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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 05 Aug 2010 14:12:26 +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/05/t1281017511z3vod4puanlqvg6.htm/, Retrieved Thu, 05 Aug 2010 16:11:55 +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/05/t1281017511z3vod4puanlqvg6.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

390 389 388 386 406 405 390 380 381 381 382 384 394 393 388 381 399 396 378 368 369 373 374 379 385 385 395 387 400 390 365 350 365 374 367 375 382 380 378 363 375 366 341 326 338 345 336 342 347 360 360 334 347 336 305 289 303 308 294 299 306 313 321 287 296 283 248 235 241 244 237 241 251 259 264 229 237 228 197 182 182 176 172 175 185 195 206 175 185 174 140 130 133 130 131 136 149 155 161 131 145 134 93 87 86 80 79 91 108 105 112 78 87 74 32 25 26 25 22 36

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	1
beta	0.0112924114735404
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	388	388	0
4	386	387	-1
5	406	384.988707588526	21.0112924114736
6	405	405.225975748028	-0.225975748027679
7	390	404.223423936898	-14.2234239368979
8	380	389.06280718124	-9.06280718123986
9	381	378.960466233444	2.03953376655602
10	381	379.98349748795	1.01650251204990
11	382	379.99497625258	2.00502374741995
12	384	381.01761780575	2.98238219424985
13	394	383.051296092659	10.9487039073410
14	393	393.174933362283	-0.174933362282616
15	388	392.172957942775	-4.17295794277527
16	381	387.125835184624	-6.12583518462367
17	399	380.0566597331	18.9433402669002
18	396	398.270575726077	-2.27057572607691
19	378	395.244935450696	-17.2449354506962
20	368	377.050198543752	-9.05019854375234
21	369	366.947999977879	2.05200002212098
22	373	367.971172006473	5.02882799352744
23	374	372.027959601405	1.97204039859486
24	379	373.050228693028	5.94977130697151
25	385	378.1174159588	6.88258404119972
26	385	384.195136929795	0.804863070205272
27	395	384.204225774763	10.7957742252366
28	387	394.32613609949	-7.32613609949016
29	400	386.243406356144	13.7565936438564
30	390	399.398751472044	-9.3987514720443
31	365	389.292616903084	-24.2926169030844
32	350	364.018294677246	-14.0182946772457
33	365	348.859994325593	16.1400056744071
34	374	364.042253910854	9.95774608914644
35	367	373.154700877041	-6.15470087704125
36	375	366.085199462241	8.91480053775888
37	382	374.185869058118	7.81413094188196
38	380	381.274109440022	-1.27410944002190
39	378	379.259721671963	-1.25972167196289
40	363	377.245496376501	-14.2454963765009
41	375	362.084630369773	12.9153696302274
42	366	374.23047603797	-8.23047603797005
43	341	365.137534115926	-24.1375341159261
44	326	339.864963148732	-13.8649631487325
45	338	324.708394279792	13.2916057202085
46	345	336.858488560728	8.14151143927177
47	336	343.950425857917	-7.95042585791703
48	342	334.860646377739	7.1393536222605
49	347	340.941266896497	6.05873310350279
50	360	346.00968460371	13.9903153962897
51	360	359.16766900181	0.832330998190173
52	334	359.177068025924	-25.1770680259236
53	347	332.892758214078	14.1072417859225
54	336	346.052062993081	-10.0520629930809
55	305	334.938550961605	-29.9385509616051
56	289	303.600472525225	-14.6004725252251
57	303	287.435597981762	15.5644020182379
58	308	301.611357613692	6.38864238630833
59	294	306.683500792275	-12.6835007922751
60	299	292.540273482404	6.45972651759621
61	306	297.613219372247	8.38678062775296
62	313	304.707926350034	8.29207364996608
63	321	311.801563857658	9.19843614234173
64	287	319.905436383491	-32.9054363834907
65	296	285.533854656132	10.4661453438681
66	283	294.652042675897	-11.6520426758967
67	248	281.520463015493	-33.5204630154932
68	235	246.141936154339	-11.1419361543387
69	241	233.016116826672	7.98388317332802
70	244	239.106274120622	4.89372587937811
71	237	242.161536086891	-5.16153608689055
72	241	235.103249897562	5.89675010243815
73	251	239.169838426075	11.8301615739248
74	259	249.303429478366	9.69657052163356
75	264	257.412927142579	6.58707285742105
76	229	262.487311079691	-33.4873110796911
77	237	227.109158583837	9.8908414161632
78	228	235.220850034928	-7.22085003492765
79	197	226.139309225145	-29.1393092251445
80	182	194.810256155319	-12.8102561553195
81	182	179.665597471732	2.33440252826787
82	176	179.691958505626	-3.69195850562619
83	172	173.650267391037	-1.65026739103743
84	175	169.631631892616	5.36836810738353
85	185	172.692253714226	12.3077462857735
86	195	182.831237849597	12.1687621504026
87	206	192.968652518923	13.0313474810766
88	175	204.115807856734	-29.1158078567344
89	185	172.787020174032	12.2129798259684
90	174	182.924934167544	-8.92493416754445
91	140	171.824150138550	-31.8241501385503
92	130	137.46477874039	-7.46477874039005
93	133	127.380483387295	5.61951661270537
94	130	130.443941281168	-0.443941281167696
95	131	127.438928113551	3.56107188644934
96	136	128.479141202579	7.52085879742069
97	149	133.564069834754	15.4359301652458
98	155	146.738378709657	8.26162129034304
99	161	152.831672336706	8.16832766329392
100	131	158.923912453731	-27.9239124537307
101	145	128.608584144352	16.3914158556479
102	134	142.793682756828	-8.79368275682793
103	93	131.69438087277	-38.6943808727701
104	87	90.2574280022409	-3.25742800224086
105	86	84.2206437848941	1.77935621510588
106	80	83.2407370074331	-3.2407370074331
107	79	77.2041412716676	1.79585872833236
108	91	76.2244208473763	14.7755791526237
109	108	88.3912727669276	19.6087272330724
110	105	105.612702583316	-0.612702583315865
111	112	102.605783693634	9.39421630636583
112	78	109.711867049637	-31.7118670496371
113	87	75.3537635983184	11.6462364016816
114	74	84.4852776918843	-10.4852776918843
115	32	71.3668736217732	-39.3668736217732
116	25	28.9223266864093	-3.92232668640928
117	26	21.8780341595327	4.1219658404673
118	25	22.9245810938831	2.07541890611687
119	22	21.9480175781510	0.0519824218490292
120	36	18.9486045850479	17.0513954149521

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	33.1411559582716	5.79390527622464	60.4884066403185
122	30.2823119165431	-8.61152007159018	69.1761439046764
123	27.4234678748147	-20.4802363213140	75.3271720709434
124	24.5646238330862	-31.0606130830907	80.1898607492632
125	21.7057797913578	-40.8332258025907	84.2447853853062
126	18.8469357496294	-50.0430949293769	87.7369664286356
127	15.9880917079009	-58.834933063564	90.8111164793658
128	13.1292476661725	-67.3024878790546	93.5609832113995
129	10.2704036244440	-75.5105045235792	96.0513117724673
130	7.4115595827156	-83.50585420994	98.3289733753712
131	4.55271554098716	-91.3237184879251	100.429149569899
132	1.69387149925872	-98.9912731443912	102.379016142909

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/05/t1281017511z3vod4puanlqvg6/1namg1281017544.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/05/t1281017511z3vod4puanlqvg6/1namg1281017544.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/05/t1281017511z3vod4puanlqvg6/2g2311281017544.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/05/t1281017511z3vod4puanlqvg6/2g2311281017544.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/05/t1281017511z3vod4puanlqvg6/3g2311281017544.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/05/t1281017511z3vod4puanlqvg6/3g2311281017544.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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=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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