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Partial autocorrelation function 2 Paper

*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: Sun, 20 Dec 2009 10:18:56 -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/20/t12613299975ywgjderognedfk.htm/, Retrieved Sun, 20 Dec 2009 18:26:39 +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/20/t12613299975ywgjderognedfk.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 «

-1.2 -2.4 0.8 -0.1 -1.5 -4.4 -4.2 3.5 10 8.6 9.5 9.9 10.4 16 12.7 10.2 8.9 12.6 13.6 14.8 9.5 13.7 17 14.7 17.4 9 9.1 12.2 15.9 12.9 10.9 10.6 13.2 9.6 6.4 5.8 -1 -0.2 2.7 3.6 -0.9 0.3 -1.1 -2.5 -3.4 -3.5 -3.9 -4.6 -0.1 4.3 10.2 8.7 13.3 15 20.7 20.7 26.4 31.2 31.4 26.6 26.6 19.2 6.5 3.1 -0.2 -4 -12.6 -13 -17.6 -21.7 -23.2 -16.8 -19.8

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	0.228661	1.9403	0.028133
2	0.131458	1.1155	0.134181
3	0.120377	1.0214	0.155235
4	0.260462	2.2101	0.015139
5	0.081838	0.6944	0.244827
6	0.097512	0.8274	0.205367
7	-0.029539	-0.2506	0.401401
8	-0.147211	-1.2491	0.107832
9	-0.133764	-1.135	0.130064
10	-0.061526	-0.5221	0.301612
11	0.119211	1.0115	0.157573
12	-0.441471	-3.746	0.00018
13	-0.222294	-1.8862	0.031649
14	-0.136375	-1.1572	0.125512
15	0.026009	0.2207	0.412979
16	-0.15917	-1.3506	0.090527
17	-0.076853	-0.6521	0.2582
18	-0.172141	-1.4607	0.074229
19	0.023021	0.1953	0.422839
20	0.001342	0.0114	0.495472
21	0.001288	0.0109	0.495655
22	0.072126	0.612	0.27123
23	-0.155085	-1.3159	0.096184
24	-0.037995	-0.3224	0.374044
25	0.041953	0.356	0.361446
26	0.146243	1.2409	0.109332
27	-0.071515	-0.6068	0.272939
28	0.055048	0.4671	0.320919
29	0.009131	0.0775	0.469227
30	0.097457	0.8269	0.205499
31	0.010345	0.0878	0.465149
32	0.0664	0.5634	0.287448
33	0.068707	0.583	0.280857
34	-0.088951	-0.7548	0.226423
35	-0.001946	-0.0165	0.493436
36	0.090596	0.7687	0.222283

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.228661	1.9403	0.028133
2	0.08354	0.7089	0.240349
3	0.07834	0.6647	0.254171
4	0.223758	1.8987	0.030809
5	-0.031781	-0.2697	0.394092
6	0.045993	0.3903	0.348748
7	-0.105069	-0.8915	0.187804
8	-0.217086	-1.842	0.034794
9	-0.094711	-0.8037	0.212122
10	-0.030664	-0.2602	0.397728
11	0.242055	2.0539	0.021809
12	-0.485664	-4.121	5e-05
13	0.03871	0.3285	0.371755
14	-0.02101	-0.1783	0.429504
15	0.079465	0.6743	0.251146
16	0.01707	0.1448	0.44262
17	-0.105567	-0.8958	0.186682
18	-0.01872	-0.1588	0.43712
19	0.107243	0.91	0.182933
20	-0.073082	-0.6201	0.268566
21	-0.122393	-1.0385	0.151246
22	0.066335	0.5629	0.287635
23	-0.031857	-0.2703	0.393846
24	-0.205571	-1.7443	0.042685
25	0.006389	0.0542	0.478457
26	0.061527	0.5221	0.30161
27	0.029401	0.2495	0.40185
28	0.07724	0.6554	0.257148
29	-0.029878	-0.2535	0.400294
30	-0.120587	-1.0232	0.154816
31	0.119742	1.016	0.156505
32	-0.000715	-0.0061	0.497586
33	-0.054737	-0.4645	0.32186
34	-0.080145	-0.6801	0.249325
35	0.00215	0.0182	0.492749
36	0.009473	0.0804	0.46808

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/20/t12613299975ywgjderognedfk/1j7u51261329534.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t12613299975ywgjderognedfk/1j7u51261329534.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t12613299975ywgjderognedfk/2kow41261329534.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t12613299975ywgjderognedfk/2kow41261329534.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; 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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