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Exponential Smoothing aantal stuks product Y

*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 15:17:53 +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/t12822310458fkkprli1bx53s5.htm/, Retrieved Thu, 19 Aug 2010 17:17:26 +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/t12822310458fkkprli1bx53s5.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:

Sebastien Delforge

Dataseries X:

» Textbox « » Textfile « » CSV «

152 151 150 148 146 145 146 148 149 149 150 152 154 164 167 162 164 172 169 174 181 181 172 181 183 200 199 190 197 194 190 195 204 197 185 193 192 211 210 197 191 182 170 166 175 163 153 171 165 184 179 163 163 148 132 127 130 118 113 137 133 155 151 132 134 118 102 98 91 77 74 102 98 113 114 96 102 90 72 67 62 48 43 75

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	0.68474816558974
beta	0.0484142369247786
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	154	144.835967267461	9.16403273253883
14	164	161.134327150874	2.86567284912621
15	167	165.974154161445	1.0258458385552
16	162	161.363438148573	0.63656185142682
17	164	163.902957486157	0.0970425138432347
18	172	172.206012609827	-0.20601260982744
19	169	167.935558761424	1.06444123857591
20	174	172.623373433226	1.37662656677364
21	181	175.695105878869	5.30489412113099
22	181	180.363370904279	0.63662909572102
23	172	183.005512855122	-11.0055128551225
24	181	177.874454727201	3.12554527279937
25	183	185.769098014831	-2.76909801483075
26	200	193.081577467039	6.91842253296088
27	199	200.299674096934	-1.29967409693418
28	190	192.590318968473	-2.59031896847293
29	197	192.693589362458	4.30641063754163
30	194	205.047316652563	-11.0473166525628
31	190	192.661589180187	-2.66158918018743
32	195	194.789331234293	0.210668765707368
33	204	198.012961847578	5.98703815242203
34	197	200.989829140711	-3.98982914071127
35	185	195.771548158604	-10.7715481586036
36	193	195.193438722546	-2.19343872254629
37	192	197.012799544763	-5.0127995447634
38	211	205.570387101034	5.42961289896593
39	210	208.222296083506	1.77770391649355
40	197	201.007652023794	-4.00765202379412
41	191	201.621407359169	-10.6214073591685
42	182	197.49976665005	-15.4997666500497
43	170	183.481191098833	-13.4811910988334
44	166	177.111132856874	-11.1111328568743
45	175	171.834063544559	3.16593645544128
46	163	168.481072611454	-5.48107261145361
47	153	158.914898331573	-5.91489833157252
48	171	161.001697733286	9.99830226671415
49	165	168.459043447272	-3.45904344727165
50	184	177.736799256541	6.26320074345924
51	179	178.645672062248	0.354327937751975
52	163	168.737820776871	-5.73782077687088
53	163	164.31916293143	-1.31916293143036
54	148	163.330836659677	-15.3308366596767
55	132	149.048683472034	-17.0486834720345
56	127	138.675541179729	-11.6755411797294
57	130	134.398375136249	-4.39837513624875
58	118	123.375456794781	-5.3754567947815
59	113	113.519716842537	-0.519716842537136
60	137	119.552804263329	17.4471957366711
61	133	127.289650196454	5.71034980354649
62	155	141.634688465996	13.3653115340036
63	151	145.566709839836	5.43329016016389
64	132	138.481315791507	-6.48131579150703
65	134	134.017262240619	-0.0172622406192886
66	118	129.320401850065	-11.3204018500655
67	102	116.977404334652	-14.9774043346518
68	98	108.210193541373	-10.2101935413729
69	91	105.132757856971	-14.1327578569713
70	77	88.0546121733445	-11.0546121733445
71	74	75.7623205168778	-1.76232051687779
72	102	80.3356348839407	21.6643651160593
73	98	88.2390067483624	9.76099325163764
74	113	102.600761992884	10.3992380071156
75	114	102.988524489102	11.011475510898
76	96	98.9267959768588	-2.92679597685881
77	102	97.5481584720942	4.45184152790577
78	90	93.5835723365682	-3.58357233656815
79	72	85.8936956684969	-13.8936956684969
80	67	77.8467294371392	-10.8467294371392
81	62	71.2022309296126	-9.20223092961255
82	48	59.3055385324514	-11.3055385324514
83	43	49.3224024174947	-6.32240241749469
84	75	50.6767454046428	24.3232545953572

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	59.0406049575362	41.7817822924733	76.2994276225991
86	62.0712464415173	40.0611690474486	84.081323835586
87	56.5214133621168	31.5101456949358	81.5326810292978
88	46.7362067922406	20.5412695869369	72.9311439975443
89	46.2586613496034	15.7786132538234	76.7387094453834
90	40.0674547583405	8.33770792935277	71.7972015873281
91	34.3963069959911	1.70365096176521	67.088963030217
92	33.9067363299783	-3.45966970045161	71.2731423604082
93	33.1087477135537	-9.01704873509713	75.2345441622046
94	28.4635178206857	-14.0332659449993	70.9603015863707
95	27.2522466805133	-19.9297813094741	74.4342746705008
96	35.127576383553	-32.0373669776888	102.292519744795

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/19/t12822310458fkkprli1bx53s5/1jtzh1282231068.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t12822310458fkkprli1bx53s5/1jtzh1282231068.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t12822310458fkkprli1bx53s5/2jtzh1282231068.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t12822310458fkkprli1bx53s5/2jtzh1282231068.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t12822310458fkkprli1bx53s5/3t2y21282231068.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t12822310458fkkprli1bx53s5/3t2y21282231068.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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