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*The author of this computation has been verified*

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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Fri, 27 Nov 2009 10:14:17 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/27/t1259342105tw0pmq3897erta3.htm/, Retrieved Fri, 27 Nov 2009 18:15:07 +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/2009/Nov/27/t1259342105tw0pmq3897erta3.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 «

252,5 251,1 255,1 258,3 255,3 261,1 253,8 252,9 253,9 255,5 262 262,8 263,3 262,5 269,2 270,8 274,1 273 267,3 267,1 268,2 270,2 271,5 281 280,1 281,5 285,9 289,8 292,9 291,2 291,8 289,8 292,5 290,3 297,5 307,5 304,7 304,6 310,7 310,7 315,7 314,7 312,2 312,8 314,3 319,7 319,9 329,5 326,9 329,7 335,7 337,2 339,7 338,3 339,2 342,5 342,2 338,3 339 345,9

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

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.950624	7.3635	0
2	0.906231	7.0196	0
3	0.864025	6.6927	0
4	0.81826	6.3382	0
5	0.769572	5.9611	0
6	0.725118	5.6167	0
7	0.674346	5.2235	1e-06
8	0.618475	4.7907	6e-06
9	0.566307	4.3866	2.4e-05
10	0.512682	3.9712	9.7e-05
11	0.469674	3.6381	0.000286
12	0.426153	3.301	0.000813
13	0.371988	2.8814	0.002742
14	0.323835	2.5084	0.007424
15	0.279627	2.166	0.017148
16	0.238711	1.849	0.03469
17	0.201977	1.5645	0.061479
18	0.164843	1.2769	0.103284
19	0.117935	0.9135	0.182312
20	0.069468	0.5381	0.296251
21	0.024308	0.1883	0.425642
22	-0.02225	-0.1723	0.431872
23	-0.061819	-0.4788	0.316895
24	-0.095204	-0.7374	0.231863
25	-0.138636	-1.0739	0.143591
26	-0.174348	-1.3505	0.090965
27	-0.200277	-1.5513	0.06304
28	-0.226785	-1.7567	0.042038
29	-0.24769	-1.9186	0.029898
30	-0.27201	-2.107	0.019654
31	-0.297141	-2.3016	0.012422
32	-0.325974	-2.525	0.007116
33	-0.350478	-2.7148	0.004324
34	-0.375586	-2.9093	0.002537
35	-0.389027	-3.0134	0.00189
36	-0.396133	-3.0684	0.001614

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.950624	7.3635	0
2	0.026414	0.2046	0.419287
3	0.001927	0.0149	0.49407
4	-0.05732	-0.444	0.32932
5	-0.058571	-0.4537	0.325845
6	0.011919	0.0923	0.463373
7	-0.087968	-0.6814	0.24912
8	-0.086407	-0.6693	0.252933
9	-0.005921	-0.0459	0.481785
10	-0.046536	-0.3605	0.359881
11	0.085903	0.6654	0.254171
12	-0.027827	-0.2155	0.415036
13	-0.141184	-1.0936	0.139249
14	0.018168	0.1407	0.444276
15	-0.001561	-0.0121	0.495197
16	0.021286	0.1649	0.434797
17	0.009753	0.0755	0.470015
18	-0.061429	-0.4758	0.317962
19	-0.118877	-0.9208	0.180417
20	-0.068386	-0.5297	0.299133
21	-0.017337	-0.1343	0.44681
22	-0.049986	-0.3872	0.349993
23	0.002367	0.0183	0.492716
24	0.033987	0.2633	0.396626
25	-0.11297	-0.8751	0.192515
26	0.03908	0.3027	0.381579
27	0.060564	0.4691	0.32034
28	-0.038851	-0.3009	0.382251
29	0.010133	0.0785	0.46885
30	-0.102574	-0.7945	0.215008
31	-0.023178	-0.1795	0.42906
32	-0.078957	-0.6116	0.271556
33	-0.03576	-0.277	0.391369
34	-0.041095	-0.3183	0.375673
35	0.035561	0.2755	0.391956
36	0.057459	0.4451	0.328933

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259342105tw0pmq3897erta3/1b0ep1259342055.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259342105tw0pmq3897erta3/1b0ep1259342055.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259342105tw0pmq3897erta3/2lu5t1259342055.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259342105tw0pmq3897erta3/2lu5t1259342055.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

R code (references can be found in the software module):

if (par1 == 'Default') {

par1 = 10*log10(length(x))

} else {

par1 <- as.numeric(par1)

}

par2 <- as.numeric(par2)

par3 <- as.numeric(par3)

par4 <- as.numeric(par4)

par5 <- as.numeric(par5)

if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'

par7 <- as.numeric(par7)

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')

dev.off()

(myacf <- c(racf$acf))

(mypacf <- c(rpacf$acf))

lengthx <- length(x)

sqrtn <- sqrt(lengthx)

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Autocorrelation Function',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Time lag k',header=TRUE)

a<-table.element(a,hyperlink('http://www.xycoon.com/basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)

a<-table.element(a,'T-STAT',header=TRUE)

a<-table.element(a,'P-value',header=TRUE)

a<-table.row.end(a)

for (i in 2:(par1+1)) {

a<-table.row.start(a)

a<-table.element(a,i-1,header=TRUE)

a<-table.element(a,round(myacf[i],6))

mytstat <- myacf[i]*sqrtn

a<-table.element(a,round(mytstat,4))

a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))

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,'Partial Autocorrelation Function',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Time lag k',header=TRUE)

a<-table.element(a,hyperlink('http://www.xycoon.com/basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)

a<-table.element(a,'T-STAT',header=TRUE)

a<-table.element(a,'P-value',header=TRUE)

a<-table.row.end(a)

for (i in 1:par1) {

a<-table.row.start(a)

a<-table.element(a,i,header=TRUE)

a<-table.element(a,round(mypacf[i],6))

mytstat <- mypacf[i]*sqrtn

a<-table.element(a,round(mytstat,4))

a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable1.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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