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Exponential smoothing omzet 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: Sun, 15 Aug 2010 16:29:17 +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/t128188985236qr8mcu57dcq00.htm/, Retrieved Sun, 15 Aug 2010 18:30:56 +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/t128188985236qr8mcu57dcq00.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

118 117 116 114 112 111 112 114 115 115 116 118 126 131 122 124 119 112 109 108 117 122 127 124 129 141 127 133 114 98 93 101 111 128 126 134 140 158 144 146 138 119 113 120 127 141 144 150 156 174 163 167 160 141 132 144 155 164 162 181 187 209 189 201 193 177 159 158 155 164 163 185 191 217 193 192 184 166 145 146 138 149 145 166

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	0.84931647663477
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	126	122.835202991453	3.16479700854697
14	131	131.214696490096	-0.214696490095662
15	122	122.515597144328	-0.515597144327671
16	124	124.019271248424	-0.0192712484235642
17	119	118.569483113691	0.43051688630861
18	112	111.543374119449	0.4566258805513
19	109	116.914439924205	-7.91443992420471
20	108	111.592488280654	-3.59248828065422
21	117	109.024574712523	7.9754252874768
22	122	115.448147404759	6.55185259524059
23	127	121.620989687125	5.37901031287457
24	124	128.172717694584	-4.17271769458407
25	129	133.505555155625	-4.50555515562456
26	141	134.861258192080	6.13874180792021
27	127	131.512897905336	-4.51289790533644
28	133	129.696386745775	3.30361325422487
29	114	127.136554830006	-13.1365548300059
30	98	108.591642482656	-10.5916424826558
31	93	103.317850238475	-10.3178502384745
32	101	96.6058895163651	4.39411048363492
33	111	102.564219845446	8.43578015455383
34	128	109.164270562357	18.8357294376428
35	126	125.593283836469	0.406716163530916
36	134	126.482672465825	7.51732753417475
37	140	141.693904830919	-1.69390483091871
38	158	147.041508984895	10.9584910151051
39	144	146.181614511451	-2.18161451145050
40	146	147.522920191968	-1.52292019196787
41	138	138.386571443670	-0.386571443669823
42	119	131.053906422309	-12.0539064223089
43	113	124.579445301015	-11.5794453010146
44	120	119.012841182667	0.987158817332855
45	127	122.686604352752	4.31339564724793
46	141	127.35254698538	13.6474530146201
47	144	136.598122955795	7.40187704420492
48	150	144.500068952428	5.49993104757183
49	156	156.609912294237	-0.609912294236551
50	174	164.784676755256	9.21532324474353
51	163	160.464283774773	2.53571622522702
52	167	165.911350556567	1.08864944343350
53	160	159.164279962659	0.835720037340877
54	141	151.111652092507	-10.1116520925071
55	132	146.358273048785	-14.3582730487852
56	144	140.325144923815	3.67485507618511
57	155	146.782821895811	8.21717810418858
58	164	156.170799941726	7.8292000582745
59	162	159.53373241842	2.46626758157998
60	181	162.957192052188	18.0428079478118
61	187	184.799254687819	2.20074531218125
62	209	196.841658073055	12.1583419269451
63	189	194.014312630013	-5.01431263001331
64	201	192.830966384758	8.16903361524214
65	193	192.059270434799	0.94072956520111
66	177	182.446240282746	-5.44624028274643
67	159	181.015376551252	-22.0153765512520
68	158	171.196239541506	-13.1962395415060
69	155	164.009471113956	-9.00947111395593
70	164	158.708110242746	5.29188975725427
71	163	159.107957713291	3.89204228670948
72	185	166.089479280319	18.9105207196812
73	191	186.281366854775	4.71863314522503
74	217	201.962699605096	15.0373003949043
75	193	198.992864930263	-5.99286493026256
76	192	198.964931155135	-6.96493115513545
77	184	184.250523246669	-0.250523246669303
78	166	172.663331333342	-6.66333133334157
79	145	167.702076286955	-22.7020762869549
80	146	158.628612514845	-12.6286125148450
81	138	152.554816091799	-14.5548160917989
82	149	144.698681807274	4.30131819272563
83	145	144.046286577744	0.953713422256499
84	166	150.795274272285	15.2047257277148

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	165.701285478111	148.107702774827	183.294868181396
86	178.929858488613	155.847115009698	202.012601967528
87	160.019697416131	132.522571371952	187.516823460311
88	164.935128204815	133.640227104706	196.230029304923
89	157.147901725991	122.468661119518	191.827142332464
90	144.807178816675	107.045708728532	182.568648904818
91	143.088426261005	102.477990195951	183.698862326059
92	154.814114946899	111.541878910730	198.086350983068
93	159.175760068053	113.396230737292	204.955289398813
94	166.522579655722	118.366124222187	214.679035089257
95	161.712575132212	111.291120431875	212.134029832549
96	169.798951048951	117.209959917021	222.387942180881

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/15/t128188985236qr8mcu57dcq00/1g5m91281889754.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t128188985236qr8mcu57dcq00/1g5m91281889754.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t128188985236qr8mcu57dcq00/2g5m91281889754.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t128188985236qr8mcu57dcq00/2g5m91281889754.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t128188985236qr8mcu57dcq00/39f4u1281889754.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t128188985236qr8mcu57dcq00/39f4u1281889754.ps (open in new window)

Parameters (Session):

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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