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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: Thu, 10 Dec 2009 05:45:23 -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/Dec/10/t1260449187ly4gwwslnrnj4xv.htm/, Retrieved Thu, 10 Dec 2009 13:46:29 +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/Dec/10/t1260449187ly4gwwslnrnj4xv.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 «

13132.1 17665.9 16913 17318.8 16224.2 15469.6 16557.5 19414.8 17335 16525.2 18160.4 15553.8 15262.2 18581 17564.1 18948.6 17187.8 17564.8 17668.4 20811.7 17257.8 18984.2 20532.6 17082.3 16894.9 20274.9 20078.6 19900.9 17012.2 19642.9 19024 21691 18835.9 19873.4 21468.2 19406.8 18385.3 20739.3 22268.3 21569 17514.8 21124.7 21251 21393 22145.2 20310.5 23466.9 21264.6 18388.1 22635.4 22014.3 18422.7 16120.2 16037.7 16410.7 17749.8 16349.8 15662.3 17782.3 16398.9

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.486218	3.7662	0.00019
2	0.364636	2.8245	0.00321
3	0.439543	3.4047	0.000593
4	0.447739	3.4682	0.000488
5	0.374016	2.8971	0.002625
6	0.264478	2.0486	0.02244
7	0.164813	1.2766	0.103325
8	0.218937	1.6959	0.047546
9	0.078956	0.6116	0.27156
10	-0.048899	-0.3788	0.353099
11	0.077358	0.5992	0.275644
12	0.28139	2.1796	0.01661
13	-0.043218	-0.3348	0.369483
14	-0.113921	-0.8824	0.190534
15	-0.065713	-0.509	0.306306
16	0.03698	0.2864	0.387763
17	-0.043997	-0.3408	0.367224
18	-0.085444	-0.6618	0.255302
19	-0.090487	-0.7009	0.243034
20	-0.067273	-0.5211	0.302108
21	-0.184823	-1.4316	0.078719
22	-0.203931	-1.5796	0.059723
23	-0.117491	-0.9101	0.183211
24	0.006513	0.0505	0.479965
25	-0.180138	-1.3953	0.084028
26	-0.278475	-2.1571	0.017509
27	-0.189835	-1.4705	0.073332
28	-0.093614	-0.7251	0.235596
29	-0.188863	-1.4629	0.074353
30	-0.19114	-1.4806	0.071978
31	-0.176665	-1.3684	0.088138
32	-0.211468	-1.638	0.053325
33	-0.248927	-1.9282	0.029284
34	-0.239592	-1.8559	0.034192
35	-0.194668	-1.5079	0.068415
36	-0.103096	-0.7986	0.213842

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.486218	3.7662	0.00019
2	0.167928	1.3008	0.099157
3	0.2835	2.196	0.015985
4	0.195754	1.5163	0.067346
5	0.07184	0.5565	0.28998
6	-0.070869	-0.5489	0.292539
7	-0.161525	-1.2512	0.107865
8	0.018737	0.1451	0.442546
9	-0.18414	-1.4263	0.079476
10	-0.170533	-1.3209	0.095768
11	0.147839	1.1452	0.128345
12	0.448511	3.4741	0.000479
13	-0.228902	-1.7731	0.040646
14	-0.163611	-1.2673	0.104968
15	-0.152052	-1.1778	0.121765
16	0.022158	0.1716	0.432152
17	-0.138339	-1.0716	0.144102
18	0.12769	0.9891	0.163298
19	0.148191	1.1479	0.127787
20	-0.078567	-0.6086	0.27255
21	-0.159135	-1.2327	0.111257
22	-0.001942	-0.015	0.494023
23	-0.101141	-0.7834	0.218226
24	-0.033909	-0.2627	0.396858
25	0.106917	0.8282	0.205426
26	-0.018126	-0.1404	0.444407
27	-0.056296	-0.4361	0.332176
28	-0.05504	-0.4263	0.335694
29	-0.054279	-0.4204	0.337831
30	-0.114052	-0.8834	0.190261
31	-0.00134	-0.0104	0.495878
32	-0.061686	-0.4778	0.317258
33	0.031929	0.2473	0.402751
34	0.007009	0.0543	0.478443
35	-0.040942	-0.3171	0.376121
36	-0.086945	-0.6735	0.251615

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260449187ly4gwwslnrnj4xv/1ty0e1260449120.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260449187ly4gwwslnrnj4xv/1ty0e1260449120.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260449187ly4gwwslnrnj4xv/2wn5m1260449120.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260449187ly4gwwslnrnj4xv/2wn5m1260449120.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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