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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: Tue, 24 Nov 2009 02:55:25 -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/24/t1259056573w82a0pmcje796lj.htm/, Retrieved Tue, 24 Nov 2009 10:56:15 +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/24/t1259056573w82a0pmcje796lj.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 «

95.1 97 112.7 102.9 97.4 111.4 87.4 96.8 114.1 110.3 103.9 101.6 94.6 95.9 104.7 102.8 98.1 113.9 80.9 95.7 113.2 105.9 108.8 102.3 99 100.7 115.5 100.7 109.9 114.6 85.4 100.5 114.8 116.5 112.9 102 106 105.3 118.8 106.1 109.3 117.2 92.5 104.2 112.5 122.4 113.3 100 110.7 112.8 109.8 117.3 109.1 115.9 96

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	0.058742	0.4356	0.3324
2	-0.134354	-0.9964	0.161712
3	0.085258	0.6323	0.264908
4	-0.056039	-0.4156	0.339662
5	0.221825	1.6451	0.052826
6	0.35661	2.6447	0.005318
7	0.209519	1.5538	0.06298
8	-0.057774	-0.4285	0.334995
9	-0.016197	-0.1201	0.452414
10	-0.188239	-1.396	0.08416
11	0.042587	0.3158	0.376661
12	0.666786	4.945	4e-06
13	-0.001022	-0.0076	0.496989
14	-0.143694	-1.0657	0.145617
15	-0.001791	-0.0133	0.494727
16	-0.15062	-1.117	0.134419
17	0.150098	1.1132	0.135241
18	0.187929	1.3937	0.084505
19	0.048355	0.3586	0.36063
20	-0.133162	-0.9876	0.163847
21	-0.098185	-0.7282	0.234803
22	-0.261627	-1.9403	0.02874
23	-0.015781	-0.117	0.453629
24	0.335895	2.4911	0.007891
25	-0.093634	-0.6944	0.245173
26	-0.152835	-1.1335	0.13097
27	-0.122431	-0.908	0.183926
28	-0.166687	-1.2362	0.110822
29	0.032809	0.2433	0.404331
30	0.033163	0.2459	0.40332
31	-0.013732	-0.1018	0.459626
32	-0.158806	-1.1777	0.121987
33	-0.158583	-1.1761	0.122313
34	-0.175952	-1.3049	0.098681
35	-0.080083	-0.5939	0.277504
36	0.151142	1.1209	0.1336

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.058742	0.4356	0.3324
2	-0.138281	-1.0255	0.154803
3	0.104722	0.7766	0.22035
4	-0.091692	-0.68	0.249678
5	0.272157	2.0184	0.02422
6	0.310289	2.3012	0.012598
7	0.319975	2.373	0.010583
8	0.002994	0.0222	0.491183
9	0.051269	0.3802	0.352624
10	-0.371353	-2.754	0.003982
11	-0.165892	-1.2303	0.111913
12	0.501566	3.7197	0.000235
13	-0.046887	-0.3477	0.364689
14	-0.01146	-0.085	0.466288
15	-0.073318	-0.5437	0.294409
16	-0.051157	-0.3794	0.352929
17	0.016488	0.1223	0.451563
18	-0.204355	-1.5155	0.067682
19	-0.211457	-1.5682	0.061284
20	-0.196965	-1.4607	0.074889
21	0.014359	0.1065	0.457791
22	-0.044567	-0.3305	0.371133
23	0.059861	0.4439	0.329414
24	-0.130728	-0.9695	0.168269
25	0.070779	0.5249	0.300877
26	0.082028	0.6083	0.272736
27	0.005458	0.0405	0.483929
28	0.040711	0.3019	0.381926
29	-0.172366	-1.2783	0.103256
30	-0.121524	-0.9012	0.185693
31	0.014779	0.1096	0.456561
32	-0.034834	-0.2583	0.398556
33	-0.068803	-0.5103	0.305958
34	0.159849	1.1855	0.120464
35	-0.023984	-0.1779	0.429739
36	0.13316	0.9875	0.163851

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259056573w82a0pmcje796lj/1d03m1259056523.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259056573w82a0pmcje796lj/1d03m1259056523.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259056573w82a0pmcje796lj/26uz91259056523.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259056573w82a0pmcje796lj/26uz91259056523.ps (open in new window)

Parameters (Session):

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