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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: Thu, 17 Dec 2009 15:55:30 -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/17/t1261090565uebraya7ytns7nk.htm/, Retrieved Thu, 17 Dec 2009 23:56:07 +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/17/t1261090565uebraya7ytns7nk.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 «

0.8 1.1 1.3 1.2 1.3 1.1 1.3 1.2 1.6 1.7 1.5 0.9 1.5 1.4 1.6 1.7 1.4 1.8 1.7 1.4 1.2 1 1.7 2.4 2 2.1 2 1.8 2.7 2.3 1.9 2 2.3 2.8 2.4 2.3 2.7 2.7 2.9 3 2.2 2.3 2.8 2.8 2.8 2.2 2.6 2.8 2.5 2.4 2.3 1.9 1.7 2 2.1 1.7 1.8 1.8 1.8 1.3 1.3 1.3 1.2 1.4 2.2 2.9 3.1 3.5 3.6 4.4 4.1 5.1 5.8 5.9 5.4 5.5 4.8 3.2 2.7 2.1 1.9 0.6 0.7 -0.2 -1 -1.7 -0.7

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	0.152098	1.4105	0.081
2	0.116085	1.0765	0.142351
3	0.139278	1.2916	0.099976
4	0.222785	2.066	0.020918
5	0.067682	0.6277	0.265945
6	0.049398	0.4581	0.324017
7	0.025181	0.2335	0.407957
8	0.000352	0.0033	0.498703
9	-0.188326	-1.7465	0.042151
10	-0.093496	-0.867	0.194164
11	0.08003	0.7422	0.230004
12	-0.485092	-4.4986	1.1e-05
13	-0.203369	-1.886	0.031337
14	-0.051604	-0.4786	0.316733
15	0.014827	0.1375	0.445478
16	-0.098302	-0.9116	0.18226
17	-0.17079	-1.5838	0.05845
18	-0.043342	-0.4019	0.344363
19	0.037016	0.3433	0.366116
20	-0.077742	-0.7209	0.236448
21	0.039406	0.3654	0.357841
22	0.077174	0.7157	0.238064
23	-0.07105	-0.6589	0.255862
24	0.023888	0.2215	0.412602
25	0.094171	0.8733	0.192465
26	0.041652	0.3863	0.350127
27	-0.035771	-0.3317	0.370452
28	-0.024173	-0.2242	0.411578
29	0.096984	0.8994	0.185479
30	0.076502	0.7094	0.239982
31	-0.060127	-0.5576	0.289286
32	0.048781	0.4524	0.326069
33	0.070091	0.65	0.258715
34	0.025904	0.2402	0.405366
35	-0.050908	-0.4721	0.319026
36	0.075614	0.7012	0.242532
37	-0.013877	-0.1287	0.448952
38	-0.017629	-0.1635	0.435262
39	0.006491	0.0602	0.476071
40	0.052323	0.4852	0.314375
41	0.015923	0.1477	0.441477
42	-0.053259	-0.4939	0.311317
43	0.025355	0.2351	0.407331
44	0.050334	0.4668	0.320918
45	-0.049571	-0.4597	0.323446
46	-0.058372	-0.5413	0.294843
47	0.021308	0.1976	0.421912
48	-0.018623	-0.1727	0.431647
49	-0.011439	-0.1061	0.457882
50	0.051644	0.4789	0.316603
51	-0.050955	-0.4725	0.318869
52	-0.016331	-0.1514	0.43999
53	-0.060518	-0.5612	0.288055
54	-0.007964	-0.0739	0.470649
55	-0.040174	-0.3726	0.355196
56	-0.054952	-0.5096	0.305817
57	0.02038	0.189	0.425269
58	0.014479	0.1343	0.44675
59	0.00733	0.068	0.47298
60	-0.026872	-0.2492	0.4019

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.152098	1.4105	0.081
2	0.095152	0.8824	0.190008
3	0.112424	1.0426	0.150032
4	0.187026	1.7344	0.043214
5	-0.003984	-0.0369	0.485308
6	-0.006366	-0.059	0.47653
7	-0.031801	-0.2949	0.384388
8	-0.053399	-0.4952	0.310861
9	-0.215654	-1.9999	0.024334
10	-0.066449	-0.6162	0.269688
11	0.146546	1.359	0.088848
12	-0.514686	-4.773	4e-06
13	-0.002558	-0.0237	0.490566
14	0.123751	1.1476	0.127153
15	0.077029	0.7143	0.238476
16	0.124707	1.1565	0.125343
17	-0.151546	-1.4054	0.081755
18	0.004606	0.0427	0.483016
19	0.052843	0.49	0.312675
20	-0.035531	-0.3295	0.371288
21	-0.091172	-0.8455	0.200092
22	-0.04781	-0.4434	0.329306
23	0.091864	0.8519	0.198315
24	-0.24784	-2.2984	0.011983
25	0.049287	0.4571	0.324387
26	0.008285	0.0768	0.469468
27	-0.007264	-0.0674	0.473226
28	0.170206	1.5784	0.059069
29	-0.134532	-1.2476	0.107783
30	0.052471	0.4866	0.313892
31	0.00174	0.0161	0.493581
32	0.050764	0.4708	0.319501
33	0.026661	0.2472	0.402653
34	-0.03148	-0.2919	0.385522
35	-0.050798	-0.4711	0.319387
36	-0.070671	-0.6554	0.256986
37	0.026823	0.2487	0.402075
38	-0.053439	-0.4956	0.31073
39	0.061659	0.5718	0.284474
40	0.073987	0.6861	0.247238
41	-0.023992	-0.2225	0.412228
42	0.075633	0.7014	0.242475
43	-0.023115	-0.2144	0.415385
44	0.054696	0.5072	0.306646
45	-0.033777	-0.3132	0.377432
46	0.005959	0.0553	0.478029
47	-0.131174	-1.2165	0.113569
48	-0.016338	-0.1515	0.439964
49	0.053895	0.4998	0.309246
50	0.066931	0.6207	0.268221
51	-0.037152	-0.3445	0.365643
52	-0.038419	-0.3563	0.36125
53	0.052841	0.49	0.312683
54	-0.061957	-0.5746	0.283544
55	-0.052691	-0.4886	0.313172
56	0.039132	0.3629	0.358787
57	0.055905	0.5184	0.302741
58	0.010295	0.0955	0.462081
59	-0.013689	-0.1269	0.449641
60	-0.062444	-0.5791	0.282025

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261090565uebraya7ytns7nk/1w56d1261090528.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261090565uebraya7ytns7nk/1w56d1261090528.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261090565uebraya7ytns7nk/2bgdx1261090528.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261090565uebraya7ytns7nk/2bgdx1261090528.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = 0.0 ; par3 = 2 ; par4 = 0 ; par5 = 1 ; par6 = 2 ; par7 = 0 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

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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