Home » date » 2010 » Nov » 27 »

Workshop 8 Regression Analysis of Time Series single smoothing

*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 27 Nov 2010 13:15:31 +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/Nov/27/t1290863616hdvabccwiis6nr4.htm/, Retrieved Sat, 27 Nov 2010 14:13:40 +0100

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/Nov/27/t1290863616hdvabccwiis6nr4.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 «

24 25 17 18 18 16 20 16 18 17 23 30 23 18 15 12 21 15 20 31 27 34 21 31 19 16 20 21 22 17 24 25 26 25 17 32 33 13 32 25 29 22 18 17 20 15 20 33 29 23 26 18 20 11 28 26 22 17 12 14 17 21 19 18 10 29 31 19 9 20 28 19 30 29 26 23 13 21 19 28 23 18 21 20 23 21 21 15 28 19 26 10 16 22 19 31 31 29 19 22 23 15 20 18 23 25 21 24 25 17 13 28 21 25 9 16 19 17 25 20 29 14 22 15 19 20 15 20 18 33 22 16 17 16 21 26 18 18 17 22 30 30 24 21 21 29 31 20 16 22 20 28 38 22 20 17 28 22 31

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	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.0387398850173385
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	25	24	1
3	17	24.0387398850173	-7.03873988501734
4	18	23.7660599112048	-5.76605991120481
5	18	23.5426834132417	-5.54268341324165
6	16	23.3279604951252	-7.32796049512516
7	20	23.0440761481324	-3.04407614813242
8	16	22.9261489881697	-6.92614898816974
9	18	22.6578307727551	-4.65783077275509
10	17	22.4773869441883	-5.47738694418834
11	23	22.265193603775	0.73480639622499
12	30	22.2936599190748	7.70634008092523
13	23	22.5922026477143	0.407797352285677
14	18	22.6080006702522	-4.60800067025225
15	15	22.4294872541269	-7.42948725412686
16	12	22.1416697721642	-10.1416697721642
17	21	21.7487826513067	-0.748782651306744
18	15	21.7197748974921	-6.71977489749214
19	20	21.4594515906209	-1.4594515906209
20	31	21.4029126038119	9.59708739618812
21	27	21.7747026660416	5.22529733395845
22	34	21.9771300839405	12.0228699160595
23	21	22.4428946820671	-1.44289468206707
24	31	22.3869971079917	8.61300289200833
25	19	22.7206638496821	-3.72066384968208
26	16	22.5765257599572	-6.57652575995722
27	20	22.3217519082029	-2.32175190820292
28	21	22.2318075062404	-1.23180750624035
29	22	22.1840874250851	-0.18408742508511
30	17	22.1769558994042	-5.17695589940418
31	24	21.9764012231214	2.02359877687858
32	25	22.0547952070589	2.94520479294107
33	26	22.1688921020900	3.83110789791002
34	25	22.3173087815440	2.68269121845597
35	17	22.4212359308840	-5.42123593088404
36	32	22.2112178742697	9.78878212573028
37	33	22.5904341682803	10.4095658317197
38	13	22.9936995516815	-9.99369955168153
39	32	22.6065447801516	9.39345521984844
40	25	22.970446155284	2.02955384471599
41	29	23.0490708378648	5.9509291621352
42	22	23.2796091493522	-1.27960914935225
43	18	23.2300372380392	-5.23003723803921
44	17	23.0274261968012	-6.02742619680117
45	20	22.7939243989866	-2.7939243989866
46	15	22.6856880890227	-7.68568808902272
47	20	22.3879454161749	-2.38794541617485
48	33	22.2954366853246	10.7045633146754
49	29	22.7101302372959	6.2898697627041
50	23	22.9537990686771	0.0462009313229039
51	26	22.9555888874442	3.04441111255576
52	18	23.0735290238902	-5.07352902389016
53	20	22.8769810928725	-2.87698109287253
54	11	22.7655271761376	-11.7655271761376
55	28	22.3097320061656	5.69026799383435
56	26	22.5301723339646	3.46982766603537
57	22	22.6645930587768	-0.664593058776823
58	17	22.6388468000965	-5.63884680009649
59	12	22.4203985234304	-10.4203985234304
60	14	22.0167134827978	-8.01671348279783
61	17	21.7061469242573	-4.70614692425729
62	21	21.5238313335369	-0.523831333536862
63	19	21.5035381679072	-2.50353816790717
64	18	21.4065513871459	-3.40655138714592
65	10	21.2745819781022	-11.2745819781022
66	29	20.837805968652	8.162194031348
67	31	21.1540084269156	9.84599157308437
68	19	21.5354410083386	-2.53544100833860
69	9	21.4372183152073	-12.4372183152073
70	20	20.9554019077406	-0.955401907740647
71	28	20.9183897476894	7.08161025231057
72	19	21.1927305146015	-2.19273051460155
73	30	21.1077843865919	8.89221561340813
74	29	21.4522677970047	7.54773220299531
75	26	21.7446660746904	4.25533392530961
76	23	21.9095172216673	1.09048277833273
77	13	21.9517623991133	-8.95176239911326
78	21	21.6049721530691	-0.604972153069081
79	19	21.5815356014205	-2.58153560142049
80	28	21.4815272090533	6.5184727909467
81	23	21.7340520954632	1.26594790453678
82	18	21.7830947717229	-3.78309477172292
83	21	21.6365381152567	-0.63653811525668
84	20	21.6118787018625	-1.61187870186248
85	23	21.5494347062904	1.45056529370957
86	21	21.6056294389789	-0.605629438978887
87	21	21.5821674241497	-0.58216742414973
88	15	21.5596143250773	-6.55961432507733
89	28	21.3054956203658	6.69450437963425
90	19	21.5648399502809	-2.56483995028085
91	26	21.4654783455191	4.53452165448090
92	10	21.6411451930223	-11.6411451930223
93	16	21.1901685667745	-5.19016856677449
94	22	20.9891020332770	1.01089796672296
95	19	21.0282641042722	-2.02826410427215
96	31	20.9496893860879	10.0503106139121
97	31	21.3390372636593	9.66096273634065
98	29	21.7133018492220	7.28669815077803
99	19	21.9955876977392	-2.99558769773917
100	22	21.8795389747694	0.120461025230600
101	23	21.8842056210359	1.11579437896409
102	15	21.9274313669800	-6.92743136697997
103	20	21.6590634723577	-1.65906347235766
104	18	21.5947915442021	-3.59479154420206
105	23	21.4555297331184	1.54447026688163
106	25	21.5153623336701	3.48463766632993
107	21	21.6503567961908	-0.650356796190774
108	24	21.6251620486861	2.3748379513139
109	25	21.7171629978548	3.28283700214519
110	17	21.8443397258486	-4.84433972584858
111	13	21.6566705618843	-8.65667056188428
112	28	21.3213121396839	6.6786878603161
113	21	21.5800437394592	-0.580043739459242
114	25	21.5575729116876	3.44242708831244
115	9	21.6909321412694	-12.6909321412694
116	16	21.1992868893537	-5.19928688935374
117	19	20.9978671130880	-1.99786711308803
118	17	20.9204699708471	-3.92046997084708
119	25	20.7685914149625	4.23140858503747
120	20	20.9325156970083	-0.932515697008263
121	29	20.8963901461293	8.1036098538707
122	14	21.2103230600936	-7.21032306009362
123	22	20.9309959738077	1.06900402619227
124	15	20.9724090668655	-5.9724090668655
125	19	20.7410386263386	-1.74103862633862
126	20	20.6735909901435	-0.673590990143516
127	15	20.6474961526366	-5.64749615263664
128	20	20.4287128010476	-0.428712801047638
129	18	20.4121045164296	-2.41210451642959
130	33	20.3186598648133	12.6813401351867
131	22	20.8099335235162	1.1900664764838
132	16	20.8560365619782	-4.85603656197817
133	17	20.6679142639271	-3.66791426392715
134	16	20.5258196870892	-4.52581968708915
135	21	20.3504899528021	0.649510047197886
136	26	20.3756518973482	5.62434810265183
137	18	20.5935384961424	-2.59353849614239
138	18	20.4930651130138	-2.49306511301379
139	17	20.3964840571949	-3.3964840571949
140	22	20.2649046553559	1.73509534464406
141	30	20.3321220495016	9.66787795049843
142	30	20.7066545296655	9.29334547033445
143	24	21.0666776646127	2.93332233538729
144	21	21.1803142346044	-0.180314234604406
145	21	21.1733288818888	-0.173328881888843
146	29	21.1666141409343	7.83338585906571
147	31	21.4700786084109	9.52992139158906
148	20	21.8392666673454	-1.83926666734537
149	16	21.7680136881362	-5.76801368813619
150	22	21.5445615010794	0.455438498920639
151	20	21.56220513616	-1.56220513616002
152	28	21.5016854888117	6.49831451118832
153	38	21.7534294457816	16.2465705542184
154	22	22.3828197209781	-0.382819720978119
155	20	22.3679893290051	-2.36798932900506
156	17	22.2762536946771	-5.27625369467712
157	28	22.071852233223	5.92814776677698
158	22	22.3015079960738	-0.301507996073752
159	31	22.2898276109740	8.71017238902595

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
160	22.6272586878061	11.1496687818407	34.1048485937715
161	22.6272586878061	11.1410593496644	34.1134580259478
162	22.6272586878061	11.1324563658201	34.1220610097922
163	22.6272586878061	11.1238598158403	34.1306575597719
164	22.6272586878061	11.1152696853117	34.1392476903005
165	22.6272586878061	11.1066859598745	34.1478314157377
166	22.6272586878061	11.0981086252226	34.1564087503896
167	22.6272586878061	11.0895376671029	34.1649797085094
168	22.6272586878061	11.0809730713152	34.1735443042971
169	22.6272586878061	11.0724148237120	34.1821025519003
170	22.6272586878061	11.0638629101981	34.1906544654141
171	22.6272586878061	11.0553173167305	34.1992000588817

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290863616hdvabccwiis6nr4/1secv1290863727.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290863616hdvabccwiis6nr4/1secv1290863727.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290863616hdvabccwiis6nr4/2lncy1290863727.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290863616hdvabccwiis6nr4/2lncy1290863727.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290863616hdvabccwiis6nr4/3lncy1290863727.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290863616hdvabccwiis6nr4/3lncy1290863727.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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