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tijdreeks 1 - 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: Thu, 19 Aug 2010 21:21:24 +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/t1282252981a5a0bqcl4pihxje.htm/, Retrieved Thu, 19 Aug 2010 23:23:05 +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/t1282252981a5a0bqcl4pihxje.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:

Aerts Ellen

Dataseries X:

» Textbox « » Textfile « » CSV «

25 24 23 21 41 40 25 15 16 16 17 19 18 19 20 21 46 47 30 16 15 18 30 31 32 36 30 31 61 57 45 33 31 36 46 49 34 40 41 48 75 77 71 54 50 56 66 66 48 63 71 70 88 92 91 80 81 81 98 106 85 93 96 92 115 109 119 107 107 106 132 143 120 123 132 136 158 151 155 138 143 139 168 182 154 158 167 170 197 190 196 174 180 171 200 215 184 186 197 186 211 205 218 199 213 207 236 248 211 220 235 223 245 236 253 246 255 248 274 288

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	0.048882612475808
beta	0.161657597483346
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	18	17.3403175805076	0.659682419492437
14	19	18.3222222115775	0.677777788422503
15	20	19.5143080194186	0.485691980581375
16	21	20.6851560013707	0.314843998629325
17	46	44.626779592692	1.37322040730801
18	47	44.2410339021109	2.75896609788911
19	30	26.1233273973336	3.87667260266644
20	16	16.3215848230105	-0.321584823010500
21	15	17.8509300262992	-2.85093002629920
22	18	17.9884293958987	0.0115706041013048
23	30	19.1227938535176	10.8772061464824
24	31	21.7865817553551	9.2134182446449
25	32	21.7186090885486	10.2813909114514
26	36	23.6427073434576	12.3572926565424
27	30	25.816938440802	4.183061559198
28	31	27.6637317334764	3.33626826652364
29	61	61.684300799127	-0.684300799127037
30	57	63.6008205672313	-6.60082056723132
31	45	40.5478047363496	4.45219526365036
32	33	21.9906275119373	11.0093724880627
33	31	21.5762200195341	9.42377998046586
34	36	26.8966970326193	9.10330296738067
35	46	45.1656286489439	0.83437135105607
36	49	46.4075213338745	2.5924786661255
37	34	47.4558834629241	-13.4558834629241
38	40	51.6045402604209	-11.6045402604209
39	41	42.1979419471531	-1.19794194715305
40	48	43.2354074516473	4.76459254835267
41	75	85.4746137366246	-10.4746137366246
42	77	79.6416181372721	-2.64161813727213
43	71	62.3513914117481	8.6486085882519
44	54	44.8840432396329	9.11595676036709
45	50	41.5677319028255	8.43226809717455
46	56	47.7513087746117	8.24869122538834
47	66	61.162454809098	4.837545190902
48	66	64.935905528144	1.06409447185604
49	48	45.5233673327292	2.47663266727076
50	63	54.1849483502086	8.81505164979138
51	71	56.0930945182578	14.9069054817422
52	70	66.3327029399549	3.66729706004509
53	88	104.762930085779	-16.7629300857786
54	92	107.069985011176	-15.069985011176
55	91	97.4753145285674	-6.4753145285674
56	80	73.1312000938453	6.86879990615469
57	81	67.2749250095882	13.7250749904118
58	81	75.3754545803505	5.62454541964954
59	98	88.6615135162963	9.33848648370375
60	106	88.9146474176363	17.0853525823637
61	85	65.0830798797755	19.9169201202245
62	93	86.1363217138893	6.86367828611071
63	96	96.2787162212688	-0.278716221268837
64	92	94.5586586943847	-2.55865869438473
65	115	119.473439411829	-4.47343941182881
66	109	125.461671730956	-16.4616717309559
67	119	123.638077994263	-4.63807799426318
68	107	107.963704240528	-0.963704240527619
69	107	108.078811227408	-1.07881122740775
70	106	107.376115080397	-1.3761150803967
71	132	128.793022367278	3.20697763272221
72	143	137.722070376683	5.27792962331702
73	120	108.557674219712	11.4423257802884
74	123	118.293800888414	4.70619911158637
75	132	121.712892332623	10.2871076673769
76	136	116.749489767346	19.2505102326544
77	158	146.936191780592	11.0638082194077
78	151	140.382774253301	10.6172257466991
79	155	154.008641991384	0.99135800861609
80	138	138.535149672799	-0.535149672799463
81	143	138.535936646987	4.46406335301339
82	139	137.544349834405	1.45565016559530
83	168	171.190314126318	-3.19031412631762
84	182	184.915039224158	-2.91503922415833
85	154	154.181022699430	-0.181022699430315
86	158	157.527711166154	0.472288833846278
87	167	168.14309287129	-1.14309287129001
88	170	171.452391716854	-1.45239171685412
89	197	197.758183304578	-0.758183304578125
90	190	187.599879680578	2.40012031942177
91	196	191.890999864295	4.10900013570509
92	174	170.441527401133	3.5584725988667
93	180	175.937358127988	4.06264187201239
94	171	170.565875246075	0.434124753924976
95	200	205.707759817235	-5.70775981723472
96	215	222.018637118999	-7.01863711899881
97	184	186.989891114585	-2.98989111458459
98	186	191.062430557554	-5.06243055755434
99	197	201.090801555265	-4.09080155526541
100	186	203.9151303878	-17.9151303877999
101	211	234.450066175983	-23.4500661759826
102	205	223.899734702572	-18.8997347025715
103	218	228.648686161373	-10.6486861613727
104	199	201.250187125254	-2.25018712525417
105	213	206.728554076613	6.27144592338664
106	207	195.644743520633	11.3552564793668
107	236	228.723416363188	7.27658363681212
108	248	245.636049852908	2.36395014709171
109	211	209.707970036171	1.29202996382949
110	220	211.598424922148	8.40157507785165
111	235	224.126388372219	10.8736116277811
112	223	212.538416518352	10.4615834816476
113	245	242.567399134868	2.43260086513197
114	236	236.659599269668	-0.659599269667865
115	253	252.249975055633	0.750024944367482
116	246	230.545836572437	15.4541634275628
117	255	247.475132600746	7.52486739925425
118	248	240.434439057190	7.5655609428103
119	274	274.344258319853	-0.344258319852543
120	288	288.308135318980	-0.308135318979623

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	245.327944621114	229.590902578786	261.064986663443
122	255.407562552814	239.643662019886	271.171463085742
123	272.213213886201	256.409389540769	288.017038231633
124	257.636372890699	241.802622022783	273.470123758614
125	282.753077942025	266.843640701815	298.662515182235
126	272.231355707789	256.278035701007	288.184675714572
127	291.624554208902	275.563358892922	307.685749524883
128	282.458554241940	266.339208433247	298.577900050634
129	292.042617319936	275.802518156576	308.282716483297
130	283.228052341901	266.91990000235	299.536204681452
131	312.479099132395	295.918410124013	329.039788140776
132	327.991553968614	316.097337726568	339.885770210660

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282252981a5a0bqcl4pihxje/1yk9v1282252881.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282252981a5a0bqcl4pihxje/1yk9v1282252881.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282252981a5a0bqcl4pihxje/2yk9v1282252881.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282252981a5a0bqcl4pihxje/2yk9v1282252881.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282252981a5a0bqcl4pihxje/39bqy1282252881.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282252981a5a0bqcl4pihxje/39bqy1282252881.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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