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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 12:48:20 -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/t12593514109mqbgs92fw7g0hx.htm/, Retrieved Fri, 27 Nov 2009 20:50:13 +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/t12593514109mqbgs92fw7g0hx.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 «

519 517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516

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	0.958919	7.4278	0
2	0.917399	7.1061	0
3	0.872142	6.7556	0
4	0.827864	6.4126	0
5	0.7808	6.0481	0
6	0.732689	5.6754	0
7	0.684605	5.3029	1e-06
8	0.633588	4.9078	4e-06
9	0.573112	4.4393	2e-05
10	0.504381	3.9069	0.00012
11	0.438164	3.394	0.000613
12	0.365476	2.831	0.003153
13	0.307219	2.3797	0.010261
14	0.253073	1.9603	0.027305
15	0.1937	1.5004	0.069378
16	0.137937	1.0685	0.144798
17	0.082287	0.6374	0.263147
18	0.029592	0.2292	0.40974
19	-0.021507	-0.1666	0.434125
20	-0.069282	-0.5367	0.296745
21	-0.117834	-0.9127	0.182517
22	-0.155338	-1.2032	0.116804
23	-0.195459	-1.514	0.067636
24	-0.23805	-1.8439	0.035067
25	-0.270829	-2.0978	0.02007
26	-0.299591	-2.3206	0.011862
27	-0.318398	-2.4663	0.008263
28	-0.342958	-2.6565	0.00505
29	-0.368696	-2.8559	0.002943
30	-0.397097	-3.0759	0.001579
31	-0.420883	-3.2601	0.000919
32	-0.443589	-3.436	0.000539
33	-0.459894	-3.5623	0.000364
34	-0.462825	-3.585	0.000339
35	-0.461721	-3.5765	0.000348
36	-0.452951	-3.5085	0.00043

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.958919	7.4278	0
2	-0.026428	-0.2047	0.419247
3	-0.068095	-0.5275	0.299909
4	-0.011578	-0.0897	0.464418
5	-0.057082	-0.4422	0.329984
6	-0.040457	-0.3134	0.377541
7	-0.024347	-0.1886	0.425524
8	-0.065178	-0.5049	0.30775
9	-0.150065	-1.1624	0.124839
10	-0.142973	-1.1075	0.136256
11	-0.011005	-0.0852	0.466175
12	-0.128466	-0.9951	0.161843
13	0.131311	1.0171	0.156588
14	0.026124	0.2024	0.420163
15	-0.129987	-1.0069	0.159019
16	0.010984	0.0851	0.466239
17	-0.029766	-0.2306	0.409219
18	-0.005852	-0.0453	0.481998
19	-0.009067	-0.0702	0.47212
20	-0.006179	-0.0479	0.480993
21	-0.096041	-0.7439	0.229912
22	0.040777	0.3159	0.376603
23	-0.058897	-0.4562	0.324942
24	-0.127483	-0.9875	0.163686
25	0.098451	0.7626	0.224345
26	0.025058	0.1941	0.423378
27	0.022758	0.1763	0.430333
28	-0.111665	-0.865	0.195255
29	-0.082162	-0.6364	0.263459
30	-0.112136	-0.8686	0.194264
31	-0.002479	-0.0192	0.492371
32	0.006261	0.0485	0.480741
33	-0.028267	-0.219	0.413714
34	0.141893	1.0991	0.138057
35	0.000433	0.0034	0.498668
36	-0.013264	-0.1027	0.459255

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t12593514109mqbgs92fw7g0hx/10npr1259351299.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t12593514109mqbgs92fw7g0hx/10npr1259351299.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t12593514109mqbgs92fw7g0hx/26a0g1259351299.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t12593514109mqbgs92fw7g0hx/26a0g1259351299.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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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