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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: Wed, 20 Jan 2010 12:35:56 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/20/t1264016196j9lj0w4ns7v79ib.htm/, Retrieved Wed, 20 Jan 2010 20:36:41 +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/Jan/20/t1264016196j9lj0w4ns7v79ib.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

0,62 0,62 0,62 0,63 0,62 0,63 0,63 0,62 0,63 0,63 0,63 0,64 0,64 0,64 0,64 0,64 0,64 0,64 0,64 0,63 0,64 0,64 0,64 0,64 0,64 0,64 0,64 0,64 0,64 0,64 0,64 0,64 0,65 0,65 0,65 0,65 0,65 0,65 0,66 0,66 0,66 0,66 0,68 0,69 0,7 0,7 0,7 0,7 0,7 0,7 0,7 0,7 0,7 0,71 0,7 0,71 0,7 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,7 0,7 0,7 0,7 0,7 0,7 0,7 0,7 0,7 0,71 0,71 0,7 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,7 0,7 0,68 0,68 0,69 0,69 0,7 0,7 0,7 0,7 0,7 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,71 0,76 0,77 0,78 0,85 0,89 0,9 0,91 0,91 0,91 0,9 0,89 0,88 0,87 0,86 0,87 0,87 0,87 0,85

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	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999923349407294
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	0.62	0.62	0
3	0.62	0.62	0
4	0.63	0.62	0.01
5	0.62	0.629999233494073	-0.00999923349407295
6	0.63	0.620000766447174	0.00999923355282606
7	0.63	0.629999233552822	7.66447178390806e-07
8	0.62	0.629999999941251	-0.00999999994125134
9	0.63	0.620000766505923	0.0099992334940775
10	0.63	0.629999233552826	7.66447173949913e-07
11	0.63	0.629999999941251	5.87486725933672e-11
12	0.64	0.629999999999995	0.0100000000000046
13	0.64	0.639999233494073	7.66505927063399e-07
14	0.64	0.639999999941247	5.87531134854657e-11
15	0.64	0.639999999999995	4.55191440096314e-15
16	0.64	0.64	0
17	0.64	0.64	0
18	0.64	0.64	0
19	0.64	0.64	0
20	0.63	0.64	-0.01
21	0.64	0.630000766505927	0.00999923349407295
22	0.64	0.639999233552826	7.66447173949913e-07
23	0.64	0.639999999941251	5.87486725933672e-11
24	0.64	0.639999999999995	4.55191440096314e-15
25	0.64	0.64	0
26	0.64	0.64	0
27	0.64	0.64	0
28	0.64	0.64	0
29	0.64	0.64	0
30	0.64	0.64	0
31	0.64	0.64	0
32	0.64	0.64	0
33	0.65	0.64	0.01
34	0.65	0.649999233494073	7.66505927063399e-07
35	0.65	0.649999999941247	5.87531134854657e-11
36	0.65	0.649999999999995	4.55191440096314e-15
37	0.65	0.65	0
38	0.65	0.65	0
39	0.66	0.65	0.01
40	0.66	0.659999233494073	7.66505927063399e-07
41	0.66	0.659999999941247	5.87531134854657e-11
42	0.66	0.659999999999995	4.55191440096314e-15
43	0.68	0.66	0.02
44	0.69	0.679998466988146	0.0100015330118540
45	0.7	0.689999233376567	0.0100007666234333
46	0.7	0.699999233435311	7.66564689169691e-07
47	0.7	0.699999999941242	5.87576653998667e-11
48	0.7	0.699999999999995	4.55191440096314e-15
49	0.7	0.7	0
50	0.7	0.7	0
51	0.7	0.7	0
52	0.7	0.7	0
53	0.7	0.7	0
54	0.71	0.7	0.01
55	0.7	0.709999233494073	-0.00999923349407295
56	0.71	0.700000766447174	0.00999923355282606
57	0.7	0.709999233552822	-0.00999923355282162
58	0.71	0.700000766447178	0.00999923355282162
59	0.71	0.709999233552822	7.66447178390806e-07
60	0.71	0.709999999941251	5.87486725933672e-11
61	0.71	0.709999999999995	4.55191440096314e-15
62	0.71	0.71	0
63	0.71	0.71	0
64	0.71	0.71	0
65	0.71	0.71	0
66	0.71	0.71	0
67	0.71	0.71	0
68	0.71	0.71	0
69	0.71	0.71	0
70	0.71	0.71	0
71	0.7	0.71	-0.01
72	0.7	0.700000766505927	-7.66505927063399e-07
73	0.7	0.700000000058753	-5.87531134854657e-11
74	0.7	0.700000000000005	-4.55191440096314e-15
75	0.7	0.7	0
76	0.7	0.7	0
77	0.7	0.7	0
78	0.7	0.7	0
79	0.7	0.7	0
80	0.71	0.7	0.01
81	0.71	0.709999233494073	7.66505927063399e-07
82	0.7	0.709999999941247	-0.0099999999412469
83	0.71	0.700000766505922	0.0099992334940775
84	0.71	0.709999233552826	7.66447173949913e-07
85	0.71	0.709999999941251	5.87486725933672e-11
86	0.71	0.709999999999995	4.55191440096314e-15
87	0.71	0.71	0
88	0.71	0.71	0
89	0.71	0.71	0
90	0.71	0.71	0
91	0.71	0.71	0
92	0.71	0.71	0
93	0.71	0.71	0
94	0.71	0.71	0
95	0.7	0.71	-0.01
96	0.7	0.700000766505927	-7.66505927063399e-07
97	0.68	0.700000000058753	-0.020000000058753
98	0.68	0.680001533011859	-1.53301185867871e-06
99	0.69	0.680000000117506	0.00999999988249367
100	0.69	0.689999233494082	7.66505918070592e-07
101	0.7	0.689999999941247	0.0100000000587531
102	0.7	0.699999233494068	7.66505931615313e-07
103	0.7	0.699999999941247	5.87531134854657e-11
104	0.7	0.699999999999995	4.55191440096314e-15
105	0.7	0.7	0
106	0.71	0.7	0.01
107	0.71	0.709999233494073	7.66505927063399e-07
108	0.71	0.709999999941247	5.87531134854657e-11
109	0.71	0.709999999999995	4.55191440096314e-15
110	0.71	0.71	0
111	0.71	0.71	0
112	0.71	0.71	0
113	0.71	0.71	0
114	0.71	0.71	0
115	0.76	0.71	0.05
116	0.77	0.759996167470365	0.0100038325296353
117	0.78	0.769999233200307	0.0100007667996928
118	0.85	0.779999233435297	0.0700007665647027
119	0.89	0.849994634399753	0.0400053656002471
120	0.9	0.889996933565015	0.0100030664349847
121	0.91	0.899999233259029	0.0100007667409712
122	0.91	0.909999233435302	7.66564698162497e-07
123	0.91	0.909999999941242	5.87576653998667e-11
124	0.9	0.909999999999995	-0.00999999999999546
125	0.89	0.900000766505927	-0.0100007665059271
126	0.88	0.89000076656468	-0.0100007665646802
127	0.87	0.880000766564685	-0.0100007665646847
128	0.86	0.870000766564685	-0.0100007665646847
129	0.87	0.860000766564685	0.00999923343531528
130	0.87	0.86999923355283	7.66447169397999e-07
131	0.87	0.869999999941251	5.87486725933672e-11
132	0.85	0.869999999999995	-0.0199999999999955

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
133	0.850001533011854	0.830179436859045	0.869823629164664
134	0.850001533011854	0.82196993013796	0.878033135885747
135	0.850001533011854	0.815670409763872	0.884332656259836
136	0.850001533011854	0.810359619747525	0.889643446276183
137	0.850001533011854	0.805680696478176	0.894322369545532
138	0.850001533011854	0.80145061319736	0.898552452826348
139	0.850001533011854	0.79756064172822	0.902442424295488
140	0.850001533011854	0.793939938828221	0.906063127195487
141	0.850001533011854	0.790539296203954	0.909463769819754
142	0.850001533011854	0.787322885371791	0.912680180651917
143	0.850001533011854	0.78426365858793	0.915739407435778
144	0.850001533011854	0.78134060236302	0.918662463660689

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/20/t1264016196j9lj0w4ns7v79ib/1buix1264016154.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/20/t1264016196j9lj0w4ns7v79ib/1buix1264016154.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/20/t1264016196j9lj0w4ns7v79ib/2mpzw1264016154.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/20/t1264016196j9lj0w4ns7v79ib/2mpzw1264016154.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/20/t1264016196j9lj0w4ns7v79ib/3oegg1264016154.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/20/t1264016196j9lj0w4ns7v79ib/3oegg1264016154.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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