Home » date » 2010 » Aug » 05 »

Omzet product X

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 05 Aug 2010 15:06:05 +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/05/t1281020784pabbe0oyop8dv8a.htm/, Retrieved Thu, 05 Aug 2010 17:06:28 +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/05/t1281020784pabbe0oyop8dv8a.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:

Philippe De Vocht

Dataseries X:

» Textbox « » Textfile « » CSV «

73 72 71 69 89 88 73 63 64 64 65 67 69 71 70 72 88 83 76 70 75 71 75 81 87 90 80 85 105 104 98 94 107 112 121 118 120 122 109 112 132 127 116 113 123 125 137 127 123 128 114 120 143 135 119 117 132 139 158 141 139 150 142 149 166 150 139 140 158 169 186 177 175 187 176 185 204 188 171 171 182 185 200 192 185 195 190 195 213 194 171 171 186 182 193 185 172 185 179 182 193 173 155 164 188 186 200 185 173 190 190 193 195 178 163 165 188 182 200 177

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	0.691910685724984
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	72	73	-1
3	71	72.308089314275	-1.30808931427501
4	69	71.4030083398455	-2.40300833984546
5	89	69.7403411916201	19.2596588083799
6	88	83.0663049245555	4.93369507544452
7	73	86.4799812673643	-13.4799812673643
8	63	77.1530381851023	-14.1530381851023
9	64	67.3603998293563	-3.36039982935628
10	64	65.0353032791162	-1.03530327911625
11	65	64.3189658773296	0.681034122670397
12	67	64.7901806641486	2.20981933585141
13	69	66.3191782761459	2.68082172385414
14	71	68.1740674734042	2.82593252659578
15	70	70.1293603856936	-0.129360385693644
16	72	70.0398545525227	1.96014544747729
17	88	71.3961001332074	16.6038998667926
18	83	82.8845158757489	0.115484124251140
19	76	82.9644205753498	-6.96442057534982
20	70	78.1456635593823	-8.14566355938234
21	75	72.5095919003251	2.49040809967491
22	71	74.2327318763062	-3.23273187630622
23	75	71.9959701470062	3.00402985299382
24	81	74.0744905025295	6.92550949747054
25	87	78.8663245279192	8.13367547208081
26	90	84.4941015012711	5.5058984987289
27	80	88.3036915070588	-8.30369150705877
28	85	82.558278622361	2.441721377639
29	105	84.2477317351126	20.7522682648874
30	104	98.6064479006197	5.39355209938034
31	98	102.338304232195	-4.33830423219534
32	94	99.3365851760135	-5.33658517601346
33	107	95.6441448674482	11.3558551325518
34	112	103.501382379206	8.4986176207943
35	121	109.381666724924	11.6183332750761
36	118	117.420515668263	0.579484331736779
37	120	117.821467069602	2.17853293039789
38	122	119.328817283348	2.67118271665183
39	109	121.177037148523	-12.1770371485235
40	112	112.75161502499	-0.751615024990002
41	132	112.231564557648	19.7684354423520
42	127	125.909556280276	1.09044371972415
43	116	126.664045942135	-10.6640459421347
44	113	119.285478601710	-6.28547860170954
45	123	114.936488792291	8.06351120770901
46	125	120.515718361368	4.48428163863198
47	137	123.618440744938	13.3815592550622
48	127	132.877284585177	-5.87728458517742
49	123	128.810728577646	-5.81072857764642
50	128	124.790223382925	3.20977661707468
51	114	127.011102123069	-13.0111021230695
52	120	118.008581531059	1.99141846894132
53	143	119.386465249469	23.6135347505307
54	135	135.724922271100	-0.724922271099729
55	119	135.223340805406	-16.2233408054058
56	117	123.998237943987	-6.99823794398733
57	132	119.156082329296	12.8439176707035
58	139	128.042926212228	10.9570737877718
59	158	135.624242650265	22.3757573497354
60	141	151.106268261736	-10.1062682617359
61	139	144.113633258638	-5.11363325863758
62	150	140.575455764108	9.42454423589243
63	142	147.096398629009	-5.09639862900934
64	149	143.570145958884	5.42985404111639
65	166	147.327119991859	18.6728800081410
66	150	160.247085202752	-10.2470852027522
67	139	153.157017453434	-14.1570174534336
68	140	143.361625799408	-3.36162579940776
69	158	141.035680987389	16.9643190126113
70	169	152.773474588262	16.226525411738
71	186	164.000780912832	21.9992190871685
72	177	179.222275676848	-2.22227567684845
73	175	177.684659389410	-2.68465938941029
74	187	175.827114870345	11.1728851296546
75	176	183.557753481931	-7.55775348193117
76	185	178.328463087708	6.6715369122922
77	204	182.944570767531	21.0554292324686
78	188	197.513047246003	-9.51304724600266
79	171	190.930868202687	-19.9308682026868
80	171	177.140487517471	-6.14048751747148
81	182	172.891818588572	9.10818141142792
82	185	179.193866634661	5.80613336533926
83	200	183.211192352883	16.7888076471166
84	192	194.827547764505	-2.82754776450469
85	185	192.871137251846	-7.8711372518461
86	195	187.425013278486	7.5749867215142
87	190	192.666227535326	-2.66622753532633
88	195	190.821436213060	4.17856378694017
89	213	193.712629148227	19.2873708517728
90	194	207.057767140109	-13.0577671401094
91	171	198.022958524159	-27.0229585241592
92	171	179.325484761390	-8.32548476139038
93	186	173.564992891144	12.4350071088562
94	182	182.168907186828	-0.168907186827568
95	193	182.052038499366	10.9479615006342
96	185	189.627050048560	-4.62705004856036
97	172	186.425544676577	-14.4255446765771
98	185	176.444356167450	8.55564383254975
99	179	182.364097558448	-3.36409755844849
100	182	180.036442509937	1.96355749006335
101	193	181.395048919347	11.6049510806532
102	173	189.424638579366	-16.4246385793665
103	155	178.060255637132	-23.060255637132
104	164	162.104618346251	1.89538165374944
105	188	163.416053166007	24.5839468339931
106	186	180.425948677742	5.57405132225838
107	200	184.282694350392	15.7173056496083
108	185	195.157666080161	-10.1576660801613
109	173	188.129468377272	-15.1294683772715
110	190	177.661227537699	12.3387724623009
111	190	186.198556053094	3.80144394690575
112	193	188.828815741143	4.17118425885712
113	195	191.714902701974	3.28509729802602
114	178	193.987896626124	-15.9878966261244
115	163	182.925700108243	-19.9257001082425
116	165	169.138895282798	-4.13889528279805
117	188	166.275149409533	21.7248505904666
118	182	181.306805678856	0.693194321144034
119	200	181.786434236939	18.2135657630606
120	177	194.388595013556	-17.3885950135557

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	182.357240313932	160.436308701556	204.278171926309
122	182.357240313932	155.700626768136	209.013853859728
123	182.357240313932	151.687665020079	213.026815607786
124	182.357240313932	148.142175624811	216.572305003054
125	182.357240313932	144.931066923427	219.783413704438
126	182.357240313932	141.974493284643	222.739987343222
127	182.357240313932	139.220086251489	225.494394376376
128	182.357240313932	136.631297310180	228.083183317685
129	182.357240313932	134.181419962247	230.533060665618
130	182.357240313932	131.850236150814	232.864244477051
131	182.357240313932	129.622002829792	235.092477798073
132	182.357240313932	127.484177017957	237.230303609907

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/05/t1281020784pabbe0oyop8dv8a/19uzf1281020762.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/05/t1281020784pabbe0oyop8dv8a/19uzf1281020762.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/05/t1281020784pabbe0oyop8dv8a/2klz11281020762.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/05/t1281020784pabbe0oyop8dv8a/2klz11281020762.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/05/t1281020784pabbe0oyop8dv8a/3klz11281020762.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/05/t1281020784pabbe0oyop8dv8a/3klz11281020762.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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

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