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*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: Tue, 28 Dec 2010 22:16:05 +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/Dec/28/t1293574505hkgbdjvvziqpedq.htm/, Retrieved Tue, 28 Dec 2010 23:15:06 +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/Dec/28/t1293574505hkgbdjvvziqpedq.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 «

19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 20.1 21.64 20.95 19.46 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.39 19.94 20.69 20.69 21.64 20.86 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.7 20.67 20.67 20.67 20.67 23.42 30.02 42.03 32.52 29.13 28.57 28.88 27.49 23.75 23.09 23.24 23.52 22.99 23.75 23.05 21.66 20.84 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 20.67 24.44 34.94 35 35 35 35 35 etc...

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

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999949133676386
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	19.39	19.39	0
3	19.39	19.39	0
4	19.39	19.39	0
5	19.39	19.39	0
6	19.39	19.39	0
7	19.39	19.39	0
8	19.39	19.39	0
9	19.39	19.39	0
10	19.39	19.39	0
11	19.39	19.39	0
12	19.39	19.39	0
13	19.39	19.39	0
14	19.39	19.39	0
15	19.39	19.39	0
16	19.39	19.39	0
17	19.39	19.39	0
18	19.39	19.39	0
19	19.39	19.39	0
20	19.39	19.39	0
21	19.39	19.39	0
22	19.39	19.39	0
23	19.39	19.39	0
24	20.1	19.39	0.710000000000001
25	21.64	20.0999638849102	1.54003611508977
26	20.95	21.6399216640246	-0.689921664024595
27	19.46	20.9500350937786	-1.49003509377863
28	19.39	19.4600757926073	-0.0700757926072768
29	19.39	19.3900035644979	-3.56449794480795e-06
30	19.39	19.3900000001813	-1.81312742597584e-10
31	19.39	19.39	-1.06581410364015e-14
32	19.39	19.39	0
33	19.39	19.39	0
34	19.39	19.39	0
35	19.39	19.39	0
36	19.39	19.39	0
37	19.39	19.39	0
38	19.39	19.39	0
39	19.39	19.39	0
40	19.39	19.39	0
41	19.39	19.39	0
42	19.39	19.39	0
43	19.39	19.39	0
44	19.94	19.39	0.550000000000001
45	20.69	19.939972023522	0.750027976477988
46	20.69	20.6899618488342	3.81511657714384e-05
47	21.64	20.6899999980594	0.950000001940609
48	20.86	21.6399516769925	-0.779951676992468
49	20.67	20.8600396732744	-0.190039673274402
50	20.67	20.6700096666195	-9.66661951906644e-06
51	20.67	20.6700000004917	-4.91706231287026e-10
52	20.67	20.67	-2.48689957516035e-14
53	20.67	20.67	0
54	20.67	20.67	0
55	20.67	20.67	0
56	20.67	20.67	0
57	20.67	20.67	0
58	20.67	20.67	0
59	20.67	20.67	0
60	20.67	20.67	0
61	20.67	20.67	0
62	20.67	20.67	0
63	20.67	20.67	0
64	20.67	20.67	0
65	20.67	20.67	0
66	20.67	20.67	0
67	20.7	20.67	0.0299999999999976
68	20.67	20.6999984740103	-0.0299984740102879
69	20.67	20.6700015259121	-1.52591208646413e-06
70	20.67	20.6700000000776	-7.76161357407545e-11
71	20.67	20.67	-3.5527136788005e-15
72	23.42	20.67	2.75
73	30.02	23.4198601176101	6.60013988238994
74	42.03	30.0196642751488	12.0103357248512
75	32.52	42.0293890783763	-9.5093890783763
76	29.13	32.5204837076622	-3.39048370766224
77	28.57	29.1301724614415	-0.560172461441482
78	28.88	28.5700284939137	0.309971506086296
79	27.49	28.8799842328891	-1.38998423288906
80	23.75	27.4900707033878	-3.74007070338781
81	23.09	23.7501902436467	-0.660190243646738
82	23.24	23.0900335814506	0.149966418549418
83	23.52	23.2399923717596	0.28000762824038
84	22.99	23.5199857570414	-0.52998575704137
85	23.75	22.990026958427	0.759973041572973
86	23.05	23.7499613429653	-0.699961342965327
87	21.66	23.0500356044602	-1.39003560446019
88	20.84	21.6600707060009	-0.820070706000891
89	20.67	20.8400417139819	-0.170041713981917
90	20.67	20.6700086493969	-8.64939685030208e-06
91	20.67	20.67000000044	-4.39964509268975e-10
92	20.67	20.67	-2.1316282072803e-14
93	20.67	20.67	0
94	20.67	20.67	0
95	20.67	20.67	0
96	20.67	20.67	0
97	20.67	20.67	0
98	20.67	20.67	0
99	20.67	20.67	0
100	20.67	20.67	0
101	20.67	20.67	0
102	20.67	20.67	0
103	20.67	20.67	0
104	20.67	20.67	0
105	20.67	20.67	0
106	20.67	20.67	0
107	20.67	20.67	0
108	20.67	20.67	0
109	20.67	20.67	0
110	20.67	20.67	0
111	20.67	20.67	0
112	20.67	20.67	0
113	20.67	20.67	0
114	20.67	20.67	0
115	20.67	20.67	0
116	20.67	20.67	0
117	20.67	20.67	0
118	20.67	20.67	0
119	20.67	20.67	0
120	20.67	20.67	0
121	20.67	20.67	0
122	20.67	20.67	0
123	20.67	20.67	0
124	20.67	20.67	0
125	20.67	20.67	0
126	20.67	20.67	0
127	20.67	20.67	0
128	20.67	20.67	0
129	20.67	20.67	0
130	20.67	20.67	0
131	20.67	20.67	0
132	20.67	20.67	0
133	20.67	20.67	0
134	20.67	20.67	0
135	20.67	20.67	0
136	20.67	20.67	0
137	20.67	20.67	0
138	20.67	20.67	0
139	20.67	20.67	0
140	20.67	20.67	0
141	20.67	20.67	0
142	20.67	20.67	0
143	24.44	20.67	3.77
144	34.94	24.43980823396	10.50019176604
145	35	34.9394658938476	0.0605341061523816
146	35	34.9999969208526	3.07914743302717e-06
147	35	34.9999999998434	1.56624935243599e-10
148	35	35	7.105427357601e-15
149	35	35	0
150	35	35	0
151	35	35	0
152	35	35	0
153	35	35	0
154	35	35	0
155	35	35	0
156	35	35	0
157	35	35	0
158	35	35	0
159	35	35	0
160	35	35	0
161	35	35	0
162	35	35	0
163	35	35	0
164	35	35	0
165	35	35	0
166	35	35	0
167	35	35	0
168	35	35	0
169	35	35	0
170	35	35	0
171	35	35	0
172	35	35	0
173	35	35	0
174	35	35	0
175	35	35	0
176	35	35	0
177	35	35	0
178	39.26	35	4.26
179	41.51	39.2597833094614	2.25021669053859
180	36.41	41.5098855397496	-5.09988553974962
181	41.25	36.4102594124283	4.83974058757175
182	58.6	41.2497538201891	17.3502461798109
183	97.81	58.599117456763	39.210882543237
184	159.74	97.8080054865594	61.9319945134406
185	161.49	159.736849747125	1.75315025287497
186	125.32	161.489910823692	-36.1699108236919
187	148.31	125.321839830389	22.988160169611
188	193.55	148.308830676806	45.2411693231945
189	307.5	193.547698748041	113.952301251959
190	612.56	307.494203665368	305.065796334632
191	459.64	612.54448242448	-152.90448242448
192	375.91	459.647777688885	-83.737777688885
193	424	375.914259432899	48.0857405671013
194	360.66	423.997554055159	-63.337554055159
195	317.66	360.663221748521	-43.0032217485215
196	368.24	317.662187415794	50.5778125842061
197	447.95	368.237427292617	79.7125727073825
198	438.31	447.945945314481	-9.63594531448058
199	382.58	438.310490145113	-55.7304901451127
200	384.93	382.582834805147	2.34716519485312
201	363.29	384.929880608336	-21.6398806083356
202	344.97	363.29110074117	-18.32110074117
203	360.91	344.970931927039	15.9390680729607
204	385.42	360.909189238205	24.5108107617947
205	385.5	385.418753225168	0.0812467748322092
206	389.09	385.499995867275	3.59000413272474
207	332.39	389.089817389688	-56.699817389688
208	295.24	332.39288411126	-37.1528841112602
209	279.91	295.241889830626	-15.3318898306264
210	280.1	279.91077987687	0.189220123130269
211	272.22	280.099990375068	-7.87999037506796
212	311.33	272.220400826141	39.1095991738595
213	364.8	311.328010638472	53.471989361528
214	410.52	364.797280076485	45.7227199235151
215	446	410.517674253332	35.4823257466682
216	606	445.998195144536	160.001804855464
217	699	605.991861296415	93.0081387035846
218	768	698.995269017918	69.004730982082
219	950	767.996489983023	182.003510016977

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
220	949.99074215056	883.560682805727	1016.42080149539

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293574505hkgbdjvvziqpedq/1itpm1293574560.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293574505hkgbdjvvziqpedq/1itpm1293574560.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293574505hkgbdjvvziqpedq/2tkpp1293574560.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293574505hkgbdjvvziqpedq/2tkpp1293574560.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293574505hkgbdjvvziqpedq/3tkpp1293574560.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293574505hkgbdjvvziqpedq/3tkpp1293574560.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 1 ; par3 = 1 ; par4 = 1 ;

Parameters (R input):

par1 = 1 ; par2 = Single ; par3 = additive ; par4 = 1 ;

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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