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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, 16 Dec 2010 00:38:04 +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/Dec/16/t12924598198iocrlyb2qrrjik.htm/, Retrieved Thu, 16 Dec 2010 01:37:02 +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/Dec/16/t12924598198iocrlyb2qrrjik.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

46 62 66 59 58 61 41 27 58 70 49 59 44 36 72 45 56 54 53 35 61 52 47 51 52 63 74 45 51 64 36 30 55 64 39 40 63 45 59 55 40 64 27 28 45 57 45 69 60 56 58 50 51 53 37 22 55 70 62 58 39 49 58 47 42 62 39 40 72 70 54 65

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.32741	-2.7588	0.003687
2	-0.339512	-2.8608	0.002773
3	0.275033	2.3175	0.011683
4	-0.054891	-0.4625	0.32256
5	-0.18859	-1.5891	0.058242
6	0.222618	1.8758	0.032396
7	-0.109603	-0.9235	0.179429
8	-0.059735	-0.5033	0.308144
9	0.214504	1.8074	0.037465
10	-0.24925	-2.1002	0.019631
11	-0.056729	-0.478	0.317057
12	0.444788	3.7479	0.00018
13	-0.152034	-1.2811	0.10217
14	-0.297798	-2.5093	0.00719
15	0.282335	2.379	0.010026
16	-0.052136	-0.4393	0.330886
17	-0.157278	-1.3252	0.094669
18	0.189864	1.5998	0.05704
19	-0.15344	-1.2929	0.100117
20	-0.014846	-0.1251	0.450401
21	0.224664	1.8931	0.031213
22	-0.205014	-1.7275	0.044215
23	-0.10795	-0.9096	0.183056
24	0.372176	3.136	0.001246
25	-0.019654	-0.1656	0.434468
26	-0.366215	-3.0858	0.001447
27	0.290419	2.4471	0.008439
28	-0.076406	-0.6438	0.260887
29	-0.119623	-1.008	0.158448
30	0.123942	1.0444	0.149932
31	-0.06101	-0.5141	0.304396
32	0.009602	0.0809	0.467871
33	0.171011	1.441	0.076996
34	-0.229717	-1.9356	0.028448
35	-0.071036	-0.5986	0.275686
36	0.306948	2.5864	0.005875
37	-0.082618	-0.6961	0.244304
38	-0.169543	-1.4286	0.078752
39	0.161195	1.3583	0.089342
40	-0.01462	-0.1232	0.451152
41	-0.173242	-1.4598	0.074382
42	0.108109	0.9109	0.182704
43	0.0486	0.4095	0.341697
44	-0.064545	-0.5439	0.29412
45	0.095871	0.8078	0.210945
46	-0.138276	-1.1651	0.123932
47	-0.007085	-0.0597	0.476281
48	0.18788	1.5831	0.058921

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.32741	-2.7588	0.003687
2	-0.500345	-4.216	3.6e-05
3	-0.083018	-0.6995	0.243257
4	-0.179429	-1.5119	0.067499
5	-0.252623	-2.1286	0.018377
6	-0.039617	-0.3338	0.369751
7	-0.229299	-1.9321	0.028669
8	-0.137548	-1.159	0.12517
9	0.013229	0.1115	0.455778
10	-0.301959	-2.5443	0.006562
11	-0.312158	-2.6303	0.005227
12	0.099002	0.8342	0.203481
13	0.141095	1.1889	0.119223
14	-0.041969	-0.3536	0.36233
15	0.061064	0.5145	0.304238
16	0.036268	0.3056	0.380402
17	0.055803	0.4702	0.319824
18	0.108037	0.9103	0.182864
19	-0.132943	-1.1202	0.133202
20	-0.072079	-0.6073	0.272779
21	0.017032	0.1435	0.443145
22	-0.044362	-0.3738	0.354832
23	-0.203541	-1.7151	0.045347
24	-0.118847	-1.0014	0.160011
25	0.210781	1.7761	0.040003
26	-0.025928	-0.2185	0.413842
27	0.143838	1.212	0.114765
28	-0.063739	-0.5371	0.296448
29	0.082273	0.6932	0.24521
30	0.04866	0.41	0.341515
31	-0.002201	-0.0185	0.492627
32	0.118033	0.9946	0.161663
33	0.068602	0.578	0.282531
34	0.033715	0.2841	0.388586
35	-0.051664	-0.4353	0.332322
36	-0.146326	-1.233	0.110827
37	-0.117336	-0.9887	0.163086
38	-0.030434	-0.2564	0.399177
39	-0.008243	-0.0695	0.472409
40	-0.013857	-0.1168	0.453688
41	-0.094517	-0.7964	0.214223
42	-0.136561	-1.1507	0.126862
43	0.072287	0.6091	0.2722
44	0.028182	0.2375	0.40649
45	-0.091335	-0.7696	0.222044
46	-0.099954	-0.8422	0.201244
47	0.01775	0.1496	0.440767
48	0.012505	0.1054	0.458191

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/16/t12924598198iocrlyb2qrrjik/1dcje1292459882.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12924598198iocrlyb2qrrjik/1dcje1292459882.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12924598198iocrlyb2qrrjik/26l0h1292459882.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12924598198iocrlyb2qrrjik/26l0h1292459882.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12924598198iocrlyb2qrrjik/36l0h1292459882.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12924598198iocrlyb2qrrjik/36l0h1292459882.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; 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 (par8 != '') par8 <- as.numeric(par8)

ox <- x

if (par8 == '') {

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

} else {

x <- log(x,base=par8)

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='picts.png')

op <- par(mfrow=c(2,1))

plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')

if (par8=='') {

mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

} else {

mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

}

plot(x,type='l', main=mytitle,xlab='time',ylab='value')

par(op)

dev.off()

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)

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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