Home » date » 2009 » Jun » 03 »

opgave 10 oefening 2 exponential smoothing - Kathleen Geets

*Unverified author*

R Software Module: rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Wed, 03 Jun 2009 07:04:21 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/03/t1244034418e8bf8m596q9p0ah.htm/, Retrieved Wed, 03 Jun 2009 15:07:03 +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/2009/Jun/03/t1244034418e8bf8m596q9p0ah.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

112 118 129 99 116 168 118 129 205 147 150 267 126 129 124 97 102 127 222 214 118 141 154 226 89 77 82 97 127 121 117 117 106 112 134 169 75 108 115 85 101 108 109 124 105 95 135 164 88 85 112 87 91 87 87 142 95 108 139 159 61 82 124 93 108 75 87 103 90 108 123 129 57 65 67 71 76 67 110 118 99 85 107 141 58 65 70 86 93 74 87 73 101 100 96 157 63 115 70 66 67 83 79 77 102 116 100 135 71 60 89 74 73 91 86 74 87 87 109 137 43 69 73 77 69 76 78 70 83 65 110 132 54 55 66 65 60 65 96 55 71 63 74 106 34 47 56 53 53 55 67 52 46 51 58 91 33 40 46 45 41 55 57 54 46 52 48 77 30 35 42 48 44 45 1 1 46 51 63 84 30 39 45 52 28 40 62

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	7 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.109310071929840
beta	0.0423714166076927
gamma	0.472651426343311

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	126	130.144329985792	-4.14432998579227
14	129	126.497336475202	2.50266352479839
15	124	122.354103073797	1.64589692620297
16	97	98.6545153114343	-1.65451531143428
17	102	103.969145181214	-1.96914518121376
18	127	130.955762730820	-3.95576273082045
19	222	124.116955503769	97.8830444962313
20	214	147.278510110102	66.7214898898984
21	118	247.190435707455	-129.190435707455
22	141	168.439700539795	-27.4397005397954
23	154	170.457645185292	-16.457645185292
24	226	306.402041255351	-80.4020412553512
25	89	136.587960570770	-47.5879605707703
26	77	130.795017573918	-53.7950175739177
27	82	119.840986676980	-37.8409866769804
28	97	91.525637795896	5.474362204104
29	127	96.7339451097543	30.2660548902457
30	121	125.284544776200	-4.28454477620036
31	117	156.494041345659	-39.494041345659
32	117	149.366479212369	-32.3664792123691
33	106	149.786376099908	-43.786376099908
34	112	125.960237358704	-13.9602373587043
35	134	130.953652332217	3.04634766778256
36	169	218.523586317661	-49.5235863176611
37	75	92.710859859669	-17.710859859669
38	108	86.5726081126977	21.4273918873023
39	115	89.3866959074346	25.6133040925654
40	85	86.488885504333	-1.48888550433298
41	101	99.4378598022224	1.56214019777758
42	108	108.617948701567	-0.617948701566576
43	109	122.534659682694	-13.5346596826945
44	124	120.539214291064	3.46078570893609
45	105	119.338657358978	-14.3386573589780
46	95	111.535628022854	-16.5356280228535
47	135	122.209138327075	12.7908616729245
48	164	183.629086168514	-19.6290861685139
49	88	80.2918601359244	7.70813986407559
50	85	92.9576922612251	-7.95769226122508
51	112	93.8216540538348	18.1783459461652
52	87	79.8039180758455	7.19608192415453
53	91	94.076640908052	-3.076640908052
54	87	101.224984207056	-14.2249842070565
55	87	107.310872316043	-20.3108723160434
56	142	110.916949263325	31.083050736675
57	95	105.693510297452	-10.6935102974518
58	108	97.661173302112	10.3388266978881
59	139	122.689160835852	16.3108391641485
60	159	169.274115650301	-10.2741156503008
61	61	81.1515729239403	-20.1515729239403
62	82	83.7547036208831	-1.75470362088309
63	124	95.3751687526565	28.6248312473435
64	93	78.8520695172339	14.1479304827661
65	108	89.2602757264641	18.7397242735359
66	75	94.14773091836	-19.14773091836
67	87	97.0203589012782	-10.0203589012782
68	103	123.080645145108	-20.0806451451076
69	90	95.9497204919883	-5.94972049198826
70	108	97.1484441221936	10.8515558778064
71	123	123.424604610866	-0.424604610866453
72	129	154.820279590623	-25.8202795906231
73	57	67.1183231968959	-10.1183231968959
74	65	77.7096229868696	-12.7096229868696
75	67	98.4845779076198	-31.4845779076198
76	71	72.451782263067	-1.45178226306703
77	76	80.6943199911947	-4.69431999119467
78	67	68.9183976927783	-1.91839769277827
79	110	75.3674332456849	34.6325667543151
80	118	98.43562562087	19.56437437913
81	99	83.4198374542445	15.5801625457555
82	85	93.2049268688733	-8.20492686887327
83	107	110.378052456493	-3.37805245649258
84	141	128.129535386432	12.8704646135680
85	58	57.6081865559435	0.39181344405651
86	65	67.4930286704089	-2.49302867040886
87	70	80.366355043281	-10.3663550432809
88	86	69.7552187459242	16.2447812540758
89	93	78.8300590182252	14.1699409817748
90	74	70.3539436795757	3.64605632042425
91	87	93.513167006661	-6.51316700666105
92	73	105.723599750896	-32.7235997508964
93	101	84.34407648762	16.6559235123800
94	100	84.3219722952278	15.6780277047722
95	96	105.652081361223	-9.65208136122297
96	157	128.736734983304	28.2632650166963
97	63	56.5347686907976	6.46523130920243
98	115	65.933846467818	49.066153532182
99	70	82.319287870801	-12.3192878708009
100	66	83.15865050909	-17.1586505090899
101	67	88.1707224094827	-21.1707224094827
102	83	71.6020457321321	11.3979542678679
103	79	91.6658929831596	-12.6658929831596
104	77	91.8747830897244	-14.8747830897244
105	102	93.4146969453411	8.58530305465885
106	116	92.1508184744516	23.8491815255484
107	100	104.148636217526	-4.14863621752573
108	135	145.197400604675	-10.1974006046750
109	71	59.4594307619298	11.5405692380702
110	60	86.2717697122337	-26.2717697122337
111	89	69.6620025021063	19.3379974978937
112	74	71.6817849589103	2.31821504108967
113	73	76.757687398338	-3.75768739833806
114	91	75.8051641644437	15.1948358355563
115	86	86.1570604728685	-0.157060472868451
116	74	86.8638230110096	-12.8638230110096
117	87	98.8913423461226	-11.8913423461226
118	87	101.623020259607	-14.6230202596071
119	109	97.6327499994452	11.3672500005548
120	137	136.592257988313	0.407742011687219
121	43	62.7763506832564	-19.7763506832564
122	69	68.9980146364453	0.00198536355466672
123	73	73.9125795614875	-0.912579561487505
124	77	66.948268841779	10.051731158221
125	69	70.0298800105226	-1.02988001052262
126	76	76.6213658097904	-0.621365809790447
127	78	78.3829041718505	-0.382904171850512
128	70	73.8553433508115	-3.85534335081151
129	83	85.8842650801318	-2.88426508013177
130	65	87.9837359146015	-22.9837359146015
131	110	92.9724700893041	17.0275299106959
132	132	124.854460635934	7.14553936406553
133	54	49.6395462546526	4.36045374534736
134	55	66.1450372810717	-11.1450372810717
135	66	69.1418178231420	-3.14181782314205
136	65	66.5706481831012	-1.57064818310121
137	60	63.8228212725377	-3.82282127253774
138	65	69.5399033418519	-4.53990334185191
139	96	70.6254850435753	25.3745149564247
140	55	67.7738374466076	-12.7738374466076
141	71	78.165138937122	-7.16513893712205
142	63	71.4643714419119	-8.4643714419119
143	74	92.9901554363611	-18.9901554363611
144	106	113.618334282811	-7.61833428281113
145	34	44.9526527142143	-10.9526527142143
146	47	51.4009355245357	-4.4009355245357
147	56	57.0296222918702	-1.02962229187025
148	53	55.3102296008446	-2.31022960084461
149	53	51.8203165145401	1.17968348545986
150	55	56.559898144611	-1.55989814461095
151	67	67.6276825350254	-0.627682535025372
152	52	49.7028450679528	2.29715493204721
153	46	61.166521607355	-15.1665216073550
154	51	53.9298742678942	-2.92987426789417
155	58	67.4384165077437	-9.43841650774372
156	91	87.8301916396185	3.16980836038145
157	33	32.1655143577622	0.834485642237809
158	40	40.626355744086	-0.626355744086027
159	46	46.5771942330355	-0.57719423303547
160	45	44.5450632561296	0.454936743870405
161	41	42.9532110429528	-1.95321104295283
162	55	45.3383359951741	9.66166400482589
163	57	55.8855999661917	1.11440003380825
164	54	42.0275216902981	11.9724783097019
165	46	46.3809366490888	-0.380936649088767
166	52	45.9363144506122	6.06368554938776
167	48	56.4439993452249	-8.44399934522492
168	77	79.3332731066916	-2.33327310669156
169	30	28.7310202575468	1.26897974245322
170	35	35.7454419282666	-0.745441928266573
171	42	41.0206154243279	0.97938457567215
172	48	39.7836036267689	8.21639637323113
173	44	38.3320970863949	5.6679029136051
174	45	45.960199225339	-0.960199225338975
175	1	51.2903227976446	-50.2903227976446
176	1	37.8417441670556	-36.8417441670556
177	46	31.8338012267375	14.1661987732625
178	51	34.6088128124804	16.3911871875196
179	63	38.7415635537276	24.2584364462724
180	84	62.0953855546256	21.9046144453744
181	30	24.0997294533702	5.90027054662983
182	39	29.7727648199247	9.22723518007533
183	45	36.0965627673271	8.90343723267287
184	52	38.594295529131	13.405704470869
185	28	37.0193499770225	-9.0193499770225
186	40	39.725970626746	0.274029373253995
187	62	24.1360819049073	37.8639180950927

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
188	23.8899227431420	0.873100617442834	46.9067448688411
189	50.1288359963641	24.8623071150822	75.395364877646
190	53.5552318929448	27.2233180990961	79.8871456867935
191	60.8241893694735	32.6898243882988	88.9585543506482
192	84.8546679956306	51.213170684509	118.496165306752
193	30.9053035795961	6.01164670506834	55.7989604541238
194	38.4778023923227	11.6648288304322	65.2907759542131
195	44.5280984698435	15.5955667279536	73.4606302117334
196	48.4172042105804	17.5643320341535	79.2700763870073
197	35.2983084277868	7.27696786111685	63.3196489944568
198	43.9590484949792	12.4115617786995	75.5065352112588
199	41.9343190305836	-47.6216166954913	131.490254756658

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244034418e8bf8m596q9p0ah/1xlb51244034253.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244034418e8bf8m596q9p0ah/1xlb51244034253.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244034418e8bf8m596q9p0ah/2fehv1244034253.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244034418e8bf8m596q9p0ah/2fehv1244034253.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244034418e8bf8m596q9p0ah/3whr21244034253.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244034418e8bf8m596q9p0ah/3whr21244034253.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=0, beta=0)

if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)

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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