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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: Wed, 05 May 2010 16:47:18 +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/May/05/t12730780953l0sgzlt95824cq.htm/, Retrieved Wed, 05 May 2010 18:48:15 +0200

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/May/05/t12730780953l0sgzlt95824cq.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:

KDGP2W21

Dataseries X:

» Textbox « » Textfile « » CSV «

77 70 67 76 85 106 108 120 108 111 109 104 104 117 111 110 116 118 115 111 112 97 106 93 95 97 81 71 75 70 72 80 78 80 81 99 87 100 95 128 112 104 102 108 103 99 96 85 78 74 106 100 109 87 107 106 109 83 84 83 65 68 61 75 66 78 68 68 174 64 48 45

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.45329	3.8463	0.000128
2	0.305969	2.5962	0.005709
3	0.19258	1.6341	0.053302
4	0.261022	2.2148	0.014968
5	0.166377	1.4118	0.081164
6	0.050293	0.4268	0.335417
7	0.020803	0.1765	0.43019
8	-0.044739	-0.3796	0.352672
9	-0.00676	-0.0574	0.477208
10	-0.073515	-0.6238	0.267365
11	-0.072692	-0.6168	0.269651
12	-0.058771	-0.4987	0.309761
13	-0.067286	-0.5709	0.28491
14	-0.131664	-1.1172	0.133809
15	-0.175657	-1.4905	0.070231
16	-0.13326	-1.1307	0.130958
17	-0.118355	-1.0043	0.159305
18	-0.110778	-0.94	0.175184
19	-0.198912	-1.6878	0.047886
20	-0.173889	-1.4755	0.072219
21	-0.126196	-1.0708	0.143916
22	-0.055177	-0.4682	0.32053
23	-0.058524	-0.4966	0.310494
24	-0.028399	-0.241	0.405129
25	-0.004564	-0.0387	0.484608
26	0.031031	0.2633	0.396532
27	0.029312	0.2487	0.402144
28	0.096167	0.816	0.208594
29	0.162796	1.3814	0.085719
30	0.099391	0.8434	0.20091
31	0.102146	0.8667	0.194482
32	0.110673	0.9391	0.175411
33	0.190443	1.616	0.055238
34	0.136842	1.1611	0.12471
35	0.100871	0.8559	0.197442
36	0.076039	0.6452	0.260421
37	0.078102	0.6627	0.254814
38	0.019734	0.1674	0.433744
39	-0.014087	-0.1195	0.452594
40	-0.025691	-0.218	0.414025
41	-0.049324	-0.4185	0.338404
42	-0.05614	-0.4764	0.31763
43	-0.010464	-0.0888	0.464749
44	-0.045865	-0.3892	0.349146
45	-0.060844	-0.5163	0.303621
46	-0.051461	-0.4367	0.331831
47	-0.091192	-0.7738	0.220794
48	-0.081777	-0.6939	0.244987

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.45329	3.8463	0.000128
2	0.126486	1.0733	0.143368
3	0.018029	0.153	0.43942
4	0.179793	1.5256	0.065746
5	-0.026107	-0.2215	0.412655
6	-0.102235	-0.8675	0.194276
7	-4e-04	-0.0034	0.498649
8	-0.097673	-0.8288	0.204982
9	0.030532	0.2591	0.398158
10	-0.054311	-0.4608	0.323151
11	-0.022187	-0.1883	0.4256
12	0.034374	0.2917	0.385688
13	-0.04136	-0.3509	0.363325
14	-0.099681	-0.8458	0.200227
15	-0.07626	-0.6471	0.259817
16	-0.013791	-0.117	0.453584
17	-0.016522	-0.1402	0.444448
18	-0.011313	-0.096	0.461895
19	-0.118462	-1.0052	0.159087
20	-0.028441	-0.2413	0.404994
21	0.003583	0.0304	0.487915
22	0.030524	0.259	0.398185
23	0.004459	0.0378	0.484961
24	0.033074	0.2806	0.389896
25	-0.002748	-0.0233	0.49073
26	0.018845	0.1599	0.436702
27	-0.019605	-0.1664	0.434173
28	0.085289	0.7237	0.235798
29	0.093913	0.7969	0.21407
30	-0.070332	-0.5968	0.27626
31	0.032173	0.273	0.392819
32	0.040357	0.3424	0.366509
33	0.072952	0.619	0.26893
34	-0.022011	-0.1868	0.426183
35	-0.023706	-0.2012	0.420572
36	0.008009	0.068	0.473005
37	0.010214	0.0867	0.465588
38	-0.089397	-0.7586	0.225297
39	-0.012207	-0.1036	0.458895
40	-0.013316	-0.113	0.455175
41	-0.036174	-0.3069	0.379886
42	-0.001973	-0.0167	0.493345
43	0.107558	0.9127	0.182234
44	-0.030234	-0.2565	0.399131
45	-0.023442	-0.1989	0.421446
46	0.003734	0.0317	0.487404
47	-0.066628	-0.5654	0.286795
48	0.044043	0.3737	0.354856

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/05/t12730780953l0sgzlt95824cq/1q5oo1273078034.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/05/t12730780953l0sgzlt95824cq/1q5oo1273078034.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/05/t12730780953l0sgzlt95824cq/2q5oo1273078034.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/05/t12730780953l0sgzlt95824cq/2q5oo1273078034.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; 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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