Home » date » 2011 » Jan » 07 »

Katrien Monnens

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 07 Jan 2011 10:21:28 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/07/t1294395895sib1reesfo9zs9c.htm/, Retrieved Fri, 07 Jan 2011 11:24:59 +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/2011/Jan/07/t1294395895sib1reesfo9zs9c.htm/},
    year = {2011},
}
@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 = {2011},
    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 «

103,6 103,5 110,9 115,8 117,8 121,1 128,7 112,7 111,3 116,2 109,8 137,9 98,7 100,5 128,7 98,7 115 121 125,9 117,3 115 113,8 115,7 145,5 101,7 106,9 116,4 114,6 122,5 120,4 116,5 117 114,3 111,5 117,8 141,5 102,6 103,8 119,8 113,6 121,8 123,9 122,7 120 111,6 117,6 121,3 143,7 107,1 107,7 126,4 111,5 127,9 124,9 122 124,9 113,9 120,8 123,3 143,5 107,1 106,5 114,6 122,2 120,2 123,1 127,1 118,5 116,1 120,6 115,7 146,5 108 106,6 122,2 115,8 115,6 124,5 121,7 118,7 113,7 113,4 115,1 143,9 101 103,4 121,5 111,9 117,4 124,3 122 119,7 115 112,2 115,3 142,6 104,1 105,3 124,4 113,9 124,8 131,8 125,6 125 119,7 116,1 120 148,1 109,2 109,4 135,1 114,9 129 138,5 125,6 130,4 120,3 126,2 127,6 150,9 114,6 118,6 131,4 124,5 136,8 136,8 136,6 131 125,8 129,4 124,8 157,1 116,6 114,2 128,4 127,3 133,5 137,2 137,7 131,2 127,7 133,9 124,3 160,6

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	3 seconds
R Server	'Herman Ole Andreas Wold' @ www.yougetit.org

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.124782904318567
beta	0.0179039618345825
gamma	0.642046556523616

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	98.7	99.5514792359552	-0.851479235955182
14	100.5	101.186626498397	-0.686626498396592
15	128.7	129.071289161111	-0.371289161111491
16	98.7	98.894621967739	-0.194621967738982
17	115	115.043003778345	-0.0430037783449251
18	121	120.442163637786	0.557836362214118
19	125.9	128.64681669265	-2.74681669265038
20	117.3	112.660135858013	4.63986414198695
21	115	111.233542754004	3.76645724599564
22	113.8	116.59693691349	-2.79693691349004
23	115.7	110.635688745786	5.06431125421422
24	145.5	139.902854093338	5.59714590666169
25	101.7	100.272599321441	1.42740067855866
26	106.9	102.339644947242	4.56035505275817
27	116.4	131.719787717374	-15.319787717374
28	114.6	99.558895670506	15.0411043294939
29	122.5	118.189015746914	4.31098425308571
30	120.4	124.722408429877	-4.32240842987672
31	116.5	130.6914079712	-14.1914079712002
32	117	117.249337309124	-0.249337309124485
33	114.3	114.702800798375	-0.402800798375239
34	111.5	115.871898419633	-4.37189841963331
35	117.8	114.115000115475	3.68499988452494
36	141.5	143.614551806	-2.1145518059997
37	102.6	100.785412315067	1.81458768493341
38	103.8	104.629414267297	-0.829414267296826
39	119.8	121.857412789078	-2.05741278907756
40	113.6	108.213721171233	5.38627882876717
41	121.8	119.476905362189	2.32309463781097
42	123.9	120.858776734004	3.04122326599558
43	122.7	122.074908044993	0.625091955007392
44	120	118.295145797496	1.70485420250371
45	111.6	115.895519604463	-4.29551960446308
46	117.6	114.340982243072	3.2590177569281
47	121.3	118.140590828397	3.15940917160302
48	143.7	144.766002801597	-1.0660028015966
49	107.1	103.598728787232	3.50127121276817
50	107.7	106.23990271352	1.46009728647982
51	126.4	123.480752787933	2.91924721206662
52	111.5	114.410825733881	-2.91082573388114
53	127.9	123.115700233735	4.78429976626526
54	124.9	125.273425080016	-0.373425080016062
55	122	124.72602874031	-2.7260287403101
56	124.9	121.105306227268	3.79469377273169
57	113.9	115.502693278039	-1.60269327803894
58	120.8	118.622061084378	2.17793891562235
59	123.3	122.321272339387	0.978727660613458
60	143.5	146.752824609563	-3.25282460956251
61	107.1	107.271661800121	-0.17166180012147
62	106.5	108.328972168201	-1.82897216820149
63	114.6	126.121282809906	-11.5212828099064
64	122.2	112.024428922888	10.1755710771124
65	120.2	126.782278955051	-6.58227895505138
66	123.1	124.60708749814	-1.50708749814044
67	127.1	122.577818863349	4.52218113665064
68	118.5	123.511011359969	-5.01101135996871
69	116.1	113.811294649121	2.28870535087886
70	120.6	119.50645302323	1.09354697676989
71	115.7	122.365314346164	-6.66531434616431
72	146.5	143.157171512787	3.34282848721301
73	108	106.453386508266	1.5466134917344
74	106.6	106.773525126446	-0.173525126445867
75	122.2	119.198375024767	3.001624975233
76	115.8	119.050635154009	-3.25063515400946
77	115.6	122.663658891911	-7.0636588919115
78	124.5	123.255301794453	1.24469820554653
79	121.7	124.93180113119	-3.23180113119049
80	118.7	119.544149057245	-0.844149057245218
81	113.7	114.470922408307	-0.770922408307456
82	113.4	119.044535840836	-5.6445358408355
83	115.1	116.663351260973	-1.56335126097279
84	143.9	143.368526417607	0.531473582393147
85	101	105.800564697147	-4.80056469714739
86	103.4	104.335173676482	-0.935173676482023
87	121.5	118.066195241768	3.4338047582316
88	111.9	114.494917880283	-2.59491788028278
89	117.4	115.926899215197	1.47310078480349
90	124.3	122.129634326975	2.17036567302506
91	122	121.383131363254	0.616868636745693
92	119.7	117.832249216703	1.86775078329663
93	115	113.160154590355	1.8398454096447
94	112.2	115.283096800987	-3.08309680098731
95	115.3	115.507571867246	-0.207571867245747
96	142.6	143.530933651912	-0.93093365191217
97	104.1	102.855438426174	1.24456157382554
98	105.3	104.332121953469	0.967878046530643
99	124.4	120.884412463825	3.51558753617505
100	113.9	113.891606279026	0.00839372097395596
101	124.8	117.997224079009	6.80277592099112
102	131.8	125.394268453629	6.40573154637129
103	125.6	124.307999525309	1.2920004746906
104	125	121.522863171056	3.47713682894432
105	119.7	116.962479025664	2.73752097433604
106	116.1	116.450764964515	-0.350764964514937
107	120	118.750559747777	1.24944025222312
108	148.1	147.469402401354	0.630597598646062
109	109.2	106.983031653351	2.2169683466487
110	109.4	108.522292879591	0.877707120408928
111	135.1	127.172899822996	7.9271001770043
112	114.9	118.459370337954	-3.55937033795384
113	129	126.262756082715	2.73724391728493
114	138.5	133.168508508643	5.33149149135727
115	125.6	128.97991129073	-3.37991129073023
116	130.4	126.829826516594	3.57017348340644
117	120.3	121.755316356364	-1.45531635636365
118	126.2	118.956719991437	7.24328000856278
119	127.6	123.25336702844	4.34663297156024
120	150.9	153.067323096253	-2.16732309625272
121	114.6	111.852876079132	2.74712392086769
122	118.6	112.769493032074	5.83050696792559
123	131.4	136.934545576043	-5.53454557604331
124	124.5	119.671288830693	4.82871116930671
125	136.8	132.54570897072	4.25429102928027
126	136.8	141.456402244201	-4.65640224420054
127	136.6	130.870887239933	5.72911276006693
128	131	133.900169820853	-2.90016982085334
129	125.8	124.960880153177	0.839119846823039
130	129.4	127.434248264991	1.96575173500862
131	124.8	129.523521267203	-4.72352126720308
132	157.1	155.110230052031	1.98976994796917
133	116.6	116.24092977826	0.359070221740154
134	114.2	118.639110975567	-4.43911097556681
135	128.4	135.305651392091	-6.90565139209136
136	127.3	123.566682280528	3.73331771947244
137	133.5	136.061330560736	-2.56133056073585
138	137.2	139.083020496537	-1.88302049653663
139	137.7	134.623188246196	3.07681175380372
140	131.2	132.437914391599	-1.23791439159888
141	127.7	125.766740899979	1.93325910002123
142	133.9	128.998994431238	4.90100556876195
143	124.3	127.657601896051	-3.35760189605145
144	160.6	157.39941239284	3.20058760715978

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
145	117.418455390456	111.749787679765	123.087123101147
146	117.052279094637	111.288247667941	122.816310521332
147	133.062275809172	127.145566274249	138.978985344096
148	128.075932643284	122.08422648088	134.067638805688
149	136.701686126751	130.55228060113	142.851091652373
150	140.501162596636	134.217157901978	146.785167291293
151	139.046247670726	132.671093882388	145.421401459063
152	133.976352361688	127.549644560669	140.403060162706
153	129.164861206277	122.688499854547	135.641222558007
154	133.893570864278	127.246643057547	140.540498671008
155	127.21420442533	120.555704891543	133.872703959117
156	161.563355429668	108.982952144954	214.143758714383

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/07/t1294395895sib1reesfo9zs9c/1svl71294395685.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/07/t1294395895sib1reesfo9zs9c/1svl71294395685.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/07/t1294395895sib1reesfo9zs9c/200r61294395685.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/07/t1294395895sib1reesfo9zs9c/200r61294395685.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/07/t1294395895sib1reesfo9zs9c/3ky1j1294395685.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/07/t1294395895sib1reesfo9zs9c/3ky1j1294395685.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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