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TIJDREEKS - STAP32

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 19 Aug 2010 20:45:08 +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/19/t12822507739u2q9k5tijgkv51.htm/, Retrieved Thu, 19 Aug 2010 22:46:13 +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/19/t12822507739u2q9k5tijgkv51.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:

Mertens Jeroen

Dataseries X:

» Textbox « » Textfile « » CSV «

349 348 347 345 365 364 349 339 340 340 341 343 341 343 341 335 355 357 337 325 336 338 337 328 326 327 319 310 320 322 303 292 303 315 311 307 308 312 309 310 309 304 287 275 290 298 294 286 294 292 287 281 280 271 264 259 271 279 279 273 286 286 280 277 269 255 252 245 257 267 261 258 271 262 258 253 236 228 235 226 231 235 227 222 233 221 218 220 204 196 208 190 191 194 179 162 179 176 168 170 153 142 155 136 136 144 135 114 135 132 123 123 103 97 113 108 111 121 111 97

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	0.531154412223295
beta	0.0234130278133079
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	341	344.971005098799	-3.97100509879908
14	343	345.230084535257	-2.23008453525716
15	341	342.031277410535	-1.03127741053476
16	335	334.961361197232	0.0386388027675366
17	355	354.43622356125	0.563776438749869
18	357	356.760407072831	0.239592927169099
19	337	340.962517825021	-3.96251782502145
20	325	328.868357744425	-3.86835774442505
21	336	327.365575032792	8.6344249672075
22	338	331.852138619124	6.14786138087607
23	337	336.248590106486	0.75140989351371
24	328	338.656364206358	-10.6563642063585
25	326	329.227864980564	-3.22786498056416
26	327	330.433855824206	-3.43385582420603
27	319	327.065605231230	-8.06560523123034
28	310	316.837320985567	-6.8373209855668
29	320	331.263876005043	-11.2638760050435
30	322	326.471034633389	-4.47103463338897
31	303	307.277186128511	-4.27718612851055
32	292	295.435934275592	-3.4359342755921
33	303	298.783531252887	4.21646874711342
34	315	299.242676600137	15.7573233998633
35	311	305.854408188781	5.14559181121939
36	307	305.030028199762	1.96997180023806
37	308	305.538420223475	2.46157977652547
38	312	309.303769913428	2.6962300865722
39	309	307.047794162493	1.95220583750677
40	310	302.888043117739	7.11195688226121
41	309	322.610335665247	-13.6103356652467
42	304	319.873465336919	-15.8734653369193
43	287	295.275493038155	-8.27549303815533
44	275	282.029435349058	-7.0294353490579
45	290	286.539307443089	3.46069255691071
46	298	291.539167893954	6.46083210604621
47	294	288.419975683605	5.58002431639483
48	286	286.439241295129	-0.439241295128795
49	294	285.667443830981	8.33255616901937
50	292	292.341572900368	-0.341572900368249
51	287	288.173121250955	-1.17312125095521
52	281	284.681943920705	-3.68194392070501
53	280	287.876034282732	-7.87603428273155
54	271	286.31467221216	-15.3146722121599
55	264	266.245851842678	-2.24585184267846
56	259	257.113523706497	1.88647629350316
57	271	270.310769897146	0.689230102854026
58	279	274.716165390592	4.28383460940785
59	279	270.278907563854	8.7210924361458
60	273	267.487340650798	5.51265934920156
61	286	273.661883104419	12.3381168955813
62	286	278.467856263020	7.53214373698034
63	280	278.331495093703	1.66850490629741
64	277	275.408983534337	1.59101646566251
65	269	279.546521296137	-10.5465212961367
66	255	273.066915316	-18.066915316
67	252	257.940750965684	-5.9407509656844
68	245	249.051848488310	-4.05184848830973
69	257	257.961202050557	-0.961202050557006
70	267	262.818639635673	4.18136036432747
71	261	260.520528579927	0.479471420072628
72	258	252.237221825492	5.7627781745079
73	271	261.036379678613	9.96362032138666
74	262	262.367878948694	-0.367878948693885
75	258	255.568252648599	2.43174735140101
76	253	253.055750819112	-0.0557508191115801
77	236	250.447748694841	-14.4477486948412
78	228	238.157417061136	-10.1574170611362
79	235	232.590167607075	2.4098323929249
80	226	229.192164888464	-3.19216488846354
81	231	238.947510546337	-7.94751054633679
82	235	241.53163023721	-6.53163023720987
83	227	232.049073345839	-5.0490733458391
84	222	223.499654305332	-1.49965430533229
85	233	228.639646522368	4.36035347763192
86	221	222.767286701235	-1.76728670123529
87	218	216.645284690256	1.35471530974414
88	220	212.47616214352	7.52383785647987
89	204	207.737225301989	-3.73722530198881
90	196	202.938562717491	-6.93856271749127
91	208	203.811378631308	4.18862136869248
92	190	199.227057633402	-9.22705763340161
93	191	201.675223548629	-10.6752235486290
94	194	201.692966021135	-7.69296602113548
95	179	192.469333396527	-13.4693333965270
96	162	181.090369306887	-19.090369306887
97	179	176.476873979083	2.52312602091683
98	176	168.252141071971	7.74785892802885
99	168	168.494785808252	-0.494785808251777
100	170	165.639871926519	4.36012807348078
101	153	156.268837803188	-3.26883780318838
102	142	150.243512661275	-8.24351266127513
103	155	152.028965146592	2.9710348534083
104	136	142.808469363308	-6.80846936330826
105	136	142.870668125711	-6.87066812571109
106	144	143.181118537295	0.81888146270461
107	135	136.611460286680	-1.61146028667986
108	114	129.298602276119	-15.2986022761191
109	135	131.883536184493	3.11646381550671
110	132	127.206571026194	4.79342897380643
111	123	123.085158709136	-0.0851587091361665
112	123	121.805782460192	1.19421753980778
113	103	110.479564649033	-7.47956464903281
114	97	100.779417214822	-3.77941721482249
115	113	105.592283799236	7.40771620076369
116	108	97.663230980736	10.3367690192641
117	111	105.197589085138	5.80241091486204
118	121	113.835101793862	7.16489820613818
119	111	110.664326344468	0.335673655531906
120	97	99.6124134355594	-2.61241343555938

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	114.816336493040	101.307662274083	128.325010711998
122	109.937861190096	94.633224997304	125.242497382889
123	102.265824995242	85.5186842746664	119.012965715817
124	101.515558884285	82.9645523451852	120.066565423386
125	87.9586018874726	69.0316348189462	106.885568955999
126	84.4431352797586	64.1282615071186	104.758009052399
127	94.84402736932	70.8973535825154	118.790701156125
128	85.6716481002423	61.5890113991952	109.754284801289
129	85.1616035253664	59.2495411975863	111.073665853146
130	89.2864481680714	60.3402311909033	118.232665145240
131	81.1325281080684	52.3728565984233	109.892199617713
132	71.3014872418878	46.4314347299195	96.171539753856

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/19/t12822507739u2q9k5tijgkv51/1dd6c1282250703.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t12822507739u2q9k5tijgkv51/1dd6c1282250703.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t12822507739u2q9k5tijgkv51/2dd6c1282250703.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t12822507739u2q9k5tijgkv51/2dd6c1282250703.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t12822507739u2q9k5tijgkv51/3645x1282250703.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t12822507739u2q9k5tijgkv51/3645x1282250703.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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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