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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: Mon, 21 Dec 2009 08:02:09 -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/21/t1261407758dnhbb1zmuscge0b.htm/, Retrieved Mon, 21 Dec 2009 16:02:40 +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/21/t1261407758dnhbb1zmuscge0b.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 «

103.5 104.6 118.6 106.3 110.7 121.6 107 107.6 125.6 113.5 129.2 130.9 104.7 115.2 124.5 112.3 127.5 120.6 117.5 117.7 120.4 125 131.6 121.1 114.2 112.1 127 116.8 112 129.7 113.6 115.7 119.5 125.8 129.6 128 112.8 101.6 123.9 118.8 109.1 130.6 112.4 111 116.2 119.8 117.2 127.3 107.7 97.5 120.1 110.6 111.3 119.8 105.5 108.7 128.7 119.5 121.1 128.4

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	0.020251	0.1403	0.444505
2	0.242302	1.6787	0.049853
3	0.429169	2.9734	0.002298
4	-0.063189	-0.4378	0.331752
5	0.293556	2.0338	0.023759
6	0.19359	1.3412	0.093079
7	-0.110715	-0.7671	0.223402
8	0.279147	1.934	0.029511
9	0.063227	0.438	0.331659
10	-0.096431	-0.6681	0.253637
11	0.092511	0.6409	0.262307
12	-0.132164	-0.9157	0.182211
13	-0.01829	-0.1267	0.449846
14	0.06118	0.4239	0.336778
15	-0.052851	-0.3662	0.357926
16	-0.017487	-0.1212	0.452039
17	0.092412	0.6403	0.262527
18	-0.035065	-0.2429	0.404545
19	-0.143793	-0.9962	0.162068
20	0.030222	0.2094	0.417518
21	-0.044712	-0.3098	0.379038
22	-0.114269	-0.7917	0.216222
23	0.114741	0.7949	0.215279
24	-0.217244	-1.5051	0.069424
25	-0.056029	-0.3882	0.3498
26	-0.017035	-0.118	0.453273
27	-0.140653	-0.9745	0.167354
28	-0.153601	-1.0642	0.146287
29	-0.115444	-0.7998	0.213878
30	-0.196851	-1.3638	0.089492
31	-0.082679	-0.5728	0.28472
32	-0.150107	-1.04	0.151781
33	-0.202951	-1.4061	0.08307
34	-0.0621	-0.4302	0.334472
35	-0.129685	-0.8985	0.186707
36	-0.104102	-0.7212	0.23713
37	-0.045136	-0.3127	0.377927
38	-0.059325	-0.411	0.341445
39	-0.048847	-0.3384	0.368259
40	0.041956	0.2907	0.386273
41	-0.00953	-0.066	0.473817
42	0.045291	0.3138	0.377522
43	0.074134	0.5136	0.304939
44	0.018133	0.1256	0.450276
45	0.020732	0.1436	0.443196
46	0.007153	0.0496	0.480341
47	0.00058	0.004	0.498407
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.020251	0.1403	0.444505
2	0.241991	1.6766	0.050065
3	0.446891	3.0962	0.001635
4	-0.118691	-0.8223	0.207482
5	0.100936	0.6993	0.243868
6	0.089335	0.6189	0.269444
7	-0.15993	-1.108	0.136686
8	0.06211	0.4303	0.334449
9	0.088981	0.6165	0.270247
10	-0.124791	-0.8646	0.195785
11	-0.179472	-1.2434	0.109876
12	-0.087997	-0.6097	0.272481
13	0.066335	0.4596	0.323947
14	0.053159	0.3683	0.357136
15	0.129367	0.8963	0.187288
16	-0.022159	-0.1535	0.439315
17	0.063833	0.4423	0.330147
18	0.017595	0.1219	0.451743
19	-0.255585	-1.7707	0.041476
20	-0.041296	-0.2861	0.388013
21	0.121867	0.8443	0.20134
22	-0.102477	-0.71	0.240575
23	0.029123	0.2018	0.420474
24	-0.129502	-0.8972	0.187041
25	-0.047956	-0.3322	0.370574
26	-0.108053	-0.7486	0.228871
27	0.216296	1.4985	0.070271
28	-0.152655	-1.0576	0.147761
29	-0.176457	-1.2225	0.113738
30	-0.075066	-0.5201	0.302702
31	-0.044759	-0.3101	0.378913
32	-0.064172	-0.4446	0.329304
33	0.041796	0.2896	0.386697
34	0.068756	0.4764	0.317992
35	-0.026674	-0.1848	0.427081
36	0.004575	0.0317	0.487422
37	0.063773	0.4418	0.330298
38	-0.004125	-0.0286	0.48866
39	0.044904	0.3111	0.378534
40	0.016836	0.1166	0.453816
41	0.001564	0.0108	0.495699
42	0.09814	0.6799	0.249906
43	-0.040491	-0.2805	0.390138
44	-0.118887	-0.8237	0.207099
45	0.022171	0.1536	0.439283
46	-0.019383	-0.1343	0.446867
47	-0.062119	-0.4304	0.334426
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261407758dnhbb1zmuscge0b/1eqr31261407726.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261407758dnhbb1zmuscge0b/1eqr31261407726.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261407758dnhbb1zmuscge0b/2zfqr1261407726.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261407758dnhbb1zmuscge0b/2zfqr1261407726.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; 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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