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ACF (d=D=0)

*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: Sun, 20 Dec 2009 05:18:59 -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/Dec/20/t126131160826c0rjff2vrbo7n.htm/, Retrieved Sun, 20 Dec 2009 13:20:11 +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/Dec/20/t126131160826c0rjff2vrbo7n.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 «

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

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	0.802613	6.217	0
2	0.471165	3.6496	0.000276
3	0.07859	0.6088	0.272493
4	-0.290623	-2.2512	0.014026
5	-0.535233	-4.1459	5.4e-05
6	-0.614509	-4.76	6e-06
7	-0.51252	-3.97	9.7e-05
8	-0.251061	-1.9447	0.028251
9	0.104766	0.8115	0.21014
10	0.444977	3.4468	0.000521
11	0.665309	5.1535	2e-06
12	0.74526	5.7728	0
13	0.572052	4.4311	2e-05
14	0.294389	2.2803	0.013078
15	-0.023663	-0.1833	0.427594
16	-0.319515	-2.475	0.008084
17	-0.508492	-3.9388	0.000108
18	-0.557567	-4.3189	3e-05
19	-0.465414	-3.6051	0.000318
20	-0.254927	-1.9747	0.026457
21	0.031723	0.2457	0.403367
22	0.296265	2.2949	0.012627
23	0.458746	3.5534	0.000374
24	0.50991	3.9497	0.000104
25	0.371982	2.8814	0.002743
26	0.160733	1.245	0.108981
27	-0.069772	-0.5405	0.295443
28	-0.275695	-2.1355	0.018405
29	-0.400444	-3.1018	0.001465
30	-0.432586	-3.3508	0.000699
31	-0.360289	-2.7908	0.00352
32	-0.206805	-1.6019	0.057215
33	-0.001397	-0.0108	0.495702
34	0.18187	1.4088	0.082034
35	0.284787	2.206	0.015614
36	0.305292	2.3648	0.010646
37	0.198788	1.5398	0.064433
38	0.047604	0.3687	0.35681
39	-0.098457	-0.7626	0.224333
40	-0.223093	-1.7281	0.04456
41	-0.290964	-2.2538	0.013937
42	-0.298836	-2.3148	0.012032
43	-0.23865	-1.8486	0.034724
44	-0.14201	-1.1	0.137862
45	-0.017717	-0.1372	0.445654
46	0.08663	0.671	0.252387
47	0.130712	1.0125	0.157685
48	0.12771	0.9892	0.163259
49	0.058198	0.4508	0.32688
50	-0.023332	-0.1807	0.428595
51	-0.084592	-0.6552	0.257406
52	-0.128579	-0.996	0.161633
53	-0.13592	-1.0528	0.148319
54	-0.124928	-0.9677	0.168542
55	-0.087565	-0.6783	0.250102
56	-0.040606	-0.3145	0.377103
57	0.012473	0.0966	0.461676
58	0.04329	0.3353	0.369277
59	0.029929	0.2318	0.40873
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.802613	6.217	0
2	-0.486271	-3.7666	0.00019
3	-0.342966	-2.6566	0.005049
4	-0.248823	-1.9274	0.029336
5	-0.058897	-0.4562	0.324943
6	-0.0115	-0.0891	0.464657
7	0.09142	0.7081	0.240801
8	0.192044	1.4876	0.071051
9	0.253735	1.9654	0.027
10	0.179915	1.3936	0.084288
11	0.072981	0.5653	0.286986
12	0.205669	1.5931	0.058196
13	-0.315823	-2.4464	0.00869
14	0.140147	1.0856	0.141005
15	0.044497	0.3447	0.365772
16	-0.003473	-0.0269	0.489313
17	-0.037954	-0.294	0.384889
18	-0.066425	-0.5145	0.304389
19	-0.125317	-0.9707	0.167797
20	-0.119614	-0.9265	0.178943
21	0.003235	0.0251	0.490046
22	-0.062257	-0.4822	0.315694
23	-0.009249	-0.0716	0.471562
24	-0.008426	-0.0653	0.47409
25	-0.139931	-1.0839	0.141372
26	0.040002	0.3099	0.378872
27	0.049434	0.3829	0.351567
28	0.080343	0.6223	0.26804
29	0.045425	0.3519	0.363088
30	-0.033364	-0.2584	0.398476
31	-0.004646	-0.036	0.485705
32	-0.037339	-0.2892	0.386703
33	-0.008876	-0.0688	0.472709
34	-0.026453	-0.2049	0.419172
35	-0.009814	-0.076	0.469828
36	-0.079488	-0.6157	0.270207
37	-0.097873	-0.7581	0.225673
38	-0.070804	-0.5484	0.292709
39	0.009033	0.07	0.472225
40	0.001672	0.0129	0.494856
41	-0.000693	-0.0054	0.497866
42	-0.010247	-0.0794	0.468501
43	-0.011507	-0.0891	0.464636
44	-0.085465	-0.662	0.255249
45	-0.022487	-0.1742	0.431153
46	0.004172	0.0323	0.487163
47	-0.015826	-0.1226	0.451421
48	-0.011646	-0.0902	0.464212
49	-0.013623	-0.1055	0.458155
50	-0.01685	-0.1305	0.448297
51	0.008229	0.0637	0.474694
52	0.02089	0.1618	0.435998
53	0.058607	0.454	0.325744
54	-0.001939	-0.015	0.494032
55	-0.00685	-0.0531	0.478931
56	0.012606	0.0976	0.461269
57	-0.009768	-0.0757	0.469971
58	-0.026475	-0.2051	0.419103
59	-0.043088	-0.3338	0.369862
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/20/t126131160826c0rjff2vrbo7n/1bbf01261311537.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t126131160826c0rjff2vrbo7n/1bbf01261311537.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t126131160826c0rjff2vrbo7n/2skj81261311537.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t126131160826c0rjff2vrbo7n/2skj81261311537.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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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