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Workshop 9

*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, 14 Dec 2010 13:09:27 +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/14/t12923320828lhallxvd63ib1l.htm/, Retrieved Tue, 14 Dec 2010 14:08:04 +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/14/t12923320828lhallxvd63ib1l.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 «

921365 987921 1132614 1332224 1418133 1411549 1695920 1636173 1539653 1395314 1127575 1036076 989236 1008380 1207763 1368839 1469798 1498721 1761769 1653214 1599104 1421179 1163995 1037735 1015407 1039210 1258049 1469445 1552346 1549144 1785895 1662335 1629440 1467430 1202209 1076982 1039367 1063449 1335135 1491602 1591972 1641248 1898849 1798580 1762444 1622044 1368955 1262973 1195650 1269530 1479279 1607819 1712466 1721766 1949843 1821326 1757802 1590367 1260647 1149235 1016367 1027885 1262159 1520854 1544144 1564709 1821776 1741365 1623386 1498658 1241822 1136029

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.117342	-0.9013	0.185542
2	-0.034053	-0.2616	0.397284
3	0.16125	1.2386	0.110202
4	0.212291	1.6306	0.054147
5	-0.152159	-1.1688	0.123602
6	0.050741	0.3897	0.349063
7	0.089492	0.6874	0.247261
8	0.059876	0.4599	0.323633
9	-0.220189	-1.6913	0.048028
10	-0.023456	-0.1802	0.428818
11	0.014281	0.1097	0.456513
12	-0.27455	-2.1089	0.019606
13	-0.165833	-1.2738	0.103867
14	0.038671	0.297	0.383739
15	-0.186019	-1.4288	0.079162
16	-0.014886	-0.1143	0.454677
17	-0.098537	-0.7569	0.226069
18	0.049213	0.378	0.353388
19	-0.161144	-1.2378	0.110352
20	-0.02998	-0.2303	0.409336
21	0.12517	0.9614	0.170126
22	0.047644	0.366	0.357852
23	-0.08959	-0.6882	0.247027
24	0.01367	0.105	0.458366
25	0.141688	1.0883	0.140438
26	-0.053143	-0.4082	0.342303
27	0.023124	0.1776	0.429815
28	-0.033387	-0.2565	0.399247
29	0.15378	1.1812	0.121131
30	-0.028216	-0.2167	0.414584
31	-0.016151	-0.1241	0.450846
32	0.057267	0.4399	0.330818
33	-0.061959	-0.4759	0.317947
34	-0.130123	-0.9995	0.160819
35	0.095324	0.7322	0.233473
36	-0.014649	-0.1125	0.455395
37	0.024099	0.1851	0.426889
38	0.023716	0.1822	0.42804
39	0.053565	0.4114	0.341119
40	-0.047611	-0.3657	0.357946
41	-0.03062	-0.2352	0.407435
42	-0.0016	-0.0123	0.495118
43	0.135573	1.0414	0.150979
44	-0.178365	-1.37	0.087932
45	0.107134	0.8229	0.206937
46	0.048568	0.3731	0.355223
47	-0.018567	-0.1426	0.443541
48	-0.07733	-0.594	0.277397
49	0.119635	0.9189	0.180937
50	-0.068813	-0.5286	0.299546
51	-0.020341	-0.1562	0.438187
52	-0.018277	-0.1404	0.444415
53	0.06861	0.527	0.300082
54	-0.055679	-0.4277	0.33522
55	0.023349	0.1793	0.429139
56	0.019271	0.148	0.441415
57	-0.031124	-0.2391	0.405939
58	-0.003311	-0.0254	0.489899
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.117342	-0.9013	0.185542
2	-0.048489	-0.3725	0.355445
3	0.153846	1.1817	0.121031
4	0.258137	1.9828	0.026027
5	-0.088234	-0.6777	0.250293
6	0.000515	0.004	0.49843
7	0.01619	0.1244	0.450727
8	0.071866	0.552	0.291513
9	-0.177181	-1.361	0.089352
10	-0.136605	-1.0493	0.149163
11	-0.054265	-0.4168	0.339162
12	-0.266628	-2.048	0.022509
13	-0.162514	-1.2483	0.108428
14	-0.044493	-0.3418	0.366873
15	-0.147206	-1.1307	0.131376
16	0.127635	0.9804	0.165451
17	-0.049731	-0.382	0.351921
18	0.083261	0.6395	0.262473
19	-0.08884	-0.6824	0.248831
20	-0.054717	-0.4203	0.3379
21	0.120361	0.9245	0.179494
22	-0.005643	-0.0433	0.482787
23	-0.022278	-0.1711	0.432358
24	-0.24055	-1.8477	0.03483
25	-0.03247	-0.2494	0.401956
26	-0.09209	-0.7074	0.241065
27	-0.045176	-0.347	0.364912
28	-0.144821	-1.1124	0.135241
29	0.010478	0.0805	0.468062
30	0.06271	0.4817	0.315906
31	0.007859	0.0604	0.476035
32	0.002067	0.0159	0.493694
33	-0.11886	-0.913	0.182484
34	-0.168133	-1.2915	0.100791
35	0.048524	0.3727	0.355346
36	-0.094755	-0.7278	0.234798
37	0.046783	0.3593	0.360309
38	0.00397	0.0305	0.487888
39	0.022975	0.1765	0.430264
40	0.01757	0.135	0.446553
41	-0.106729	-0.8198	0.207816
42	-0.012544	-0.0964	0.461784
43	-0.028669	-0.2202	0.413234
44	-0.120529	-0.9258	0.179161
45	-0.015058	-0.1157	0.454156
46	-0.133177	-1.023	0.155253
47	-0.050312	-0.3865	0.350275
48	-0.072012	-0.5531	0.291132
49	0.136365	1.0474	0.149584
50	-0.00356	-0.0273	0.489138
51	-0.05366	-0.4122	0.340854
52	0.015221	0.1169	0.453663
53	-0.065529	-0.5033	0.308302
54	0.027295	0.2097	0.417328
55	0.048188	0.3701	0.356303
56	-0.068825	-0.5287	0.299513
57	-0.102444	-0.7869	0.217248
58	-0.017873	-0.1373	0.445638
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/14/t12923320828lhallxvd63ib1l/1f69l1292332165.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t12923320828lhallxvd63ib1l/1f69l1292332165.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t12923320828lhallxvd63ib1l/2f69l1292332165.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t12923320828lhallxvd63ib1l/2f69l1292332165.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 = 1 ; par4 = 1 ; 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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