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Exponential smoothing index benzine

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 18 Aug 2009 16:05:12 -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/19/t12506331903ny7hrp8w44el6s.htm/, Retrieved Wed, 19 Aug 2009 00:06:30 +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/19/t12506331903ny7hrp8w44el6s.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

105.46 104.66 103.52 103.71 103.78 103.67 103.66 102.76 102 101.5 101.5 99.22 98.97 98.9 99.78 104.4 106.21 105.46 108.33 111.72 111.88 112.86 113.09 116.9 114.62 118.86 124.71 122.53 127.89 136.16 134.12 130.26 135.35 131.43 129.61 123.96 121.1 125.38 123.1 129.92 136.68 131.17 124.82 122.47 126.15 118.74 116.8 116.64 116.53 117.68 119.46 126.19 124.39 121.9 122.53 122.93 124.66 124.41 120.93 120.18 123.44 126.1 125.82 122.18 117.27 117.86 119.09 123.08 125.42 121.81 121.66 121.27 120.92 122.16 124.17 127.26 134.16 134.09 135.57 136.13 136.23 140.6 136.5 130.59 129.5 135.25 138.06 146.28 145.04 147.96 156.71 160.97 168.17 163.91 153.05 151.76 119.55 119.44 120.25 124.92 126.34 125.88 127.34 127.48 119.41 114.82 115.28 116.37 111.99 113.57 117.69 120.74 122.37 123.57 124.86 122.08 123.56 126.92 134.88 130.64 131.65 130.97 136.77 138.17 146.4 152.07 153.05 142.89 141.11 131.9 118.42 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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	103.52	104.66	-1.14
4	103.71	103.52	0.189999999999998
5	103.78	103.71	0.0700000000000074
6	103.67	103.78	-0.109999999999999
7	103.66	103.67	-0.0100000000000051
8	102.76	103.66	-0.899999999999991
9	102	102.76	-0.760000000000005
10	101.5	102	-0.5
11	101.5	101.5	0
12	99.22	101.5	-2.28
13	98.97	99.22	-0.25
14	98.9	98.97	-0.0699999999999932
15	99.78	98.9	0.879999999999995
16	104.4	99.78	4.62
17	106.21	104.4	1.80999999999999
18	105.46	106.21	-0.75
19	108.33	105.46	2.87000000000000
20	111.72	108.33	3.39
21	111.88	111.72	0.159999999999997
22	112.86	111.88	0.980000000000004
23	113.09	112.86	0.230000000000004
24	116.9	113.09	3.81
25	114.62	116.9	-2.28
26	118.86	114.62	4.23999999999999
27	124.71	118.86	5.85
28	122.53	124.71	-2.17999999999999
29	127.89	122.53	5.36
30	136.16	127.89	8.27
31	134.12	136.16	-2.03999999999999
32	130.26	134.12	-3.86000000000001
33	135.35	130.26	5.09
34	131.43	135.35	-3.91999999999999
35	129.61	131.43	-1.81999999999999
36	123.96	129.61	-5.65000000000002
37	121.1	123.96	-2.86
38	125.38	121.1	4.28
39	123.1	125.38	-2.28
40	129.92	123.1	6.81999999999999
41	136.68	129.92	6.76000000000002
42	131.17	136.68	-5.51000000000002
43	124.82	131.17	-6.35
44	122.47	124.82	-2.34999999999999
45	126.15	122.47	3.68000000000001
46	118.74	126.15	-7.41000000000001
47	116.8	118.74	-1.94000000000000
48	116.64	116.8	-0.159999999999997
49	116.53	116.64	-0.109999999999999
50	117.68	116.53	1.15000000000001
51	119.46	117.68	1.77999999999999
52	126.19	119.46	6.73
53	124.39	126.19	-1.80000000000000
54	121.9	124.39	-2.48999999999999
55	122.53	121.9	0.629999999999995
56	122.93	122.53	0.400000000000006
57	124.66	122.93	1.72999999999999
58	124.41	124.66	-0.25
59	120.93	124.41	-3.47999999999999
60	120.18	120.93	-0.75
61	123.44	120.18	3.25999999999999
62	126.1	123.44	2.66000000000000
63	125.82	126.1	-0.280000000000001
64	122.18	125.82	-3.63999999999999
65	117.27	122.18	-4.91000000000001
66	117.86	117.27	0.590000000000003
67	119.09	117.86	1.23000000000000
68	123.08	119.09	3.98999999999999
69	125.42	123.08	2.34000000000000
70	121.81	125.42	-3.61
71	121.66	121.81	-0.150000000000006
72	121.27	121.66	-0.390000000000001
73	120.92	121.27	-0.349999999999994
74	122.16	120.92	1.23999999999999
75	124.17	122.16	2.01000000000001
76	127.26	124.17	3.09000000000000
77	134.16	127.26	6.89999999999999
78	134.09	134.16	-0.0699999999999932
79	135.57	134.09	1.47999999999999
80	136.13	135.57	0.560000000000002
81	136.23	136.13	0.0999999999999943
82	140.6	136.23	4.37000000000000
83	136.5	140.6	-4.09999999999999
84	130.59	136.5	-5.91
85	129.5	130.59	-1.09000000000000
86	135.25	129.5	5.75
87	138.06	135.25	2.81
88	146.28	138.06	8.22
89	145.04	146.28	-1.24000000000001
90	147.96	145.04	2.92000000000002
91	156.71	147.96	8.75
92	160.97	156.71	4.25999999999999
93	168.17	160.97	7.19999999999999
94	163.91	168.17	-4.25999999999999
95	153.05	163.91	-10.8600000000000
96	151.76	153.05	-1.29000000000002
97	119.55	151.76	-32.21
98	119.44	119.55	-0.109999999999999
99	120.25	119.44	0.810000000000002
100	124.92	120.25	4.67
101	126.34	124.92	1.42000000000000
102	125.88	126.34	-0.460000000000008
103	127.34	125.88	1.46000000000001
104	127.48	127.34	0.140000000000001
105	119.41	127.48	-8.07
106	114.82	119.41	-4.59
107	115.28	114.82	0.460000000000008
108	116.37	115.28	1.09000000000000
109	111.99	116.37	-4.38000000000001
110	113.57	111.99	1.58000000000000
111	117.69	113.57	4.12000000000000
112	120.74	117.69	3.05
113	122.37	120.74	1.63000000000001
114	123.57	122.37	1.19999999999999
115	124.86	123.57	1.29000000000001
116	122.08	124.86	-2.78
117	123.56	122.08	1.48000000000000
118	126.92	123.56	3.36
119	134.88	126.92	7.96
120	130.64	134.88	-4.24000000000001
121	131.65	130.64	1.01000000000002
122	130.97	131.65	-0.680000000000007
123	136.77	130.97	5.80000000000001
124	138.17	136.77	1.39999999999998
125	146.4	138.17	8.23000000000002
126	152.07	146.4	5.66999999999999
127	153.05	152.07	0.980000000000018
128	142.89	153.05	-10.1600000000000
129	141.11	142.89	-1.77999999999997
130	131.9	141.11	-9.21
131	118.42	131.9	-13.48
132	108.27	118.42	-10.15

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
133	108.27	98.4685328537376	118.071467146262
134	108.27	94.4086322306014	122.131367769399
135	108.27	91.2933609139563	125.246639086044
136	108.27	88.6670657074751	127.872934292525
137	108.27	86.3532531817263	130.186746818274
138	108.27	84.2614067610039	132.278593238996
139	108.27	82.3377554474197	134.202244552580
140	108.27	80.5472644612027	135.992735538797
141	108.27	78.8655985612127	137.674401438787
142	108.27	77.2750394065	139.2649605935
143	108.27	75.762211080852	140.777788919148
144	108.27	74.3167218279127	142.223278172087

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t12506331903ny7hrp8w44el6s/1cx7w1250633107.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t12506331903ny7hrp8w44el6s/1cx7w1250633107.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t12506331903ny7hrp8w44el6s/2gb3w1250633107.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t12506331903ny7hrp8w44el6s/2gb3w1250633107.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t12506331903ny7hrp8w44el6s/3xa5d1250633107.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t12506331903ny7hrp8w44el6s/3xa5d1250633107.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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=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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