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Vermeulennickopgave10

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 04 Aug 2009 04:33:55 -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/Aug/04/t12493820806dernklvgus4gk4.htm/, Retrieved Tue, 04 Aug 2009 12:34:44 +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/Aug/04/t12493820806dernklvgus4gk4.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:

roze garnalen

Dataseries X:

» Textbox « » Textfile « » CSV «

112 118 132 129 121 135 148 148 136 119 104 118 115 126 141 135 125 149 170 170 158 133 114 140 145 150 178 163 172 178 199 199 184 162 146 166 171 180 193 181 183 218 230 242 209 191 172 194 196 196 236 235 229 243 264 272 237 211 180 201 204 188 235 227 234 264 302 293 259 229 203 229 242 233 267 269 270 315 364 347 312 274 237 278 284 277 317 313 318 374 413 405 355 306 271 306 315 301 356 348 355 422 465 467 404 347 305 336 340 318 362 348 363 435 491 505 404 359 310 337 360 342 406 396 420 472 548 559 463 407 362 405 417 391 419 461 472 535 622 606 508 461 390 432

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	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.247959489735621
beta	0.0345337296488465
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	115	110.643162393162	4.35683760683766
14	126	122.073143387587	3.92685661241272
15	141	137.430132053628	3.56986794637163
16	135	132.062503983316	2.93749601668370
17	125	123.06322697046	1.93677302954006
18	149	147.499062384579	1.50093761542098
19	170	160.131347416214	9.86865258378634
20	170	163.506325051358	6.4936749486424
21	158	153.850050071908	4.14994992809187
22	133	138.731495445679	-5.73149544567858
23	114	123.321997399522	-9.32199739952222
24	140	135.609043041043	4.39095695895742
25	145	136.860463840114	8.13953615988564
26	150	149.177864159562	0.822135840438364
27	178	163.742778738725	14.2572212612748
28	163	160.887368307280	2.1126316927203
29	172	151.261667119480	20.7383328805204
30	178	180.523451938488	-2.52345193848808
31	199	198.907941418776	0.0920585812235686
32	199	197.694112643342	1.30588735665759
33	184	185.317990243194	-1.31799024319366
34	162	161.694628859307	0.305371140692898
35	146	145.415787851415	0.584212148585237
36	166	170.890657487435	-4.89065748743522
37	171	172.999007307477	-1.99900730747714
38	180	177.551972077215	2.44802792278534
39	193	202.890186966572	-9.89018696657155
40	181	184.973617184964	-3.9736171849643
41	183	187.853581322794	-4.8535813227945
42	218	193.064187605336	24.9358123946635
43	230	220.247948846113	9.75205115388661
44	242	222.448490221367	19.5515097786334
45	209	212.885752351812	-3.88575235181227
46	191	190.087007403601	0.912992596399391
47	172	174.41421857194	-2.41421857193995
48	194	195.248286577791	-1.24828657779145
49	196	200.685635881057	-4.6856358810567
50	196	208.144971709426	-12.1449717094261
51	236	220.689112540808	15.3108874591920
52	235	213.789920520889	21.2100794791114
53	229	222.787331740528	6.21266825947168
54	243	253.774189579802	-10.7741895798022
55	264	261.00816897443	2.99183102556992
56	272	269.167807518786	2.83219248121378
57	237	237.95618678454	-0.956186784540307
58	211	219.640392882199	-8.6403928821988
59	180	199.162435425533	-19.1624354255327
60	201	216.642919355326	-15.6429193553264
61	204	215.725163322482	-11.7251633224824
62	188	215.568185948207	-27.5681859482071
63	235	244.542771479218	-9.5427714792177
64	227	235.311347905093	-8.31134790509267
65	234	224.851226946991	9.14877305300945
66	264	242.957703039887	21.0422969601127
67	302	267.872319298870	34.1276807011296
68	293	283.337779746876	9.66222025312373
69	259	250.734646991179	8.26535300882136
70	229	228.76948330091	0.230516699089975
71	203	202.497007296170	0.502992703829761
72	229	227.587791285747	1.41220871425273
73	242	234.078621708001	7.92137829199925
74	233	227.280122971016	5.71987702898392
75	267	278.751213081092	-11.7512130810916
76	269	270.565926630948	-1.56592663094830
77	270	275.634536741208	-5.63453674120785
78	315	299.618595266555	15.3814047334445
79	364	333.520636813287	30.4793631867127
80	347	330.201563104207	16.7984368957933
81	312	298.897647562399	13.1023524376011
82	274	272.710985777354	1.28901422264624
83	237	247.53659554364	-10.5365955436402
84	278	271.109952789839	6.89004721016096
85	284	284.437307658672	-0.437307658672239
86	277	274.422083339494	2.57791666050576
87	317	312.459730593004	4.54026940699589
88	313	316.597926811575	-3.59792681157455
89	318	318.70963058687	-0.709630586870162
90	374	360.368584499746	13.6314155002536
91	413	405.824869710265	7.17513028973451
92	405	386.873019883061	18.1269801169390
93	355	353.564640637353	1.43535936264681
94	306	315.946740877587	-9.94674087758744
95	271	279.342602124885	-8.3426021248847
96	306	316.83391044474	-10.8339104447402
97	315	320.372592752746	-5.3725927527455
98	301	311.475546446946	-10.4755464469461
99	356	347.714814000746	8.28518599925422
100	348	346.655993774083	1.3440062259167
101	355	352.202179299065	2.79782070093495
102	422	405.582887635467	16.4171123645332
103	465	446.965379597209	18.034620402791
104	467	439.12632237637	27.8736776236296
105	404	395.949259167776	8.05074083222434
106	347	351.735857721495	-4.73585772149539
107	305	317.998757010999	-12.9987570109991
108	336	352.790665052808	-16.7906650528075
109	340	359.237140476179	-19.2371404761793
110	318	343.223593245563	-25.2235932455625
111	362	389.947459573453	-27.9474595734534
112	348	374.406789879841	-26.4067898798411
113	363	373.650027638874	-10.6500276388742
114	435	433.308118043726	1.69188195627368
115	491	471.499333939276	19.5006660607241
116	505	470.679272945316	34.3207270546843
117	404	413.504477870092	-9.50447787009193
118	359	354.483041056435	4.51695894356527
119	310	316.066448406359	-6.06644840635863
120	337	349.025200176063	-12.0252001760634
121	360	354.153856208751	5.84614379124918
122	342	339.413066656394	2.58693334360578
123	406	390.777674042406	15.2223259575936
124	396	387.262984667483	8.73701533251727
125	420	407.534097462558	12.4659025374422
126	472	482.867470544423	-10.8674705444230
127	548	531.891710015522	16.1082899844778
128	559	541.901021739745	17.0989782602554
129	463	447.875390224938	15.1246097750618
130	407	406.094345030001	0.905654969998693
131	362	359.380907870101	2.61909212989923
132	405	390.644236750491	14.3557632495089
133	417	416.612314574266	0.387685425733935
134	391	398.878286514509	-7.87828651450872
135	419	457.871953443463	-38.8719534434628
136	461	436.325333374695	24.6746666253047
137	472	463.747561389847	8.2524386101527
138	535	520.847393660953	14.1526063390472
139	622	596.935578762723	25.0644212372767
140	606	610.560492406651	-4.56049240665084
141	508	510.14372167159	-2.14372167158962
142	461	453.704068818089	7.29593118191099
143	390	410.234924183382	-20.2349241833816
144	432	444.833325554046	-12.8333255540460

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
145	453.497721751322	428.415266965021	478.580176537623
146	429.390569251949	403.49600160324	455.285136900659
147	467.036052088739	440.301472551841	493.770631625637
148	503.25740665386	475.655792079981	530.859021227739
149	512.339520167	483.844695250902	540.834345083098
150	571.887965749639	542.474571456702	601.301360042575
151	652.609534991379	622.252994696779	682.966075285979
152	637.462256917306	606.138741269289	668.785772565324
153	539.754768946301	507.441160256026	572.068377636576
154	490.72498608621	457.398842867375	524.051129305044
155	424.459265263961	390.098787394926	458.819743132996
156	469.531518789793	434.115513646617	504.947523932969

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/04/t12493820806dernklvgus4gk4/1qj5g1249382032.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/04/t12493820806dernklvgus4gk4/1qj5g1249382032.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/04/t12493820806dernklvgus4gk4/23cac1249382032.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/04/t12493820806dernklvgus4gk4/23cac1249382032.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/04/t12493820806dernklvgus4gk4/354e31249382032.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/04/t12493820806dernklvgus4gk4/354e31249382032.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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=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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