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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: Sat, 12 Dec 2009 13:14:07 -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/12/t12606488832a20tzu1hzu41hl.htm/, Retrieved Sat, 12 Dec 2009 21:14:46 +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/12/t12606488832a20tzu1hzu41hl.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 «

2360 2214 2825 2355 2333 3016 2155 2172 2150 2533 2058 2160 2260 2498 2695 2799 2947 2930 2318 2540 2570 2669 2450 2842 3440 2678 2981 2260 2844 2546 2456 2295 2379 2479 2057 2280 2351 2276 2548 2311 2201 2725 2408 2139 1898 2537 2069 2063 2524 2437 2189 2793 2074 2622 2278 2144 2427 2139 1828 2072 1800

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	-0.538541	-4.1715	4.9e-05
2	0.0451	0.3493	0.364027
3	0.086728	0.6718	0.252146
4	-0.006796	-0.0526	0.479095
5	-0.0403	-0.3122	0.377998
6	-0.080418	-0.6229	0.267851
7	0.018719	0.145	0.442601
8	0.046386	0.3593	0.360315
9	0.00076	0.0059	0.497661
10	0.002302	0.0178	0.492916
11	-0.081676	-0.6327	0.264681
12	0.170547	1.3211	0.09575
13	-0.09019	-0.6986	0.243749
14	-0.082797	-0.6413	0.261871
15	0.172533	1.3364	0.093227
16	-0.147621	-1.1435	0.128694
17	0.068451	0.5302	0.298959
18	-0.095455	-0.7394	0.231275
19	0.162038	1.2551	0.107147
20	-0.232192	-1.7986	0.03856
21	0.195597	1.5151	0.0675
22	-0.079925	-0.6191	0.269099
23	-0.039571	-0.3065	0.380135
24	0.057134	0.4426	0.329837
25	0.048624	0.3766	0.353884
26	-0.080055	-0.6201	0.268769
27	0.06046	0.4683	0.320627
28	0.026692	0.2068	0.41845
29	-0.052377	-0.4057	0.343198
30	0.008288	0.0642	0.474513
31	-0.025757	-0.1995	0.421267
32	0.007687	0.0595	0.476359
33	0.051473	0.3987	0.345761
34	-0.003926	-0.0304	0.487919
35	-0.126032	-0.9762	0.166432
36	0.173993	1.3477	0.091404

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.538541	-4.1715	4.9e-05
2	-0.34498	-2.6722	0.004844
3	-0.106143	-0.8222	0.207114
4	0.034058	0.2638	0.396413
5	0.01919	0.1486	0.441166
6	-0.160815	-1.2457	0.108864
7	-0.2313	-1.7916	0.039117
8	-0.121276	-0.9394	0.175647
9	0.032878	0.2547	0.399923
10	0.109249	0.8462	0.200391
11	-0.092701	-0.7181	0.237754
12	0.013982	0.1083	0.457057
13	0.022284	0.1726	0.431768
14	-0.087985	-0.6815	0.24908
15	0.105458	0.8169	0.208615
16	-0.012722	-0.0985	0.460914
17	-0.003269	-0.0253	0.48994
18	-0.14391	-1.1147	0.134707
19	0.08232	0.6376	0.263064
20	-0.178603	-1.3835	0.085826
21	0.006138	0.0475	0.481117
22	-0.0274	-0.2122	0.41632
23	-0.090534	-0.7013	0.242922
24	-0.106542	-0.8253	0.206244
25	0.056764	0.4397	0.330871
26	0.04973	0.3852	0.350723
27	0.015118	0.1171	0.453583
28	0.112615	0.8723	0.193257
29	0.021265	0.1647	0.43486
30	0.005909	0.0458	0.481823
31	-0.070352	-0.5449	0.293905
32	0.012275	0.0951	0.462284
33	0.107736	0.8345	0.20365
34	0.116108	0.8994	0.186026
35	-0.050511	-0.3913	0.348495
36	-0.078669	-0.6094	0.272291

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/12/t12606488832a20tzu1hzu41hl/150421260648846.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/12/t12606488832a20tzu1hzu41hl/150421260648846.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/12/t12606488832a20tzu1hzu41hl/2553u1260648846.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/12/t12606488832a20tzu1hzu41hl/2553u1260648846.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 2 ; par3 = 2 ; par4 = 12 ;

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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