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workshop 9,4

*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: Tue, 01 Dec 2009 12:30:54 -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/01/t1259695923wv4q9p7qj9y6t40.htm/, Retrieved Tue, 01 Dec 2009 20:32:06 +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/01/t1259695923wv4q9p7qj9y6t40.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 «

564 581 597 587 536 524 537 536 533 528 516 502 506 518 534 528 478 469 490 493 508 517 514 510 527 542 565 555 499 511 526 532 549 561 557 566 588 620 626 620 573 573 574 580 590 593 597 595 612 628 629 621 569 567 573 584 589 591 595 594 611

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	0 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.885165	6.9134	0
2	0.727801	5.6843	0
3	0.62071	4.8479	4e-06
4	0.578274	4.5165	1.5e-05
5	0.576343	4.5014	1.5e-05
6	0.558672	4.3634	2.5e-05
7	0.501291	3.9152	0.000115
8	0.429984	3.3583	0.000678
9	0.402348	3.1424	0.001293
10	0.403951	3.155	0.001246
11	0.447271	3.4933	0.000447
12	0.442602	3.4568	0.000501
13	0.298384	2.3305	0.011553
14	0.134566	1.051	0.148703
15	0.018684	0.1459	0.442231
16	-0.038542	-0.301	0.38221
17	-0.056971	-0.445	0.328961
18	-0.081265	-0.6347	0.263998
19	-0.134196	-1.0481	0.149363
20	-0.197553	-1.5429	0.064009
21	-0.217648	-1.6999	0.047123
22	-0.213426	-1.6669	0.05033
23	-0.178906	-1.3973	0.083693
24	-0.182653	-1.4266	0.079402
25	-0.274975	-2.1476	0.017863
26	-0.37059	-2.8944	0.002632
27	-0.41718	-3.2583	0.000917
28	-0.425996	-3.3271	0.000745
29	-0.406114	-3.1719	0.001186
30	-0.387367	-3.0254	0.001816
31	-0.386942	-3.0221	0.001833
32	-0.387066	-3.0231	0.001828
33	-0.345498	-2.6984	0.004499
34	-0.300677	-2.3484	0.011057
35	-0.249625	-1.9496	0.02791
36	-0.218703	-1.7081	0.046349

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.885165	6.9134	0
2	-0.257366	-2.0101	0.024425
3	0.190436	1.4874	0.071037
4	0.15409	1.2035	0.11672
5	0.121484	0.9488	0.173228
6	-0.05067	-0.3957	0.346837
7	-0.074447	-0.5814	0.281541
8	-0.007519	-0.0587	0.476682
9	0.157446	1.2297	0.111767
10	-0.007798	-0.0609	0.475817
11	0.230961	1.8039	0.038095
12	-0.232506	-1.8159	0.037148
13	-0.537314	-4.1966	4.5e-05
14	0.024731	0.1932	0.423739
15	-0.105876	-0.8269	0.205754
16	-0.128319	-1.0022	0.160102
17	0.02084	0.1628	0.435621
18	-0.032494	-0.2538	0.400257
19	0.040309	0.3148	0.376985
20	-0.085918	-0.671	0.252364
21	0.091525	0.7148	0.23872
22	0.014558	0.1137	0.454923
23	-0.024384	-0.1904	0.424797
24	0.04504	0.3518	0.36311
25	-0.030614	-0.2391	0.405914
26	0.015049	0.1175	0.453411
27	0.060929	0.4759	0.317932
28	-0.152273	-1.1893	0.119468
29	0.068726	0.5368	0.296691
30	-0.04972	-0.3883	0.349563
31	0.035584	0.2779	0.391007
32	0.037727	0.2947	0.384627
33	0.066983	0.5232	0.301381
34	-0.076655	-0.5987	0.275796
35	-0.026467	-0.2067	0.41846
36	0.101534	0.793	0.215424

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259695923wv4q9p7qj9y6t40/1gf0a1259695852.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259695923wv4q9p7qj9y6t40/1gf0a1259695852.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259695923wv4q9p7qj9y6t40/2jwqg1259695852.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259695923wv4q9p7qj9y6t40/2jwqg1259695852.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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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