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Tijdreeks B - 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: Thu, 19 Aug 2010 13:03:28 +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/t1282223215fg3ame2ox2mf9wr.htm/, Retrieved Thu, 19 Aug 2010 15:07:22 +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/t1282223215fg3ame2ox2mf9wr.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:

Quaglia Laura

Dataseries X:

» Textbox « » Textfile « » CSV «

93 92 91 89 87 86 87 89 90 90 91 93 93 87 89 92 98 92 92 87 92 98 101 102 102 90 87 92 105 90 88 83 98 109 118 118 115 107 101 111 128 115 111 105 120 132 135 142 139 127 113 130 143 139 137 134 139 157 152 153 147 132 117 123 139 134 134 128 118 144 140 151 144 135 122 124 146 146 147 148 132 161 159 173

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	0.980528379652752
beta	0.0160501661027135
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	91	91	0
4	89	90	-1
5	87	88.0037339769854	-1.00373397698540
6	86	85.9880102762077	0.0119897237923254
7	87	84.9684211799255	2.03157882007453
8	89	85.961068770717	3.03893122928294
9	90	87.9892796029367	2.01072039706328
10	90	89.040944534408	0.959055465592002
11	91	89.0765154275679	1.92348457243214
12	93	90.0880075443606	2.91199245563942
13	93	92.1145875928878	0.885412407112241
14	87	92.1679826948873	-5.16798269488729
15	89	86.204520237573	2.79547976242705
16	92	88.0934529834809	3.9065470165191
17	98	91.1332985474512	6.86670145254875
18	92	97.1837252426362	-5.18372524263619
19	92	91.3367869571127	0.663213042887264
20	87	91.2333750049651	-4.23337500496513
21	92	86.2620961623847	5.73790383761535
22	98	91.1582402906264	6.84175970937362
23	101	97.244419602447	3.75558039755299
24	102	100.363616499244	1.63638350075622
25	102	101.430633516597	0.569366483402618
26	90	101.460370553521	-11.4603705535213
27	87	89.5142498014155	-2.51424980141554
28	92	86.3004859678526	5.69951403214738
29	105	91.2302475960373	13.7697524039627
30	90	104.289810430864	-14.2898104308641
31	88	89.6112876452242	-1.61128764522421
32	83	87.3390583926644	-4.33905839266441
33	98	82.3238859555429	15.6761140444571
34	109	97.180863208794	11.8191367912061
35	118	108.441970165222	9.55802983477786
36	118	117.636418446224	0.363581553776100
37	115	117.821171169280	-2.82117116928025
38	107	114.838784879479	-7.8387848794786
39	101	106.813121947869	-5.8131219478692
40	111	100.682194168279	10.3178058317211
41	128	110.530476815162	17.4695231848377
42	115	127.666150415616	-12.6661504156162
43	111	115.053605452864	-4.05360545286425
44	105	110.822111050179	-5.82211105017912
45	120	104.764920412431	15.2350795875688
46	132	119.594667039892	12.4053329601081
47	135	131.844997497812	3.15500250218807
48	142	135.074768724760	6.92523127523967
49	139	142.110343081477	-3.11034308147725
50	127	139.256802505169	-12.2568025051685
51	113	127.242005704005	-14.2420057040052
52	130	113.056525220478	16.943474779522
53	143	129.715943747547	13.2840562524532
54	139	142.996258295498	-3.99625829549751
55	137	139.269842332020	-2.26984233201986
56	134	137.200504246709	-3.20050424670862
57	139	134.168257347770	4.83174265222971
58	157	139.087896728296	17.9121032717042
59	152	157.115095205459	-5.11509520545908
60	153	152.482972527762	0.517027472238311
61	147	153.381442767199	-6.38144276719882
62	132	147.415338290274	-15.4153382902737
63	117	132.348641777841	-15.3486417778411
64	123	117.105791638284	5.89420836171597
65	139	122.784919874370	16.2150801256298
66	134	138.839142925832	-4.83914292583168
67	134	134.172946058252	-0.172946058252222
68	128	134.079365880996	-6.0793658809956
69	118	128.098698553294	-10.0986985532942
70	144	118.018031756888	25.9819682431121
71	140	143.724377661202	-3.72437766120177
72	151	140.244195423178	10.7558045768222
73	144	151.131513828580	-7.13151382857978
74	135	144.367575680336	-9.36757568033582
75	122	135.263691862564	-13.2636918625639
76	124	122.130816305498	1.8691836945015
77	146	123.865571244251	22.134428755749
78	146	145.819317831951	0.180682168049259
79	147	146.249636362229	0.750363637771272
80	148	147.250352696254	0.749647303745604
81	132	148.262164326352	-16.2621643263521
82	161	132.337483721372	28.6625162786277
83	159	160.913807855457	-1.91380785545707
84	173	159.479059605118	13.5209403948819

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	173.391307784884	154.584681314348	192.197934255419
86	174.045890187874	147.498913051365	200.592867324383
87	174.700472590865	142.035915484475	207.365029697254
88	175.355054993855	137.400367725493	213.309742262217
89	176.009637396846	133.281752146576	218.737522647116
90	176.664219799836	129.520925825549	223.807513774123
91	177.318802202827	126.023700576817	228.613903828836
92	177.973384605817	122.729025355155	233.21774385648
93	178.627967008808	119.594750086866	237.66118393075
94	179.282549411798	116.590388314423	241.974710509173
95	179.937131814789	113.693086674408	246.18117695517
96	180.591714217779	110.885220549799	250.298207885760

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282223215fg3ame2ox2mf9wr/10jqg1282223005.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282223215fg3ame2ox2mf9wr/10jqg1282223005.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282223215fg3ame2ox2mf9wr/2aspi1282223005.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282223215fg3ame2ox2mf9wr/2aspi1282223005.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282223215fg3ame2ox2mf9wr/3aspi1282223005.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282223215fg3ame2ox2mf9wr/3aspi1282223005.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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