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Time Series Analysis Champagne

*Unverified author*

R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Sun, 16 May 2010 10:53:21 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/May/16/t12740072453u3p5mtslh9zvkx.htm/, Retrieved Sun, 16 May 2010 12:54:06 +0200

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/2010/May/16/t12740072453u3p5mtslh9zvkx.htm/},
    year = {2010},
}
@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 = {2010},
    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:

KDGP2W21

Dataseries X:

» Textbox « » Textfile « » CSV «

2851 2672 2755 2721 2946 3036 2282 2212 2922 4301 5764 7132 2541 2475 3031 3266 3776 3230 3028 1759 3595 4474 6838 8357 3113 3006 4047 3523 3937 3986 3260 1573 3528 5211 7614 9254 5375 3088 3718 4514 4520 4539 3663 1643 4739 5428 8314 10651 3633 4292 4154 4121 4647 4753 3965 1723 5048 6922 9858 11331 4016 3975 4510 4276 4968 4677 3523 1821 5222 6873 10803 13916 2639 2899 3370 3740 2927 3986 4217 1738 5221 6424 9842 13076 3934 3162 4286 4676 5010 4874 4633 1659 5951 6981 9851 12670

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.481567	4.7184	4e-06
2	0.05012	0.4911	0.312248
3	-0.158617	-1.5541	0.061723
4	-0.253133	-2.4802	0.007436
5	-0.024492	-0.24	0.405433
6	0.052373	0.5131	0.304513
7	-0.024635	-0.2414	0.404892
8	-0.251627	-2.4654	0.00773
9	-0.176523	-1.7296	0.043461
10	0.005742	0.0563	0.477624
11	0.390302	3.8242	0.000117
12	0.838362	8.2142	0
13	0.40734	3.9911	6.4e-05
14	0.010173	0.0997	0.460404
15	-0.180952	-1.773	0.039703
16	-0.257264	-2.5207	0.006681
17	-0.057281	-0.5612	0.287973
18	0.015514	0.152	0.439752
19	-0.051372	-0.5033	0.307939
20	-0.248919	-2.4389	0.008285
21	-0.175524	-1.7198	0.044347
22	-0.019334	-0.1894	0.425078
23	0.300153	2.9409	0.002051
24	0.682281	6.685	0
25	0.319747	3.1329	0.001148
26	-0.01602	-0.157	0.437802
27	-0.185905	-1.8215	0.035823
28	-0.24073	-2.3587	0.010184
29	-0.067612	-0.6625	0.254633
30	0.00761	0.0746	0.470359
31	-0.038429	-0.3765	0.353678
32	-0.203697	-1.9958	0.024394
33	-0.15134	-1.4828	0.070698
34	-0.026724	-0.2618	0.397004
35	0.228618	2.24	0.013699
36	0.502449	4.923	2e-06
37	0.213006	2.087	0.019768
38	-0.04735	-0.4639	0.321875
39	-0.176382	-1.7282	0.043585
40	-0.219515	-2.1508	0.017001
41	-0.075436	-0.7391	0.230819
42	-0.014046	-0.1376	0.445413
43	-0.055749	-0.5462	0.29309
44	-0.179556	-1.7593	0.040857
45	-0.135778	-1.3303	0.093278
46	-0.043524	-0.4264	0.33537
47	0.158678	1.5547	0.061652
48	0.372464	3.6494	0.000214

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.481567	4.7184	4e-06
2	-0.236673	-2.3189	0.01126
3	-0.102737	-1.0066	0.158325
4	-0.145322	-1.4239	0.078864
5	0.221306	2.1683	0.016302
6	-0.108075	-1.0589	0.146147
7	-0.096159	-0.9422	0.174237
8	-0.318922	-3.1248	0.001177
9	0.248292	2.4328	0.008418
10	-0.020068	-0.1966	0.42227
11	0.542939	5.3197	0
12	0.610271	5.9794	0
13	-0.377396	-3.6977	0.000181
14	-0.05947	-0.5827	0.280735
15	0.026042	0.2552	0.399575
16	0.017385	0.1703	0.432553
17	-0.140858	-1.3801	0.085377
18	-0.056402	-0.5526	0.290901
19	0.015127	0.1482	0.441241
20	0.055545	0.5442	0.293774
21	0.015895	0.1557	0.438282
22	-0.046011	-0.4508	0.326571
23	-0.083463	-0.8178	0.207757
24	-0.00988	-0.0968	0.461542
25	-0.038717	-0.3793	0.352636
26	0.074539	0.7303	0.233484
27	-0.05142	-0.5038	0.307774
28	0.042718	0.4186	0.338239
29	-0.013085	-0.1282	0.449126
30	0.095761	0.9383	0.175233
31	0.022102	0.2166	0.414507
32	0.052526	0.5146	0.303991
33	-0.108933	-1.0673	0.144252
34	0.035673	0.3495	0.363731
35	-0.052616	-0.5155	0.303684
36	-0.214238	-2.0991	0.019216
37	0.010086	0.0988	0.460744
38	0.06735	0.6599	0.25545
39	0.049081	0.4809	0.315842
40	-0.095614	-0.9368	0.175601
41	0.019696	0.193	0.42369
42	-0.045594	-0.4467	0.32804
43	-0.057398	-0.5624	0.287584
44	-0.032147	-0.315	0.37673
45	-0.013765	-0.1349	0.446497
46	-0.077487	-0.7592	0.224792
47	0.020666	0.2025	0.419982
48	0.139342	1.3653	0.08768

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/16/t12740072453u3p5mtslh9zvkx/1p09u1274007197.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/16/t12740072453u3p5mtslh9zvkx/1p09u1274007197.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/16/t12740072453u3p5mtslh9zvkx/2p09u1274007197.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/16/t12740072453u3p5mtslh9zvkx/2p09u1274007197.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; 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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