Home » date » 2010 » Jun » 06 »

Jeroen Cornelissen - aantal liter rose wijn australie - opgave 10

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 06 Jun 2010 19:36:47 +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/Jun/06/t1275853150fz9430ezsvirhou.htm/, Retrieved Sun, 06 Jun 2010 21:39:11 +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/Jun/06/t1275853150fz9430ezsvirhou.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:

KDGP2W62

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

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.108626533512383
beta	0.0443274768222541
gamma	0.509445657854061

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	126	130.144329985792	-4.1443299857923
14	129	126.499350708393	2.50064929160706
15	124	122.353905998396	1.64609400160394
16	97	98.6534914049896	-1.65349140498957
17	102	103.969081120937	-1.96908112093722
18	127	130.956560413493	-3.95656041349349
19	222	124.118719932714	97.8812800672863
20	214	147.225480081474	66.7745199185265
21	118	247.091306508711	-129.091306508711
22	141	168.457612580986	-27.4576125809861
23	154	170.506386760306	-16.5063867603065
24	226	306.518830078138	-80.518830078138
25	89	136.515306433849	-47.5153064338487
26	77	130.979637840337	-53.9796378403368
27	82	119.99308717122	-37.9930871712199
28	97	91.5422752258281	5.45772477417189
29	127	96.7184475055048	30.2815524944952
30	121	125.17546301954	-4.17546301954009
31	117	159.414068500372	-42.4140685003724
32	117	150.982093862743	-33.982093862743
33	106	145.852715403994	-39.8527154039943
34	112	125.13574711416	-13.1357471141602
35	134	130.469817762251	3.53018223774916
36	169	216.267655581326	-47.2676555813257
37	75	91.3833731286713	-16.3833731286713
38	108	85.2355045075275	22.7644954924725
39	115	88.5796554855126	26.4203445144874
40	85	87.000067773792	-2.00006777379201
41	101	100.665060659082	0.334939340918126
42	108	108.693814580134	-0.693814580133548
43	109	122.963372933244	-13.9633729332437
44	124	120.725790784715	3.2742092152849
45	105	116.587918876876	-11.5879188768756
46	95	111.180723765643	-16.180723765643
47	135	122.586392603095	12.4136073969049
48	164	181.632752454893	-17.6327524548934
49	88	79.3857306026552	8.61426939734481
50	85	93.27617160819	-8.27617160819004
51	112	94.3601540573793	17.6398459426207
52	87	80.0364367209815	6.96356327901849
53	91	94.8042923777285	-3.80429237772853
54	87	101.359918943627	-14.3599189436274
55	87	107.235546805581	-20.2355468055815
56	142	111.3046880603	30.6953119396997
57	95	104.007214887084	-9.00721488708395
58	108	97.0298311512986	10.9701688487014
59	139	123.427936929502	15.5720630704977
60	159	167.740598016765	-8.74059801676458
61	61	80.9671572713862	-19.9671572713862
62	82	83.650412217381	-1.65041221738105
63	124	96.2433619306847	27.7566380693153
64	93	79.1761187924212	13.8238812075788
65	108	89.4959112977372	18.5040887022628
66	75	93.735469703547	-18.7354697035471
67	87	96.3595655879282	-9.35956558792824
68	103	124.456413412998	-21.4564134129979
69	90	94.8507884972093	-4.85078849720929
70	108	97.1986959491222	10.8013040508778
71	123	124.301709942004	-1.30170994200428
72	129	153.693016243385	-24.6930162433847
73	57	66.3657330346879	-9.36573303468786
74	65	77.6301027164011	-12.6301027164011
75	67	99.8318070731925	-32.8318070731925
76	71	73.066001855823	-2.06600185582302
77	76	81.3460315251906	-5.34603152519055
78	67	68.2132018611001	-1.21320186110015
79	110	74.8217599136433	35.1782400863567
80	118	98.4977073281111	19.5022926718889
81	99	82.7854977252815	16.2145022747185
82	85	93.608001161439	-8.60800116143893
83	107	110.829270887726	-3.82927088772593
84	141	126.908376437056	14.0916235629441
85	58	56.9883883481995	1.01161165180054
86	65	67.1337198501299	-2.13371985012989
87	70	80.1455610066491	-10.1455610066491
88	86	70.2558155422244	15.7441844577756
89	93	79.2877538828763	13.7122461171237
90	74	70.1464416478941	3.85355835210588
91	87	94.6207707691822	-7.6207707691822
92	73	106.536757051462	-33.5367570514619
93	101	84.5891632604955	16.4108367395045
94	100	84.2582566483616	15.7417433516384
95	96	105.809380582357	-9.80938058235658
96	157	128.57081336348	28.4291866365201
97	63	56.1938986640376	6.80610133596241
98	115	65.5984097826699	49.4015902173301
99	70	81.7385300934878	-11.7385300934878
100	66	84.0114648703145	-18.0114648703145
101	67	88.926084861005	-21.926084861005
102	83	71.6359029404532	11.3640970595468
103	79	92.0445101526066	-13.0445101526066
104	77	91.2526370269216	-14.2526370269216
105	102	94.3096772349135	7.69032276508651
106	116	92.7725914219994	23.2274085780006
107	100	103.960138512117	-3.96013851211661
108	135	146.181013095457	-11.1810130954566
109	71	59.4955810567124	11.5044189432876
110	60	87.5332581511854	-27.5332581511854
111	89	68.8503946558846	20.1496053441154
112	74	71.4261097660891	2.57389023391092
113	73	76.3830176289111	-3.38301762891111
114	91	76.2153184412705	14.7846815587295
115	86	85.9001976016533	0.0998023983467107
116	74	86.0419338854185	-12.0419338854185
117	87	99.7408559627166	-12.7408559627166
118	87	102.851090482	-15.8510904819999
119	109	97.501347692566	11.4986523074339
120	137	136.890854155909	0.109145844090847
121	43	63.2410913608103	-20.2410913608103
122	69	68.8421696230088	0.157830376991228
123	73	74.2204821720876	-1.22048217208759
124	77	66.9013956538392	10.0986043461608
125	69	69.7004023325345	-0.700402332534523
126	76	77.2606959534877	-1.26069595348767
127	78	78.193196932778	-0.193196932777923
128	70	72.994965168685	-2.99496516868504
129	83	85.8614307729271	-2.86143077292714
130	65	88.1199321684824	-23.1199321684824
131	110	93.325202744719	16.674797255281
132	132	125.028926281139	6.97107371886148
133	54	49.24419068585	4.75580931414999
134	55	66.15440499204	-11.15440499204
135	66	69.3587362360089	-3.35873623600891
136	65	66.9494609232758	-1.94946092327578
137	60	63.6802317161635	-3.68023171616355
138	65	69.8758745470156	-4.87587454701564
139	96	70.5863111852148	25.4136888147852
140	55	67.2511047857573	-12.2511047857573
141	71	78.0693430549239	-7.06934305492388
142	63	70.8236381507021	-7.82363815070211
143	74	93.7911522141888	-19.7911522141888
144	106	114.027701754812	-8.02770175481167
145	34	44.921607802382	-10.921607802382
146	47	51.0879139381878	-4.08791393818777
147	56	57.0612293037141	-1.0612293037141
148	53	55.4655056047716	-2.46550560477162
149	53	51.6844409288112	1.31555907118882
150	55	56.6164283593204	-1.61642835932037
151	67	68.3431795382831	-1.34317953828311
152	52	49.1202750112936	2.8797249887064
153	46	60.9275607944337	-14.9275607944337
154	51	53.4380160602442	-2.43801606024417
155	58	67.2627852423019	-9.26278524230189
156	91	87.8787340750151	3.12126592498485
157	33	31.8878393325384	1.11216066746162
158	40	40.4399316160069	-0.439931616006881
159	46	46.6411462022361	-0.641146202236115
160	45	44.6236108414107	0.376389158589269
161	41	42.9994463968815	-1.99944639688147
162	55	45.3858940440048	9.61410595599518
163	57	56.2649198863183	0.735080113681725
164	54	41.8978135232523	12.1021864767477
165	46	45.8726019259433	0.127398074056664
166	52	45.69499940265	6.30500059735003
167	48	56.1587551112398	-8.15875511123978
168	77	79.6008903112322	-2.60089031123218
169	30	28.673809955736	1.32619004426398
170	35	35.6824320351885	-0.682432035188498
171	42	41.0807177349621	0.919282265037879
172	48	39.8851180695252	8.1148819304748
173	44	38.3411236627599	5.65887633724012
174	45	46.3411261013661	-1.34112610136611

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
175	51.5619235009141	27.3479799346578	75.7758670671703
176	43.0363486474464	18.4732086248447	67.5994886700481
177	40.5794212762203	15.5803790367572	65.5784635156834
178	42.847035238375	17.1256684729962	68.5684020037539
179	45.545839924208	18.9257110209831	72.165968827433
180	69.2552672809538	38.3158393108681	100.194695251039
181	25.9495992914595	0.502534829184832	51.3966637537341
182	31.195120876925	4.36681396662183	58.0234277872281
183	36.6727619923777	7.95617341515892	65.3893505695965
184	38.3350252716819	8.30805773904951	68.3619928043143
185	35.1954443078291	5.1772497999042	65.213638815754
186	38.6658110623806	0.169062067663354	77.1625600570979

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275853150fz9430ezsvirhou/1pe0a1275853003.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275853150fz9430ezsvirhou/1pe0a1275853003.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275853150fz9430ezsvirhou/2znhv1275853003.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275853150fz9430ezsvirhou/2znhv1275853003.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275853150fz9430ezsvirhou/3znhv1275853003.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275853150fz9430ezsvirhou/3znhv1275853003.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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