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Tijdreeks A - 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: Tue, 10 Aug 2010 16:28:31 +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/10/t1281457743ih78f2ct9lageef.htm/, Retrieved Tue, 10 Aug 2010 18:29:07 +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/10/t1281457743ih78f2ct9lageef.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:

Platini Olivier

Dataseries X:

» Textbox « » Textfile « » CSV «

94 93 92 90 110 109 94 84 85 85 86 88 93 94 90 91 104 103 88 79 82 88 93 89 94 96 94 92 113 122 107 98 103 110 113 110 123 124 118 117 139 146 134 121 123 122 127 122 139 136 127 123 140 146 138 120 122 115 115 102 119 114 108 102 121 109 102 95 98 92 94 90 113 111 103 90 108 99 95 91 85 72 90 90 114 115 104 93 101 90 79 75 71 61 84 87 107 99 93 74 87 71 67 61 63 52 80 84 102 93 87 72 83 72 66 64 64 47 77 79

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.842738612560252
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	93	94	-1
3	92	93.1572613874397	-1.15726138743975
4	90	92.1819925314192	-2.18199253141921
5	110	90.3431431728742	19.6568568271258
6	109	106.908735422662	2.09126457733829
7	94	108.671124831064	-14.6711248310642
8	84	96.3072014462349	-12.3072014462349
9	85	85.9354475749354	-0.93544757493538
10	85	85.1471097835115	-0.147109783511482
11	86	85.023134688661	0.976865311339026
12	88	85.846376805797	2.15362319420294
13	93	87.6613182284572	5.33868177154278
14	94	92.1604314975079	1.83956850249211
15	90	93.7107069050076	-3.71070690500763
16	91	90.5835509162638	0.416449083736239
17	104	90.9345086392936	13.0654913607064
18	103	101.945302701033	1.05469729896672
19	88	102.834136839436	-14.8341368394355
20	79	90.3328369408407	-11.3328369408407
21	82	80.782217660945	1.21778233905496
22	88	81.8084898597606	6.1915101402394
23	93	87.0263145249987	5.97368547500132
24	89	92.0605699340726	-3.06056993407262
25	94	89.4813094741886	4.51869052581137
26	96	93.2893844585	2.71061554149995
27	94	95.573724839128	-1.57372483912798
28	92	94.2474861516497	-2.24748615164967
29	113	92.35344279046	20.6465572095400
30	122	109.753093767374	12.2469062326264
31	107	120.074034534013	-13.0740345340127
32	98	109.056040810254	-11.0560408102540
33	103	99.738688317411	3.26131168258898
34	110	102.487121599923	7.5128784000774
35	113	108.818514319138	4.18148568086228
36	110	112.342413760268	-2.34241376026816
37	123	110.368371237898	12.6316287621023
38	124	121.013532535248	2.98646746475202
39	118	123.530343982949	-5.53034398294943
40	117	118.869709567778	-1.86970956777768
41	139	117.294033120738	21.7059668792619
42	146	135.586489532846	10.4135104671540
43	134	144.362356895817	-10.3623568958170
44	121	135.629598622582	-14.6295986225820
45	123	123.300670977074	-0.300670977073878
46	122	123.047283935018	-1.04728393501750
47	127	122.164697324664	4.83530267533578
48	122	126.239593592586	-4.23959359258556
49	139	122.666724370551	16.3332756294493
50	136	136.431406413077	-0.431406413076957
51	127	136.067843571071	-9.06784357107088
52	123	128.426021661073	-5.42602166107321
53	140	123.853303694698	16.1466963053015
54	146	137.46074813646	8.53925186353996
55	138	144.657105404242	-6.65710540424226
56	120	139.046905632204	-19.0469056322038
57	122	122.995342806154	-0.995342806154326
58	115	122.156528990674	-7.156528990674
59	115	116.125445678326	-1.12544567832617
60	102	115.176989148862	-13.1769891488617
61	119	104.072231595828	14.9277684041715
62	114	116.652438429381	-2.65243842938075
63	108	114.417126147503	-6.41712614750293
64	102	109.009166161332	-7.00916616133219
65	121	103.102271195327	17.8977288046732
66	109	118.185378336157	-9.18537833615675
67	102	110.444505341303	-8.44450534130301
68	95	103.327994626216	-8.32799462621568
69	98	96.3096719895094	1.69032801049056
70	92	97.734176671842	-5.73417667184198
71	94	92.9017645792385	1.09823542076150
72	90	93.8272899739956	-3.82728997399558
73	113	90.6018849314448	22.3981150685552
74	111	109.477641348284	1.52235865171613
75	103	110.760591766250	-7.76059176625023
76	90	104.220441428514	-14.220441428514
77	108	92.2363263490538	15.7636736509462
78	99	105.520982810505	-6.5209828105048
79	95	100.025498804251	-5.02549880425073
80	91	95.7903169145333	-4.79031691453326
81	85	91.7533318842556	-6.75333188425559
82	72	86.0620383419591	-14.0620383419591
83	90	74.2114156598874	15.7885843401126
84	90	87.5170653209644	2.48293467903558
85	114	89.6095302474526	24.3904697525474
86	115	110.164320886407	4.83567911359282
87	104	114.239534393383	-10.2395343933830
88	93	105.610283385440	-12.6102833854404
89	101	94.9831106612028	6.01688933879723
90	90	100.053775634509	-10.0537756345093
91	79	91.5810707052909	-12.5810707052909
92	75	80.9785166345916	-5.97851663459161
93	71	75.9401898207875	-4.9401898207875
94	61	71.7769011054328	-10.7769011054328
95	84	62.6947904201413	21.3052095798587
96	87	80.6495131817768	6.35048681822319
97	107	86.0013136320484	20.9986863679516
98	99	103.697717447364	-4.6977174473638
99	93	99.7387695635723	-6.73876956357233
100	74	94.0597482512041	-20.0597482512041
101	87	77.1546238416764	9.84537615832357
102	71	85.4517024854758	-14.4517024854758
103	67	73.2726947837324	-6.27269478373239
104	61	67.9864526846758	-6.98645268467583
105	63	62.0986992424743	0.901300757525725
106	52	62.858260192371	-10.858260192371
107	80	53.7075850630341	26.2924149369659
108	84	75.8652183478712	8.13478165212882
109	102	82.7207129508668	19.2792870491332
110	93	98.9681125698041	-5.96811256980415
111	87	93.938553663124	-6.938553663124
112	72	88.091166575888	-16.0911665758880
113	83	74.5305191812483	8.46948081875175
114	72	81.6680776955488	-9.66807769554877
115	66	73.5204153122773	-7.5204153122773
116	64	67.1826709461319	-3.18267094613185
117	64	64.5005112487529	-0.500511248752872
118	47	64.078711093408	-17.0787110934081
119	77	49.685821802232	27.314178197768
120	79	72.7045344398425	6.29546556015751

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	78.0099663514305	57.0606905589908	98.9592421438702
122	78.0099663514305	50.6135644974357	105.406368205425
123	78.0099663514305	45.4177354848047	110.602197218056
124	78.0099663514305	40.9432131731266	115.076719529734
125	78.0099663514305	36.9534824603425	119.066450242518
126	78.0099663514305	33.3185180887367	122.701414614124
127	78.0099663514305	29.9577424056556	126.062190297205
128	78.0099663514305	26.8171259882238	129.202806714637
129	78.0099663514305	23.8583497294807	132.161582973380
130	78.0099663514305	21.0530680766078	134.966864626253
131	78.0099663514305	18.3796138503228	137.640318852538
132	78.0099663514305	15.8209832617849	140.198949441076

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/10/t1281457743ih78f2ct9lageef/1qnhs1281457709.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/10/t1281457743ih78f2ct9lageef/1qnhs1281457709.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/10/t1281457743ih78f2ct9lageef/21wzv1281457709.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/10/t1281457743ih78f2ct9lageef/21wzv1281457709.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/10/t1281457743ih78f2ct9lageef/31wzv1281457709.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/10/t1281457743ih78f2ct9lageef/31wzv1281457709.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

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