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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, 19 Dec 2009 08:26:00 -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/19/t12612364037fdv5xjdviict69.htm/, Retrieved Sat, 19 Dec 2009 16:26:45 +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/19/t12612364037fdv5xjdviict69.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 «

1920 2218 3032 2375 2446 2916 2434 2540 2349 2310 2189 2660 2194 2419 2742 2137 2710 2173 2363 2126 1905 2121 1983 1734 2074 2049 2406 2558 2251 2059 2397 1747 1707 2319 1631 1627 1791 2034 1997 2169 2028 2253 2218 1855 2187 1852 1570 1851 1954 1828 2251 2277 2085 2282 2266 1878 2267 2069 1746 2299 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 2526 2440 2191 2797 2074 2628 2287 2146 2430 2141 1827 2082 1788

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.416707	4.5838	6e-06
2	0.424565	4.6702	4e-06
3	0.477962	5.2576	0
4	0.241119	2.6523	0.004533
5	0.194864	2.1435	0.017037
6	0.207249	2.2797	0.012187
7	0.138723	1.526	0.064816
8	0.237475	2.6122	0.005068
9	0.318368	3.5021	0.000324
10	0.232301	2.5553	0.005924
11	0.313637	3.45	0.000386
12	0.389021	4.2792	1.9e-05
13	0.203178	2.235	0.013628
14	0.209239	2.3016	0.011533
15	0.180846	1.9893	0.024462
16	0.007659	0.0842	0.4665
17	0.022604	0.2486	0.402028
18	-0.080799	-0.8888	0.187941
19	-0.035392	-0.3893	0.348864
20	-0.029646	-0.3261	0.372453
21	0.065446	0.7199	0.236485
22	0.023898	0.2629	0.396548
23	0.114692	1.2616	0.104757
24	0.106962	1.1766	0.120836
25	0.048446	0.5329	0.297539
26	-0.04764	-0.524	0.300604
27	-0.123518	-1.3587	0.088384
28	-0.159106	-1.7502	0.041312
29	-0.246494	-2.7114	0.003837
30	-0.285344	-3.1388	0.001066
31	-0.26617	-2.9279	0.002039
32	-0.170985	-1.8808	0.031199
33	-0.194905	-2.144	0.017019
34	-0.19687	-2.1656	0.016153
35	-0.151113	-1.6622	0.049526
36	-0.104358	-1.1479	0.126628

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.416707	4.5838	6e-06
2	0.303648	3.3401	0.000557
3	0.304243	3.3467	0.000545
4	-0.105232	-1.1576	0.124663
5	-0.101713	-1.1188	0.132712
6	0.014095	0.155	0.438521
7	0.054813	0.6029	0.273836
8	0.210966	2.3206	0.010991
9	0.238157	2.6197	0.004963
10	-0.001449	-0.0159	0.493653
11	0.00398	0.0438	0.482576
12	0.12255	1.3481	0.09008
13	-0.0857	-0.9427	0.173856
14	-0.067642	-0.7441	0.229142
15	-0.051563	-0.5672	0.285817
16	-0.138948	-1.5284	0.064508
17	-0.076024	-0.8363	0.202326
18	-0.179074	-1.9698	0.025572
19	0.054356	0.5979	0.275505
20	-0.037786	-0.4156	0.339202
21	0.137544	1.513	0.066445
22	-0.024917	-0.2741	0.392244
23	0.036875	0.4056	0.342868
24	-0.033457	-0.368	0.356748
25	0.019154	0.2107	0.416738
26	-0.152614	-1.6788	0.04789
27	-0.144542	-1.59	0.057226
28	-0.0263	-0.2893	0.386422
29	-0.069912	-0.769	0.221686
30	-0.065743	-0.7232	0.235485
31	-0.092031	-1.0123	0.156698
32	0.098039	1.0784	0.141494
33	-0.057248	-0.6297	0.265031
34	-0.118874	-1.3076	0.096741
35	-0.091568	-1.0073	0.157912
36	0.05329	0.5862	0.279421

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/19/t12612364037fdv5xjdviict69/1gs8h1261236354.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t12612364037fdv5xjdviict69/1gs8h1261236354.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t12612364037fdv5xjdviict69/2mfj61261236354.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t12612364037fdv5xjdviict69/2mfj61261236354.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; 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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