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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Tue, 23 Nov 2010 15:47:34 +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/Nov/23/t1290527161bhzfp6qiwsgdmns.htm/, Retrieved Tue, 23 Nov 2010 16:46:03 +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/2010/Nov/23/t1290527161bhzfp6qiwsgdmns.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:

KDGP2W12

Dataseries X:

» Textbox « » Textfile « » CSV «

98,6 100,1 98,8 98,3 102,8 103,6 105,2 100,1 98,2 98,4 97,4 98,4 100,3 101,1 104,1 107,3 110,1 112,6 114,3 115,3 109,9 108,2 103,2 101,8 105,6 108,2 109,8 114,6 117,2 116,5 116,1 112,1 106,8 106,9 104,5 103 105,9 107,7 107,1 112,5 114,5 114,6 113,1 112,8 111,9 112 112,4 110 112,3 109,6 111,9 110,8 110,4 110,8 114 108,4 110,5 105,1 102,3 104,3 103,4 102,4 104,5 107,3 110,1 111,8 111,8 105,7 106 106,4 107,1 111,5

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	0.845371	7.1732	0
2	0.663196	5.6274	0
3	0.436442	3.7033	0.000207
4	0.206746	1.7543	0.041817
5	0.080464	0.6828	0.248476
6	0.035488	0.3011	0.382094
7	0.035745	0.3033	0.381265
8	0.104155	0.8838	0.189878
9	0.205839	1.7466	0.042485
10	0.279456	2.3713	0.010203
11	0.308583	2.6184	0.005382
12	0.289491	2.4564	0.008223
13	0.188744	1.6015	0.056818
14	0.06049	0.5133	0.304666
15	-0.063412	-0.5381	0.296094
16	-0.20934	-1.7763	0.039953
17	-0.270849	-2.2982	0.012228
18	-0.279931	-2.3753	0.0101
19	-0.226501	-1.9219	0.029287
20	-0.107038	-0.9082	0.183389
21	-0.011537	-0.0979	0.461145
22	0.072068	0.6115	0.271392
23	0.133244	1.1306	0.130985
24	0.119782	1.0164	0.156425
25	0.08164	0.6927	0.245351
26	0.008658	0.0735	0.470821
27	-0.09037	-0.7668	0.222849
28	-0.17352	-1.4724	0.07264
29	-0.201106	-1.7064	0.046118
30	-0.229348	-1.9461	0.027774
31	-0.216316	-1.8355	0.035281
32	-0.178799	-1.5172	0.066802
33	-0.151175	-1.2828	0.101844
34	-0.09963	-0.8454	0.200347
35	-0.051527	-0.4372	0.33163
36	-0.084467	-0.7167	0.237931
37	-0.125747	-1.067	0.144768
38	-0.17754	-1.5065	0.06816
39	-0.253204	-2.1485	0.017519
40	-0.287299	-2.4378	0.008623
41	-0.294489	-2.4988	0.007372
42	-0.280965	-2.3841	0.00988
43	-0.250681	-2.1271	0.018419
44	-0.178371	-1.5135	0.067262
45	-0.117339	-0.9957	0.161376
46	-0.062494	-0.5303	0.298776
47	-0.012283	-0.1042	0.458639
48	-0.003181	-0.027	0.489269
49	0.007661	0.065	0.474174
50	0.011995	0.1018	0.459608
51	-0.003565	-0.0302	0.487976
52	-0.003283	-0.0279	0.488927
53	-0.00888	-0.0754	0.470072
54	-0.005932	-0.0503	0.479997
55	0.02023	0.1717	0.432094
56	0.023065	0.1957	0.422693
57	0.048981	0.4156	0.339463
58	0.057369	0.4868	0.313941
59	0.050916	0.432	0.333502
60	0.036414	0.309	0.379115

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.845371	7.1732	0
2	-0.180325	-1.5301	0.065186
3	-0.263926	-2.2395	0.014107
4	-0.15541	-1.3187	0.095725
5	0.2358	2.0008	0.024591
6	0.170689	1.4483	0.07593
7	-0.046161	-0.3917	0.348223
8	0.084075	0.7134	0.238953
9	0.191255	1.6229	0.054496
10	0.004783	0.0406	0.48387
11	-0.140689	-1.1938	0.118241
12	-0.028376	-0.2408	0.405205
13	-0.091738	-0.7784	0.219435
14	-0.074628	-0.6332	0.264291
15	-0.043132	-0.366	0.357723
16	-0.203087	-1.7233	0.044568
17	0.09451	0.8019	0.212612
18	0.03085	0.2618	0.397123
19	0.061079	0.5183	0.302928
20	0.063547	0.5392	0.2957
21	-0.110816	-0.9403	0.175103
22	0.076584	0.6498	0.258932
23	0.138692	1.1768	0.121567
24	-0.093813	-0.796	0.214317
25	-0.003201	-0.0272	0.489205
26	-0.012399	-0.1052	0.458253
27	-0.045734	-0.3881	0.349555
28	-0.048449	-0.4111	0.341109
29	0.024069	0.2042	0.419373
30	-0.195003	-1.6547	0.051174
31	-0.051757	-0.4392	0.330927
32	-0.067391	-0.5718	0.284609
33	-0.00714	-0.0606	0.475928
34	0.049141	0.417	0.33897
35	-0.026167	-0.222	0.412458
36	-0.189475	-1.6078	0.056133
37	-0.004694	-0.0398	0.484171
38	0.104825	0.8895	0.188357
39	-0.014166	-0.1202	0.452328
40	-0.082109	-0.6967	0.244111
41	0.016037	0.1361	0.446069
42	0.116294	0.9868	0.163527
43	-0.12116	-1.0281	0.153677
44	0.003601	0.0306	0.487855
45	0.062197	0.5278	0.299644
46	-0.039574	-0.3358	0.369001
47	0.031325	0.2658	0.395574
48	-0.036086	-0.3062	0.380169
49	0.032843	0.2787	0.390644
50	0.057979	0.492	0.312118
51	0.003257	0.0276	0.489014
52	-0.013872	-0.1177	0.453313
53	-0.014995	-0.1272	0.449553
54	-0.049816	-0.4227	0.336885
55	0.045242	0.3839	0.351095
56	-0.079796	-0.6771	0.250259
57	0.039792	0.3377	0.368305
58	-0.045505	-0.3861	0.350272
59	-0.057518	-0.4881	0.313495
60	-0.075502	-0.6407	0.261891

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290527161bhzfp6qiwsgdmns/158rx1290527252.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290527161bhzfp6qiwsgdmns/158rx1290527252.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290527161bhzfp6qiwsgdmns/258rx1290527252.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290527161bhzfp6qiwsgdmns/258rx1290527252.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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