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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: Sun, 15 Aug 2010 10:38:03 +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/15/t1281868780b1f8qy0nn8359cv.htm/, Retrieved Sun, 15 Aug 2010 12:39:44 +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/15/t1281868780b1f8qy0nn8359cv.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	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.211128878579708
beta	0.136550211331593
gamma	0.948390526889117

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	563	569.188568376069	-6.18856837606882
14	552	557.092262987191	-5.09226298719102
15	552	555.872277613779	-3.87227761377858
16	555	557.631563142701	-2.63156314270122
17	575	576.326932169056	-1.32693216905648
18	567	567.217824756121	-0.217824756121104
19	548	554.336602126659	-6.33660212665893
20	541	541.939179932109	-0.939179932109255
21	544	542.029233163613	1.97076683638738
22	546	541.54047679592	4.45952320408014
23	551	542.49740212071	8.50259787928951
24	550	545.844731220821	4.15526877917864
25	546	543.22231574882	2.77768425118052
26	532	533.881034697877	-1.88103469787677
27	523	534.386132710743	-11.3861327107431
28	528	535.405013300468	-7.40501330046845
29	555	553.84875854299	1.15124145700997
30	543	545.944217032109	-2.94421703210912
31	525	527.682525999883	-2.68252599988284
32	517	519.973018099372	-2.97301809937187
33	519	521.630443341301	-2.6304433413012
34	521	521.719244208649	-0.719244208648774
35	520	524.145361001102	-4.14536100110195
36	516	520.742935922923	-4.74293592292281
37	509	514.127753015663	-5.12775301566285
38	494	498.32058844229	-4.32058844229005
39	484	489.817620430112	-5.81762043011224
40	482	493.769527579601	-11.7695275796007
41	508	516.346246663387	-8.34624666338732
42	500	501.751671121325	-1.75167112132533
43	480	482.351137516685	-2.35113751668501
44	467	472.917405498617	-5.9174054986172
45	471	472.547743919449	-1.54774391944875
46	482	472.66448489772	9.33551510228
47	481	473.309523301921	7.69047669807918
48	477	470.959476427117	6.04052357288293
49	471	465.64454457022	5.35545542977979
50	455	452.268257559028	2.73174244097163
51	441	443.951223454065	-2.95122345406514
52	434	443.954980284937	-9.9549802849374
53	459	469.427907049058	-10.4279070490578
54	448	459.219552722014	-11.2195527220143
55	432	436.990560312967	-4.99056031296652
56	414	423.87432455116	-9.87432455115953
57	415	425.367249342679	-10.3672493426792
58	423	430.938880024783	-7.93888002478303
59	425	425.382576569201	-0.382576569201262
60	427	418.537436188394	8.46256381160583
61	415	411.734941144982	3.26505885501803
62	399	394.407707278024	4.59229272197604
63	386	380.738720164393	5.26127983560656
64	377	375.980208479714	1.01979152028554
65	397	402.476552782214	-5.47655278221436
66	379	391.9241925578	-12.9241925577999
67	361	373.14932327104	-12.1493232710396
68	350	353.815206135173	-3.81520613517296
69	348	355.340649761086	-7.34064976108641
70	363	362.577392175318	0.422607824681734
71	367	363.890112984887	3.10988701511332
72	365	363.950945414734	1.04905458526565
73	354	351.032012152796	2.9679878472038
74	327	333.963796108350	-6.9637961083497
75	312	317.351092009673	-5.35109200967321
76	307	305.868346849003	1.13165315099701
77	335	326.220889682627	8.7791103173734
78	317	312.210160100831	4.78983989916918
79	298	297.369508318557	0.63049168144289
80	286	286.951802005276	-0.95180200527642
81	288	286.509742762669	1.49025723733058
82	303	301.739217809734	1.26078219026607
83	310	305.583705555165	4.4162944448347
84	301	304.760488556107	-3.76048855610691
85	293	292.505087564014	0.494912435986237
86	264	267.656193907221	-3.65619390722094
87	255	253.215737255721	1.78426274427881
88	251	248.562658419613	2.43734158038725
89	279	275.423087747294	3.57691225270594
90	253	257.690154454076	-4.69015445407632
91	233	237.823582251376	-4.82358225137577
92	226	225.000748006482	0.99925199351847
93	232	226.784096906383	5.2159030936169
94	245	242.722327431076	2.27767256892363
95	250	249.265495771227	0.734504228772607
96	242	241.564441117098	0.435558882901546
97	230	233.516648909001	-3.51664890900088
98	196	204.737453854207	-8.7374538542073
99	188	193.170363987551	-5.17036398755104
100	181	187.212915828660	-6.21291582865956
101	212	212.525567674632	-0.525567674631645
102	186	187.049100769234	-1.04910076923352
103	166	167.264095175631	-1.26409517563087
104	155	159.064449885067	-4.06444988506726
105	157	162.302719948844	-5.30271994884427
106	173	172.887950376011	0.112049623989037
107	182	176.822970709624	5.17702929037648
108	182	168.967890821339	13.0321091786608
109	168	160.117561106162	7.88243889383835
110	131	129.662530852471	1.33746914752939
111	114	123.005226209033	-9.00522620903251
112	106	115.461508164519	-9.46150816451933
113	134	144.253040546098	-10.2530405460978
114	103	115.960415475181	-12.9604154751810
115	83	92.7856157490616	-9.7856157490616
116	74	79.7319292067056	-5.73192920670564
117	83	80.6838571107754	2.31614288922464
118	96	96.1405340141688	-0.140534014168779
119	95	103.016131166620	-8.01613116662014
120	100	97.0765793783133	2.92342062168669

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	80.7719619088469	69.8170784260467	91.726845391647
122	42.0615168895032	30.7956555617631	53.3273782172433
123	25.6507723667705	14.0064616731713	37.2950830603697
124	18.193472295747	6.1013267303675	30.2856178611265
125	47.1897090697291	34.5798255641353	59.7995925753229
126	18.1311430122568	4.93428745826101	31.3279985662527
127	-0.46355244000037	-14.3150137301488	13.3879088501480
128	-8.66776420319101	-23.2391952974932	5.90366689111118
129	-0.568530952970889	-15.9225975588113	14.7855356528695
130	12.4102862363036	-3.78615607388423	28.6067285464914
131	13.2765426811373	-3.8190193944709	30.3721047567455
132	17.2982210719631	-0.750251187227761	35.3466933311539

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/15/t1281868780b1f8qy0nn8359cv/1xky41281868681.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t1281868780b1f8qy0nn8359cv/1xky41281868681.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t1281868780b1f8qy0nn8359cv/2qbg71281868681.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t1281868780b1f8qy0nn8359cv/2qbg71281868681.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t1281868780b1f8qy0nn8359cv/3qbg71281868681.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t1281868780b1f8qy0nn8359cv/3qbg71281868681.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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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