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tijdreeks 1 stap 32

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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: Mon, 16 Aug 2010 12:27:24 +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/Aug/16/t1281961613g67yisqcjrmq4uf.htm/, Retrieved Mon, 16 Aug 2010 14:26:57 +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/2010/Aug/16/t1281961613g67yisqcjrmq4uf.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:

De Reu Magali

Dataseries X:

» Textbox « » Textfile « » CSV «

333 332 331 329 349 348 333 323 324 324 325 327 329 333 329 333 355 358 338 326 320 322 322 324 326 330 331 333 364 363 341 327 313 321 312 312 312 314 312 319 356 351 329 313 298 303 278 275 276 276 273 287 320 313 281 266 258 259 237 231 237 236 229 243 271 262 227 208 212 222 200 193 204 203 190 209 240 234 210 195 202 204 180 169 178 181 163 174 194 187 160 143 151 154 141 127 134 138 120 129 151 152 124 99 104 109 96 87 94 89 63 76 100 104 80 55 60 71 62 61

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	1
beta	0
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	331	331	0
4	329	330	-1
5	349	328	21
6	348	348	0
7	333	347	-14
8	323	332	-9
9	324	322	2
10	324	323	1
11	325	323	2
12	327	324	3
13	329	326	3
14	333	328	5
15	329	332	-3
16	333	328	5
17	355	332	23
18	358	354	4
19	338	357	-19
20	326	337	-11
21	320	325	-5
22	322	319	3
23	322	321	1
24	324	321	3
25	326	323	3
26	330	325	5
27	331	329	2
28	333	330	3
29	364	332	32
30	363	363	0
31	341	362	-21
32	327	340	-13
33	313	326	-13
34	321	312	9
35	312	320	-8
36	312	311	1
37	312	311	1
38	314	311	3
39	312	313	-1
40	319	311	8
41	356	318	38
42	351	355	-4
43	329	350	-21
44	313	328	-15
45	298	312	-14
46	303	297	6
47	278	302	-24
48	275	277	-2
49	276	274	2
50	276	275	1
51	273	275	-2
52	287	272	15
53	320	286	34
54	313	319	-6
55	281	312	-31
56	266	280	-14
57	258	265	-7
58	259	257	2
59	237	258	-21
60	231	236	-5
61	237	230	7
62	236	236	0
63	229	235	-6
64	243	228	15
65	271	242	29
66	262	270	-8
67	227	261	-34
68	208	226	-18
69	212	207	5
70	222	211	11
71	200	221	-21
72	193	199	-6
73	204	192	12
74	203	203	0
75	190	202	-12
76	209	189	20
77	240	208	32
78	234	239	-5
79	210	233	-23
80	195	209	-14
81	202	194	8
82	204	201	3
83	180	203	-23
84	169	179	-10
85	178	168	10
86	181	177	4
87	163	180	-17
88	174	162	12
89	194	173	21
90	187	193	-6
91	160	186	-26
92	143	159	-16
93	151	142	9
94	154	150	4
95	141	153	-12
96	127	140	-13
97	134	126	8
98	138	133	5
99	120	137	-17
100	129	119	10
101	151	128	23
102	152	150	2
103	124	151	-27
104	99	123	-24
105	104	98	6
106	109	103	6
107	96	108	-12
108	87	95	-8
109	94	86	8
110	89	93	-4
111	63	88	-25
112	76	62	14
113	100	75	25
114	104	99	5
115	80	103	-23
116	55	79	-24
117	60	54	6
118	71	59	12
119	62	70	-8
120	61	61	0

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	60	31.8501956597191	88.1498043402809
122	59	19.1901649238258	98.8098350761742
123	58	9.24310865951067	106.756891340489
124	57	0.700391319438289	113.299608680562
125	56	-6.94487605818662	118.944876058187
126	55	-13.9526569928713	123.952656992871
127	54	-20.4773817395098	128.477381739510
128	53	-26.6196701523484	132.619670152348
129	52	-32.4494130208426	136.449413020843
130	51	-38.017497403381	140.017497403381
131	50	-43.3623389186295	143.362338918630
132	49	-48.5137826809787	146.513782680979

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281961613g67yisqcjrmq4uf/1w08q1281961642.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281961613g67yisqcjrmq4uf/1w08q1281961642.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281961613g67yisqcjrmq4uf/2w08q1281961642.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281961613g67yisqcjrmq4uf/2w08q1281961642.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281961613g67yisqcjrmq4uf/3ospb1281961642.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281961613g67yisqcjrmq4uf/3ospb1281961642.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=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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