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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 10:55:54 -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/t1259085383wspp7mw2d7xfc0o.htm/, Retrieved Tue, 24 Nov 2009 18:56:25 +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/t1259085383wspp7mw2d7xfc0o.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 «

8.9 8.8 8.3 7.5 7.2 7.4 8.8 9.3 9.3 8.7 8.2 8.3 8.5 8.6 8.5 8.2 8.1 7.9 8.6 8.7 8.7 8.5 8.4 8.5 8.7 8.7 8.6 8.5 8.3 8 8.2 8.1 8.1 8 7.9 7.9 8 8 7.9 8 7.7 7.2 7.5 7.3 7 7 7 7.2 7.3 7.1 6.8 6.4 6.1 6.5 7.7 7.9 7.5 6.9 6.6 6.9

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	0.842931	6.5293	0
2	0.585771	4.5374	1.4e-05
3	0.412013	3.1914	0.001127
4	0.422585	3.2733	0.000883
5	0.55374	4.2893	3.3e-05
6	0.654831	5.0723	2e-06
7	0.601042	4.6556	9e-06
8	0.466592	3.6142	0.000309
9	0.348155	2.6968	0.004537
10	0.305758	2.3684	0.010552
11	0.324061	2.5102	0.007391
12	0.338743	2.6239	0.005504
13	0.26755	2.0724	0.021265
14	0.180691	1.3996	0.083387
15	0.112525	0.8716	0.193447
16	0.08295	0.6425	0.261489
17	0.078879	0.611	0.271756
18	0.065911	0.5105	0.305771
19	-0.004955	-0.0384	0.484756
20	-0.075391	-0.584	0.280712
21	-0.123986	-0.9604	0.170357
22	-0.145645	-1.1282	0.131871
23	-0.141843	-1.0987	0.138142
24	-0.139553	-1.081	0.142017
25	-0.181726	-1.4076	0.082198
26	-0.218683	-1.6939	0.047734
27	-0.238768	-1.8495	0.034657
28	-0.238299	-1.8459	0.034924
29	-0.228054	-1.7665	0.041199
30	-0.227053	-1.7587	0.04186
31	-0.264092	-2.0457	0.022591
32	-0.303852	-2.3536	0.010942
33	-0.321176	-2.4878	0.007824
34	-0.303527	-2.3511	0.01101
35	-0.264098	-2.0457	0.022589
36	-0.238167	-1.8448	0.035
37	-0.265635	-2.0576	0.021991
38	-0.290055	-2.2468	0.014174
39	-0.279197	-2.1626	0.017282
40	-0.239133	-1.8523	0.03445
41	-0.197904	-1.533	0.065271
42	-0.194224	-1.5045	0.068855
43	-0.255969	-1.9827	0.025991
44	-0.298694	-2.3137	0.012064
45	-0.271822	-2.1055	0.01972
46	-0.176478	-1.367	0.088364
47	-0.074058	-0.5736	0.284174
48	-0.045857	-0.3552	0.361842
49	-0.118297	-0.9163	0.181582
50	-0.209206	-1.6205	0.055184
51	-0.229822	-1.7802	0.040054
52	-0.15039	-1.1649	0.124332
53	-0.028991	-0.2246	0.411542
54	0.045145	0.3497	0.363898
55	0.01463	0.1133	0.455077
56	-0.043188	-0.3345	0.369571
57	-0.078632	-0.6091	0.272385
58	-0.067406	-0.5221	0.301754
59	-0.030676	-0.2376	0.406495
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.842931	6.5293	0
2	-0.431	-3.3385	0.000726
3	0.291645	2.2591	0.013763
4	0.401172	3.1075	0.001441
5	0.207037	1.6037	0.057016
6	0.015926	0.1234	0.451117
7	-0.189985	-1.4716	0.073175
8	0.163068	1.2631	0.105716
9	-0.042184	-0.3268	0.372494
10	-0.131439	-1.0181	0.156354
11	-0.071287	-0.5522	0.291436
12	-0.045578	-0.353	0.362647
13	-0.241947	-1.8741	0.032893
14	0.113242	0.8772	0.191948
15	-0.101389	-0.7854	0.217668
16	-0.089678	-0.6946	0.244981
17	-0.006814	-0.0528	0.47904
18	-0.002855	-0.0221	0.491214
19	-0.130438	-1.0104	0.158188
20	0.037828	0.293	0.385262
21	-0.029544	-0.2288	0.409883
22	-0.058011	-0.4494	0.327398
23	0.046712	0.3618	0.359374
24	0.006633	0.0514	0.479598
25	-0.05723	-0.4433	0.32957
26	0.070427	0.5455	0.293708
27	0.038158	0.2956	0.384291
28	0.00382	0.0296	0.488248
29	-0.025715	-0.1992	0.421395
30	0.001516	0.0117	0.495334
31	-0.045408	-0.3517	0.363136
32	-0.111965	-0.8673	0.194624
33	0.020768	0.1609	0.43637
34	0.025114	0.1945	0.423209
35	-0.064844	-0.5023	0.308655
36	-0.035331	-0.2737	0.392639
37	-0.036716	-0.2844	0.388541
38	0.085992	0.6661	0.253952
39	0.070465	0.5458	0.293607
40	-0.048187	-0.3733	0.355136
41	-0.030233	-0.2342	0.40782
42	-0.052413	-0.406	0.343098
43	-0.151309	-1.172	0.122908
44	0.056003	0.4338	0.332996
45	0.050192	0.3888	0.349405
46	0.074878	0.58	0.282043
47	0.034283	0.2656	0.395746
48	-0.051837	-0.4015	0.34473
49	-0.001962	-0.0152	0.493963
50	-0.078747	-0.61	0.272092
51	0.011126	0.0862	0.465805
52	0.072519	0.5617	0.288195
53	-0.033216	-0.2573	0.398919
54	-0.010706	-0.0829	0.467091
55	0.007486	0.058	0.476976
56	0.097702	0.7568	0.226066
57	-0.123677	-0.958	0.170954
58	-0.103033	-0.7981	0.213982
59	-0.054717	-0.4238	0.336601
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259085383wspp7mw2d7xfc0o/1vlfr1259085353.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259085383wspp7mw2d7xfc0o/1vlfr1259085353.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259085383wspp7mw2d7xfc0o/2gzch1259085353.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259085383wspp7mw2d7xfc0o/2gzch1259085353.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; 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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