802448871767
55	283	305.003355954141	-22.0033559541409
56	258	281.977811064113	-23.9778110641133
57	255	256.949973921997	-1.94997392199673
58	248	253.947710091448	-5.94771009144753
59	244	246.940805072026	-2.94080507202600
60	249	242.937390931823	6.06260906817673
61	258	247.944429343702	10.0555706562976
62	252	256.956103401383	-4.95610340138319
63	246	250.950349591982	-4.95034959198165
64	249	244.944602462490	4.05539753751029
65	267	247.949310593573	19.0506894064266
66	284	265.971427572768	18.0285724272325
67	261	282.992357920891	-21.9923579208912
68	235	259.966825799077	-24.9668257990772
69	229	233.937840456082	-4.937840456082
70	218	227.932107849125	-9.9321078491248
71	218	216.920577126117	1.07942287388295
72	229	216.921830286711	12.0781697132894
73	237	227.935852489401	9.06414751059893
74	231	235.946375550149	-4.9463755501485
75	229	229.940633034337	-0.940633034337395
76	233	227.939541002401	5.0604589975994
77	245	231.945415963877	13.0545840361229
78	256	243.960571738944	12.039428261056
79	224	254.97454896458	-30.9745489645802
80	194	222.938588929729	-28.9385889297289
81	192	192.904992551372	-0.904992551371691
82	178	190.903941896406	-12.9039418964057
83	170	176.888961009974	-6.888961009974
84	187	168.880963241280	18.1190367587196
85	192	185.901998614356	6.09800138564412
86	182	190.909078115097	-8.90907811509697
87	178	180.898735082826	-2.89873508282628
88	186	176.895369783957	9.10463021604286
89	204	184.905939843274	19.0940601567258
90	224	202.928107173926	21.071892826074
91	194	222.952570677859	-28.9525706778587
92	173	192.918958067331	-19.9189580673313
93	178	171.895833067929	6.10416693207134
94	168	176.902919726587	-8.90291972658724
95	152	166.892583843924	-14.8925838439239
96	163	150.875294235134	12.1247057648663
97	172	161.889370464052	10.1106295359480
98	170	170.901108442574	-0.901108442574156
99	156	168.900062296881	-12.9000622968809
100	155	154.885085914487	0.114914085513220
101	178	153.885219324485	24.1147806755151
102	194	176.913215482057	17.0867845179435
103	164	192.933052457486	-28.9330524574864
104	135	162.899462506720	-27.8994625067202
105	139	133.867072506620	5.13292749338018
106	135	137.873031600706	-2.87303160070579
107	109	133.869696142404	-24.8696961424039
108	121	107.840823562498	13.1591764375017
109	131	119.85610076456	11.1438992354398
110	135	129.869038321951	5.130961678049
111	119	133.874995133815	-14.8749951338153
112	121	117.857725944713	3.14227405528689
113	151	119.861373981192	31.138626018808
114	169	149.897524502000	19.1024754980002
115	135	167.919701602478	-32.9197016024779
116	105	133.881483334368	-28.8814833343679
117	112	103.847953252995	8.15204674700465
118	105	110.857417406467	-5.85741740646749
119	82	103.850617212724	-21.8506172127241
120	81	80.8252496453903	0.174750354609671

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	79.8254525225605	53.0698731131734	106.581031931948
122	78.650905045121	40.7908312503085	116.510978839934
123	77.4763575676816	31.080512879325	123.872202256038
124	76.3018100902421	22.6974202604850	129.906199919999
125	75.1272626128027	15.1609743212278	135.093550904377
126	73.9527151353632	8.22485421333582	139.680576057391
127	72.7781676579237	1.74282118542384	143.813514130424
128	71.6036201804842	-4.38035117145721	147.587591532426
129	70.4290727030448	-10.2107685227119	151.068913928801
130	69.2545252256053	-15.7965338487652	154.305584299976
131	68.0799777481658	-21.1739398262426	157.333895322574
132	66.9054302707264	-26.3711658331901	160.182026374643

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/13/t1281709825bvw77wtm0kcscyd/1ehbg1281709748.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/13/t1281709825bvw77wtm0kcscyd/1ehbg1281709748.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/13/t1281709825bvw77wtm0kcscyd/2ehbg1281709748.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/13/t1281709825bvw77wtm0kcscyd/2ehbg1281709748.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/13/t1281709825bvw77wtm0kcscyd/3p8bj1281709748.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/13/t1281709825bvw77wtm0kcscyd/3p8bj1281709748.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

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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