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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: Thu, 26 Nov 2009 08:03:09 -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/26/t12592479267xs8r8noh3w8zfl.htm/, Retrieved Thu, 26 Nov 2009 16:05:28 +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/26/t12592479267xs8r8noh3w8zfl.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 «

1.3 1.2 1.1 1.4 1.2 1.5 1.1 1.3 1.5 1.1 1.4 1.3 1.5 1.6 1.7 1.1 1.6 1.3 1.7 1.6 1.7 1.9 1.8 1.9 1.6 1.5 1.6 1.6 1.7 2 2 1.9 1.7 1.8 1.9 1.7 2 2.1 2.4 2.5 2.5 2.6 2.2 2.5 2.8 2.8 2.9 3 3.1 2.9 2.7 2.2 2.5 2.3 2.6 2.3 2.2 1.8 1.8

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	0.84915	6.5224	0
2	0.84021	6.4538	0
3	0.741089	5.6924	0
4	0.707773	5.4365	1e-06
5	0.674011	5.1772	1e-06
6	0.643147	4.9401	3e-06
7	0.594199	4.5641	1.3e-05
8	0.559464	4.2973	3.3e-05
9	0.515555	3.9601	0.000102
10	0.414543	3.1842	0.001159
11	0.35451	2.723	0.004247
12	0.23376	1.7955	0.038844
13	0.228041	1.7516	0.042518
14	0.170813	1.312	0.097294
15	0.181142	1.3914	0.084668
16	0.129955	0.9982	0.161128
17	0.089867	0.6903	0.246361
18	0.053683	0.4123	0.340791
19	-0.008872	-0.0681	0.472948
20	-0.035223	-0.2705	0.393841
21	-0.073314	-0.5631	0.287739
22	-0.080597	-0.6191	0.269123
23	-0.084471	-0.6488	0.259483
24	-0.089824	-0.6899	0.246466
25	-0.098009	-0.7528	0.227275
26	-0.127019	-0.9756	0.166611
27	-0.177438	-1.3629	0.089042
28	-0.228809	-1.7575	0.042009
29	-0.262136	-2.0135	0.024315
30	-0.27591	-2.1193	0.019142
31	-0.271531	-2.0857	0.020671
32	-0.298994	-2.2966	0.012604
33	-0.309566	-2.3778	0.010337
34	-0.337071	-2.5891	0.00605
35	-0.369728	-2.8399	0.003091
36	-0.377775	-2.9017	0.002605
37	-0.430106	-3.3037	0.000813
38	-0.422691	-3.2467	0.000963
39	-0.432426	-3.3215	0.00077
40	-0.393224	-3.0204	0.001864
41	-0.383747	-2.9476	0.002291
42	-0.355261	-2.7288	0.004181
43	-0.368872	-2.8334	0.003147
44	-0.349119	-2.6816	0.004743
45	-0.327249	-2.5136	0.007349
46	-0.300617	-2.3091	0.01223
47	-0.261062	-2.0053	0.024765
48	-0.228094	-1.752	0.042483

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.84915	6.5224	0
2	0.427163	3.2811	0.00087
3	-0.133022	-1.0218	0.155532
4	0.021703	0.1667	0.434086
5	0.152336	1.1701	0.12333
6	0.023044	0.177	0.430054
7	-0.113825	-0.8743	0.192748
8	0.00129	0.0099	0.496065
9	0.020059	0.1541	0.439038
10	-0.337911	-2.5955	0.005949
11	-0.124122	-0.9534	0.172139
12	-0.162143	-1.2454	0.108946
13	0.199209	1.5302	0.065662
14	0.054901	0.4217	0.337387
15	0.110568	0.8493	0.199576
16	-0.005176	-0.0398	0.484211
17	-0.105924	-0.8136	0.209569
18	0.07292	0.5601	0.288763
19	-0.105767	-0.8124	0.209911
20	0.006626	0.0509	0.479791
21	0.038791	0.298	0.383391
22	-0.048108	-0.3695	0.356531
23	0.016647	0.1279	0.449344
24	-0.139217	-1.0693	0.144635
25	0.134964	1.0367	0.152058
26	-0.092413	-0.7098	0.240301
27	-0.156256	-1.2002	0.117424
28	-0.160836	-1.2354	0.110788
29	-0.080107	-0.6153	0.270356
30	0.120759	0.9276	0.178706
31	-0.040561	-0.3116	0.37824
32	-0.069531	-0.5341	0.297647
33	-0.028875	-0.2218	0.412621
34	0.036864	0.2832	0.389025
35	-0.010865	-0.0835	0.466885
36	0.021488	0.1651	0.434732
37	-0.020205	-0.1552	0.438598
38	-0.009303	-0.0715	0.471637
39	-0.033614	-0.2582	0.398578
40	0.041598	0.3195	0.375231
41	0.019132	0.147	0.441835
42	0.147745	1.1348	0.130514
43	-0.049702	-0.3818	0.352002
44	-0.050812	-0.3903	0.348864
45	0.067881	0.5214	0.302017
46	0.029749	0.2285	0.410021
47	-0.003944	-0.0303	0.487967
48	-0.02451	-0.1883	0.425659

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592479267xs8r8noh3w8zfl/1ffmc1259247787.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592479267xs8r8noh3w8zfl/1ffmc1259247787.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592479267xs8r8noh3w8zfl/2cg0n1259247787.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592479267xs8r8noh3w8zfl/2cg0n1259247787.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 0.0 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 0.0 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; 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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