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Partial Autocorrelation D=1

*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 11:41:05 -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/t1259347319cepjmw5pnuatfwi.htm/, Retrieved Fri, 27 Nov 2009 19:42:01 +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/t1259347319cepjmw5pnuatfwi.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

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	0.939418	6.5085	0
2	0.866164	6.001	0
3	0.780214	5.4055	1e-06
4	0.681134	4.719	1e-05
5	0.572121	3.9638	0.000122
6	0.46101	3.194	0.00124
7	0.347018	2.4042	0.010058
8	0.235623	1.6324	0.054565
9	0.135437	0.9383	0.176384
10	0.048303	0.3347	0.369672
11	-0.025232	-0.1748	0.430982
12	-0.10007	-0.6933	0.245729
13	-0.153979	-1.0668	0.1457
14	-0.199665	-1.3833	0.086483
15	-0.244988	-1.6973	0.048055
16	-0.296525	-2.0544	0.022703
17	-0.348398	-2.4138	0.009826
18	-0.383787	-2.659	0.00531
19	-0.41552	-2.8788	0.002972
20	-0.441641	-3.0598	0.00181
21	-0.461235	-3.1955	0.001234
22	-0.469418	-3.2522	0.001049
23	-0.472063	-3.2705	0.000995
24	-0.456495	-3.1627	0.001355
25	-0.427759	-2.9636	0.002361
26	-0.380564	-2.6366	0.005624
27	-0.344549	-2.3871	0.010484
28	-0.293736	-2.0351	0.023693
29	-0.229256	-1.5883	0.059389
30	-0.171108	-1.1855	0.120833
31	-0.12169	-0.8431	0.201679
32	-0.074272	-0.5146	0.304607
33	-0.029872	-0.207	0.41846
34	0.007909	0.0548	0.478265
35	0.051645	0.3578	0.361028
36	0.083806	0.5806	0.282106

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.939418	6.5085	0
2	-0.139099	-0.9637	0.170012
3	-0.13876	-0.9614	0.170595
4	-0.145869	-1.0106	0.158635
5	-0.124366	-0.8616	0.196587
6	-0.064016	-0.4435	0.329693
7	-0.084492	-0.5854	0.280517
8	-0.049031	-0.3397	0.367785
9	0.015184	0.1052	0.45833
10	0.020034	0.1388	0.445096
11	0.014896	0.1032	0.459116
12	-0.135882	-0.9414	0.175602
13	0.067885	0.4703	0.320128
14	-0.045739	-0.3169	0.376351
15	-0.111424	-0.772	0.221959
16	-0.17166	-1.1893	0.120086
17	-0.116362	-0.8062	0.212058
18	0.083729	0.5801	0.282283
19	-0.041839	-0.2899	0.386581
20	-0.040667	-0.2818	0.389673
21	-0.033296	-0.2307	0.409272
22	0.021303	0.1476	0.44164
23	-0.020467	-0.1418	0.443916
24	0.022452	0.1556	0.438519
25	0.015747	0.1091	0.45679
26	0.100997	0.6997	0.243738
27	-0.182349	-1.2633	0.106283
28	0.063113	0.4373	0.331942
29	0.056784	0.3934	0.34788
30	-0.035842	-0.2483	0.402472
31	-0.078455	-0.5436	0.294632
32	-0.024521	-0.1699	0.432908
33	0.004534	0.0314	0.487536
34	-0.001153	-0.008	0.49683
35	0.092721	0.6424	0.261838
36	-0.067979	-0.471	0.319897

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259347319cepjmw5pnuatfwi/1fsgj1259347263.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259347319cepjmw5pnuatfwi/1fsgj1259347263.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259347319cepjmw5pnuatfwi/278no1259347263.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259347319cepjmw5pnuatfwi/278no1259347263.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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