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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: Wed, 30 Dec 2009 08:46:40 -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/30/t1262188053w6dz1j8ae0sytu7.htm/, Retrieved Wed, 30 Dec 2009 16:47:36 +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/30/t1262188053w6dz1j8ae0sytu7.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 «

10519,20 10414,90 12476,80 12384,60 12266,70 12919,90 11497,30 12142,00 13919,40 12656,80 12034,10 13199,70 10881,30 11301,20 13643,90 12517,00 13981,10 14275,70 13425,00 13565,70 16216,30 12970,00 14079,90 14235,00 12213,40 12581,00 14130,40 14210,80 14378,50 13142,80 13714,70 13621,90 15379,80 13306,30 14391,20 14909,90 14025,40 12951,20 14344,30 16093,40 15413,60 14705,70 15972,80 16241,40 16626,40 17136,20 15622,90 18003,90 16136,10 14423,70 16789,40 16782,20 14133,80 12607,00 12004,50 12175,40 13268,00 12299,30 11800,60 13873,30 12315,00

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	0.639229	4.9925	3e-06
2	0.504687	3.9417	0.000106
3	0.566021	4.4208	2.1e-05
4	0.423374	3.3067	0.000793
5	0.35119	2.7429	0.003992
6	0.352357	2.752	0.003895
7	0.14973	1.1694	0.123391
8	0.127171	0.9932	0.162259
9	0.128849	1.0063	0.159113
10	-0.031033	-0.2424	0.404651
11	0.04383	0.3423	0.366643
12	0.174302	1.3613	0.089207
13	-0.047861	-0.3738	0.354923
14	-0.114244	-0.8923	0.187877
15	-0.04653	-0.3634	0.358776
16	-0.066879	-0.5223	0.301663
17	-0.069843	-0.5455	0.293702
18	-0.039474	-0.3083	0.379452
19	-0.062263	-0.4863	0.314253
20	-0.079195	-0.6185	0.269265
21	-0.047936	-0.3744	0.354706
22	-0.06817	-0.5324	0.298183
23	-0.027276	-0.213	0.416007
24	0.05319	0.4154	0.339643
25	-0.006423	-0.0502	0.480076
26	-0.14578	-1.1386	0.129666
27	-0.066218	-0.5172	0.30345
28	-0.059522	-0.4649	0.321835
29	-0.095699	-0.7474	0.228837
30	-0.091754	-0.7166	0.23817
31	-0.100904	-0.7881	0.216849
32	-0.218336	-1.7053	0.046617
33	-0.189671	-1.4814	0.071827
34	-0.220033	-1.7185	0.045388
35	-0.275539	-2.152	0.017681
36	-0.193115	-1.5083	0.068323
37	-0.237871	-1.8578	0.03401
38	-0.343416	-2.6822	0.004699
39	-0.253994	-1.9838	0.025894
40	-0.228743	-1.7865	0.03949
41	-0.22237	-1.7368	0.043738
42	-0.162715	-1.2708	0.104305
43	-0.163036	-1.2733	0.103863
44	-0.197718	-1.5442	0.063853
45	-0.121655	-0.9502	0.172891
46	-0.123249	-0.9626	0.169772
47	-0.108375	-0.8464	0.200309
48	-0.011675	-0.0912	0.463823
49	-0.037617	-0.2938	0.384955
50	-0.053472	-0.4176	0.338841
51	0.020966	0.1638	0.435234
52	0.074242	0.5798	0.282077
53	0.103721	0.8101	0.21052
54	0.112321	0.8773	0.191895
55	0.070518	0.5508	0.291904
56	0.062567	0.4887	0.313417
57	0.074757	0.5839	0.280731
58	0.044524	0.3477	0.364616
59	0.025397	0.1984	0.421712
60	0.026665	0.2083	0.417859

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.639229	4.9925	3e-06
2	0.162455	1.2688	0.104664
3	0.333416	2.6041	0.005777
4	-0.105582	-0.8246	0.2064
5	0.031957	0.2496	0.401869
6	0.011687	0.0913	0.463784
7	-0.268823	-2.0996	0.019955
8	0.059534	0.465	0.321803
9	-0.048584	-0.3794	0.352836
10	-0.115113	-0.8991	0.186077
11	0.213667	1.6688	0.050142
12	0.234086	1.8283	0.0362
13	-0.273975	-2.1398	0.018189
14	-0.192056	-1.5	0.069386
15	-0.03473	-0.2712	0.393559
16	0.139126	1.0866	0.140742
17	-0.044441	-0.3471	0.364857
18	0.0555	0.4335	0.333101
19	0.201438	1.5733	0.060414
20	-0.180534	-1.41	0.081807
21	-0.037469	-0.2926	0.385395
22	0.053707	0.4195	0.338175
23	-0.050997	-0.3983	0.3459
24	-0.026916	-0.2102	0.417097
25	0.098951	0.7728	0.221304
26	-0.191565	-1.4962	0.069882
27	0.000567	0.0044	0.498242
28	-0.073787	-0.5763	0.283267
29	0.1277	0.9974	0.161263
30	-0.130396	-1.0184	0.156249
31	-0.006422	-0.0502	0.480081
32	-0.099941	-0.7806	0.21904
33	-0.076608	-0.5983	0.275919
34	-0.115317	-0.9007	0.185657
35	-0.053172	-0.4153	0.339695
36	0.079108	0.6179	0.269487
37	-0.040202	-0.314	0.377302
38	0.086355	0.6745	0.251287
39	-0.044792	-0.3498	0.363833
40	-0.055345	-0.4323	0.333538
41	-0.012957	-0.1012	0.459862
42	-0.009533	-0.0745	0.470447
43	-0.052841	-0.4127	0.340637
44	0.017799	0.139	0.444949
45	0.034219	0.2673	0.395085
46	-0.041823	-0.3266	0.372526
47	0.021367	0.1669	0.434007
48	0.026633	0.208	0.417957
49	-0.012078	-0.0943	0.462577
50	-0.003288	-0.0257	0.489797
51	0.126238	0.986	0.164026
52	0.022247	0.1738	0.431317
53	-0.013182	-0.103	0.459168
54	-0.095426	-0.7453	0.229476
55	-0.033559	-0.2621	0.397063
56	-0.072972	-0.5699	0.28541
57	0.07011	0.5476	0.292991
58	-0.016531	-0.1291	0.448846
59	-0.001442	-0.0113	0.495526
60	-0.073889	-0.5771	0.283

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/30/t1262188053w6dz1j8ae0sytu7/1uioy1262187998.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/30/t1262188053w6dz1j8ae0sytu7/1uioy1262187998.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/30/t1262188053w6dz1j8ae0sytu7/250oi1262187998.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/30/t1262188053w6dz1j8ae0sytu7/250oi1262187998.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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