Home » date » 2010 » Aug » 20 »

tijdreeks 2 - stap 27

*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 08:10:35 +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/t1282291823lddyygnrbxo2or9.htm/, Retrieved Fri, 20 Aug 2010 10:11:35 +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/t1282291823lddyygnrbxo2or9.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:

Aerts Ellen

Dataseries X:

» Textbox « » Textfile « » CSV «

112 118 132 129 121 135 148 148 136 119 104 118 115 126 141 135 125 149 170 170 158 133 114 140 145 150 178 163 172 178 199 199 184 162 146 166 171 180 193 181 183 218 230 242 209 191 172 194 196 196 236 235 229 243 264 272 237 211 180 201 204 188 235 227 234 264 302 293 259 229 203 229 242 233 267 269 270 315 364 347 312 274 237 278 284 277 317 313 318 374 413 405 355 306 271 306 315 301 356 348 355 422 465 467 404 347 305 336 340 318 362 348 363 435 491 505 404 359 310 337 360 342 406 396 420 472 548 559 463 407 362 405 417 391 419 461 472 535 622 606 508 461 390 432

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999933893038648
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	118	112	6
3	132	117.999603358232	14.0003966417681
4	129	131.99907447632	-2.99907447632029
5	121	129.000198259701	-8.00019825970051
6	135	121.000528868797	13.9994711312028
7	148	134.999074537503	13.000925462497
8	148	147.999140548323	0.000859451677087009
9	136	147.999999943184	-11.9999999431843
10	119	136.000793283532	-17.0007932835325
11	104	119.001123870785	-15.0011238707845
12	118	104.000991678716	13.999008321284
13	115	117.999074568098	-2.99907456809794
14	126	115.000198259707	10.9998017402934
15	141	125.999272836531	15.0007271634685
16	135	140.999008347509	-5.99900834750915
17	125	135.000396576213	-10.000396576213
18	149	125.00066109583	23.99933890417
19	170	148.998413476631	21.0015865233694
20	170	169.998611648931	0.00138835106864121
21	158	169.99999990822	-11.9999999082203
22	133	158.00079328353	-25.0007932835302
23	114	133.001652726475	-19.0016527264754
24	140	114.001256141522	25.9987438584776
25	145	139.998281302045	5.00171869795545
26	150	144.999669351575	5.00033064842467
27	178	149.999669443335	28.0003305566649
28	163	177.99814898323	-14.99814898323
29	172	163.000991482055	8.99900851794482
30	178	171.999405102892	6.0005948971083
31	199	177.999603318905	21.0003966810949
32	199	198.998611727588	0.00138827241175932
33	184	198.999999908226	-14.9999999082255
34	162	184.000991604414	-22.0009916044142
35	146	162.001454418702	-16.0014544187017
36	166	146.001057807529	19.9989421924712
37	171	165.998677930701	5.0013220692986
38	180	170.999669377795	9.00033062220476
39	193	179.999405015491	13.0005949845086
40	181	192.99914057017	-11.9991405701698
41	183	181.000793226722	1.99920677327808
42	218	182.999867838515	35.0001321614849
43	230	217.997686247616	12.0023137523841
44	242	229.999206563509	12.0007934364914
45	209	241.999206664012	-32.9992066640121
46	191	209.00218147728	-18.0021814772796
47	172	191.001190069515	-19.0011900695152
48	194	172.001256110938	21.9987438890624
49	196	193.998545729888	2.00145427011208
50	196	195.99986768994	0.000132310060081409
51	236	195.999999991253	40.0000000087466
52	235	235.997355721545	-0.997355721545347
53	229	235.000065932156	-6.00006593215613
54	243	229.000396646127	13.9996033538733
55	264	242.999074528762	21.0009254712378
56	272	263.998611692632	8.00138830736847
57	237	271.999471052532	-34.9994710525324
58	211	237.00231370868	-26.0023137086802
59	180	211.001718933947	-31.0017189339474
60	201	180.002049429435	20.9979505705646
61	204	200.998611889293	3.00138811070684
62	188	203.999801587352	-15.9998015873522
63	235	188.001057698265	46.9989423017348
64	227	234.996893042738	-7.99689304273767
65	234	227.000528650299	6.99947134970068
66	264	233.999537286218	30.000462713782
67	302	263.998016760571	38.0019832394291
68	293	301.997487804363	-8.99748780436272
69	259	293.000594796579	-34.0005947965785
70	229	259.002247676006	-30.0022476760062
71	203	229.001983357428	-26.0019833574276
72	229	203.001718912109	25.9982810878911
73	242	228.998281332637	13.0017186673631
74	233	241.999140495887	-8.99914049588654
75	267	233.000594905833	33.999405094167
76	269	266.997752402641	2.00224759735858
77	270	268.999867637495	1.00013236250453
78	315	269.999933884289	45.0000661157114
79	364	314.997025182368	49.0029748176315
80	347	363.996760562238	-16.9967605622376
81	312	347.001123604194	-35.0011236041936
82	274	312.002313817925	-38.0023138179254
83	237	274.002512217491	-37.0025122174908
84	278	237.002446123645	40.9975538763549
85	284	277.99728977629	6.00271022370964
86	277	283.999603179067	-6.99960317906721
87	317	277.000462722497	39.9995372775032
88	313	316.997355752135	-3.99735575213509
89	318	313.000264253042	4.99973574695781
90	374	317.999669482662	56.0003305173378
91	413	373.996297988315	39.0037020116852
92	405	412.997421583779	-7.99742158377853
93	355	405.00052868524	-50.0005286852395
94	306	355.003305383017	-49.0033053830174
95	271	306.003239459615	-35.0032394596151
96	306	271.002313957798	34.9976860422018
97	315	305.997686409321	9.00231359067863
98	301	314.999404884403	-13.9994048844034
99	356	301.000925458118	54.9990745418824
100	348	355.996364178305	-7.99636417830487
101	355	348.000528615338	6.99947138466229
102	422	354.999537286216	67.0004627137843
103	465	421.995570803001	43.0044291969992
104	467	464.997157107861	2.00284289213886
105	404	466.999867598142	-62.9998675981423
106	347	404.004164729812	-57.0041647298125
107	305	347.003768372115	-42.0037683721147
108	336	305.002776741492	30.9972232585076
109	340	335.99795086776	4.00204913223996
110	318	339.999735436693	-21.9997354366927
111	362	318.00145433566	43.9985456643398
112	348	361.997091389842	-13.9970913898422
113	363	348.00092530518	14.9990746948205
114	435	362.999008456749	72.0009915432512
115	491	434.995240233235	56.0047597667652
116	505	490.996297695511	14.0037023044894
117	404	504.999074257793	-100.999074257793
118	359	404.006676741899	-45.0066767418986
119	310	359.00297525464	-49.00297525464
120	337	310.003239437791	26.9967605622087
121	360	336.998215326193	23.0017846738071
122	342	359.99847942191	-17.9984794219096
123	406	342.001189824784	63.9988101752165
124	396	405.995769233129	-9.99576923312918
125	420	396.00066078993	23.9993392100696
126	472	419.99841347661	52.0015865233896
127	548	471.996562333129	76.0034376668705
128	559	547.994975643684	11.0050243563164
129	463	558.99927249128	-95.9992724912802
130	407	463.006346220196	-56.0063462201964
131	362	407.003702409365	-45.003702409365
132	405	362.002975058016	42.9970249419841
133	417	404.997157597334	12.0028424026661
134	391	416.999206528561	-25.9992065285612
135	419	391.001718728541	27.9982812714588
136	461	418.998149118702	42.0018508812979
137	472	460.997223385267	11.0027766147329
138	535	471.999272639872	63.0007273601285
139	622	534.995835213351	87.0041647866487
140	606	621.994248419041	-15.994248419041
141	508	606.001057331162	-98.001057331162
142	461	508.006478552109	-47.0064785521095
143	390	461.003107455461	-71.0031074554609
144	432	390.00469379968	41.9953062003196

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
145	431.997223817916	365.838723296861	498.155724338972
146	431.997223817916	338.43806762164	525.556380014192
147	431.997223817916	317.412389633265	546.582058002567
148	431.997223817916	299.686783027748	564.307664608084
149	431.997223817916	284.070142933268	579.924304702565
150	431.997223817916	269.951582790402	594.04286484543
151	431.997223817916	256.968202530066	607.026245105766
152	431.997223817916	244.883550319832	619.110897316
153	431.997223817916	233.533384978413	630.461062657419
154	431.997223817916	222.798122854559	641.196324781273
155	431.997223817916	212.587487568948	651.406960066884
156	431.997223817916	202.831343116171	661.163104519661

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282291823lddyygnrbxo2or9/116r21282291830.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282291823lddyygnrbxo2or9/116r21282291830.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282291823lddyygnrbxo2or9/216r21282291830.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282291823lddyygnrbxo2or9/216r21282291830.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282291823lddyygnrbxo2or9/316r21282291830.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282291823lddyygnrbxo2or9/316r21282291830.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

We may request personal information to be submitted to our servers in order to be able to:

personalize online software applications according to your needs
enforce strict security rules with respect to the data that you upload (e.g. statistical data)
manage user sessions of online applications
alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by