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tijdreeks 1 - 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: Thu, 19 Aug 2010 10:42:04 +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/t1282214511zpbbv5mfk4x9qxm.htm/, Retrieved Thu, 19 Aug 2010 12:41:57 +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/t1282214511zpbbv5mfk4x9qxm.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:

Vanhille Olivier

Dataseries X:

» Textbox « » Textfile « » CSV «

568 567 566 564 584 583 568 558 559 559 560 562 563 552 552 555 575 567 548 541 544 546 551 550 546 532 523 528 555 543 525 517 519 521 520 516 509 494 484 482 508 500 480 467 471 482 481 477 471 455 441 434 459 448 432 414 415 423 425 427 415 399 386 377 397 379 361 350 348 363 367 365 354 327 312 307 335 317 298 286 288 303 310 301 293 264 255 251 279 253 233 226 232 245 250 242 230 196 188 181 212 186 166 155 157 173 182 182 168 131 114 106 134 103 83 74 83 96 95 100

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	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.159879826158029
beta	0.162679015015255
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	563	569.183250874616	-6.18325087461562
14	552	557.33439358698	-5.33439358698047
15	552	556.374463218462	-4.37446321846176
16	555	558.303105875734	-3.30310587573388
17	575	577.116827516407	-2.1168275164066
18	567	567.905907590769	-0.905907590769061
19	548	554.850008677484	-6.8500086774842
20	541	542.925582471361	-1.92558247136083
21	544	542.814794204801	1.18520579519884
22	546	542.016231656842	3.98376834315786
23	551	542.534784013267	8.46521598673348
24	550	545.240863310984	4.75913668901569
25	546	541.952707171691	4.04729282830931
26	532	532.708499398416	-0.708499398415938
27	523	533.276144824115	-10.2761448241147
28	528	534.876877616726	-6.87687761672566
29	555	553.076719430947	1.92328056905274
30	543	545.669373155249	-2.66937315524876
31	525	527.816738128259	-2.81673812825886
32	517	520.826727169917	-3.82672716991749
33	519	522.764195053015	-3.76419505301465
34	521	523.181445422551	-2.18144542255106
35	520	525.856627034538	-5.85662703453795
36	516	522.412863367555	-6.4128633675549
37	509	515.867723666687	-6.86772366668686
38	494	500.312420258103	-6.3124202581027
39	484	490.873109716892	-6.87310971689237
40	482	494.018407219926	-12.0184072199262
41	508	515.274577405886	-7.27457740588579
42	500	501.478023083515	-1.47802308351476
43	480	483.202757856554	-3.2027578565536
44	467	474.053853723052	-7.0538537230521
45	471	473.343060449829	-2.34306044982924
46	482	473.152196941302	8.84780305869788
47	481	472.819125874555	8.18087412544503
48	477	470.07744308909	6.92255691090969
49	471	464.796480764317	6.20351923568319
50	455	452.330958879998	2.66904112000202
51	441	444.170547781539	-3.17054778153914
52	434	443.216200539286	-9.2162005392857
53	459	466.306458446974	-7.30645844697403
54	448	457.692182392112	-9.69218239211187
55	432	437.813469603639	-5.81346960363891
56	414	425.445136318417	-11.4451363184170
57	415	426.804306564024	-11.8043065640240
58	423	432.465801311299	-9.46580131129872
59	425	427.301500995212	-2.30150099521234
60	427	420.548751117413	6.4512488825871
61	415	413.558797442319	1.44120255768121
62	399	397.456166950320	1.54383304968047
63	386	384.017264008512	1.98273599148757
64	377	377.73218555922	-0.732185559219772
65	397	398.680810987198	-1.68081098719796
66	379	388.62806665606	-9.62806665606001
67	361	372.49138231528	-11.4913823152800
68	350	355.035453869911	-5.03545386991073
69	348	355.036203170460	-7.03620317045954
70	363	360.381598749655	2.61840125034513
71	367	361.451639155931	5.54836084406901
72	365	361.962947285333	3.03705271466686
73	354	350.814530402518	3.18546959748193
74	327	336.391564304689	-9.39156430468944
75	312	322.255834734169	-10.2558347341690
76	307	311.454649951764	-4.45464995176371
77	335	325.411006123239	9.58899387676075
78	317	311.659229817382	5.34077018261831
79	298	297.831046346352	0.168953653647634
80	286	288.385916173362	-2.38591617336215
81	288	286.23797279025	1.76202720975016
82	303	297.640003790733	5.35999620926719
83	310	300.222520976197	9.77747902380327
84	301	299.042643518259	1.95735648174099
85	293	289.202700563375	3.79729943662483
86	264	268.258173423532	-4.25817342353236
87	255	256.057995209247	-1.05799520924688
88	251	252.00795861768	-1.00795861767980
89	279	273.208923197524	5.7910768024758
90	253	258.322202851802	-5.32220285180227
91	233	241.385436755265	-8.3854367552646
92	226	229.815310740906	-3.81531074090634
93	232	229.619583720847	2.38041627915322
94	245	240.268568394566	4.73143160543427
95	250	244.255897297418	5.7441027025823
96	242	236.679648494476	5.32035150552414
97	230	229.705815731806	0.294184268194044
98	196	206.5070530395	-10.5070530394999
99	188	196.735807264228	-8.73580726422759
100	181	190.901480569547	-9.90148056954718
101	212	207.705997722744	4.29400227725611
102	186	187.684545379428	-1.6845453794281
103	166	171.783155564777	-5.78315556477665
104	155	164.367775272895	-9.36777527289519
105	157	164.786971595525	-7.78697159552459
106	173	169.517173695762	3.48282630423765
107	182	170.085871714437	11.9141282855631
108	182	163.288849350816	18.7111506491844
109	168	155.849734090144	12.1502659098561
110	131	133.946072823694	-2.94607282369441
111	114	127.413737722008	-13.4137377220083
112	106	119.818643675952	-13.8186436759520
113	134	134.805710996569	-0.805710996569218
114	103	115.910168634481	-12.910168634481
115	83	99.5139545307705	-16.5139545307705
116	74	88.240643099221	-14.2406430992211
117	83	84.105161574591	-1.10516157459108
118	96	87.9944675186025	8.00553248139747
119	95	88.3941000829922	6.60589991700779
120	100	83.1005090500912	16.8994909499088

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	73.795979792655	60.105527340696	87.486432244614
122	53.8812062763403	40.0364779553761	67.7259345973045
123	44.0544301697393	29.9997043929106	58.109155946568
124	38.1575530010276	23.792232615322	52.5228733867332
125	43.53670743324	28.0145587275830	59.058856138897
126	29.9874325851658	14.5937678441178	45.3810973262138
127	21.1666807118270	5.70590452947709	36.6274568941770
128	15.7140742154541	-0.207559864033360	31.6357082949415
129	13.0351101467714	-4.69165060357955	30.7618708971223
130	8.66861068109625	-12.0756770309744	29.4128983931669
131	1.24913105866199	-21.6078337307883	24.1060958481123
132	-7.5657434885315	-30.0846625116774	14.9531755346144

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282214511zpbbv5mfk4x9qxm/1j73q1282214521.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282214511zpbbv5mfk4x9qxm/1j73q1282214521.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282214511zpbbv5mfk4x9qxm/2bglt1282214521.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282214511zpbbv5mfk4x9qxm/2bglt1282214521.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282214511zpbbv5mfk4x9qxm/3bglt1282214521.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282214511zpbbv5mfk4x9qxm/3bglt1282214521.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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