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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: Sat, 25 Dec 2010 05:18:47 +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/Dec/25/t1293254213j1euvcb1lhuddyc.htm/, Retrieved Sat, 25 Dec 2010 06:16:54 +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/2010/Dec/25/t1293254213j1euvcb1lhuddyc.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

19437.50 18885.1 16579 17203.6 19165.7 17107.6 17690.5 18664.9 15878.6 16014.6 16842.6 15986.9 16773.3 16263.1 13597.3 14285.6 15496.8 13916.8 14345.5 15761.3 14531.6 15076.6 15816.8 17180.4 20432.3 21289.5 18203.6 20159.5 21053.2 19673.6 21473.3 20244.7 19049.6 20194.3 18021.9 19537.3 20286.6 17967.7 16409.9 17802.7 18509.9 18161.3 16721.3 19106.9 16772.1 17463.6 16162.3 17862.9 17664.9 17180.8 15672.7 15189.8 17699.4 17444.6 15930.7 19691.6 16698 16896.2 17972.4 17637.4 15214

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.620724	4.848	4e-06
2	0.506243	3.9539	0.000101
3	0.587014	4.5847	1.2e-05
4	0.423769	3.3097	0.000785
5	0.314326	2.455	0.008478
6	0.326615	2.5509	0.006634
7	0.091685	0.7161	0.238335
8	-0.002633	-0.0206	0.49183
9	-0.08431	-0.6585	0.256354
10	-0.239815	-1.873	0.03293
11	-0.257652	-2.0123	0.024303
12	-0.159252	-1.2438	0.109167
13	-0.372731	-2.9111	0.002511
14	-0.424272	-3.3137	0.000776
15	-0.370218	-2.8915	0.002653
16	-0.37039	-2.8928	0.002643
17	-0.366432	-2.8619	0.002881
18	-0.283327	-2.2129	0.01533
19	-0.287726	-2.2472	0.014128
20	-0.250756	-1.9585	0.027376
21	-0.261512	-2.0425	0.022717
22	-0.213042	-1.6639	0.05063
23	-0.119003	-0.9294	0.178161
24	-0.031214	-0.2438	0.404105
25	-0.0653	-0.51	0.305942
26	-0.092956	-0.726	0.235306
27	-0.022761	-0.1778	0.429745
28	0.046142	0.3604	0.359905
29	0.044201	0.3452	0.365559
30	0.083753	0.6541	0.257742
31	0.084169	0.6574	0.256705
32	0.046425	0.3626	0.359082
33	0.063695	0.4975	0.310321
34	0.057646	0.4502	0.32707
35	0.039118	0.3055	0.380504
36	0.105869	0.8269	0.205769

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.620724	4.848	4e-06
2	0.196754	1.5367	0.064769
3	0.359574	2.8084	0.00334
4	-0.115497	-0.9021	0.185286
5	-0.061812	-0.4828	0.315494
6	0.007336	0.0573	0.477247
7	-0.329946	-2.577	0.006201
8	-0.086374	-0.6746	0.251239
9	-0.251456	-1.9639	0.02705
10	-0.135473	-1.0581	0.147096
11	0.025666	0.2005	0.420894
12	0.290942	2.2723	0.013302
13	-0.170803	-1.334	0.093579
14	-0.093292	-0.7286	0.234507
15	-0.134192	-1.0481	0.14937
16	0.075877	0.5926	0.277815
17	-0.036537	-0.2854	0.388165
18	-0.024422	-0.1907	0.424682
19	0.028089	0.2194	0.413543
20	-0.034161	-0.2668	0.395259
21	-0.146624	-1.1452	0.128306
22	-0.045873	-0.3583	0.360685
23	0.004117	0.0322	0.487227
24	0.01003	0.0783	0.468909
25	-0.001939	-0.0151	0.493984
26	-0.182016	-1.4216	0.080119
27	0.041709	0.3258	0.372862
28	-0.002403	-0.0188	0.492544
29	0.054464	0.4254	0.336028
30	-0.049455	-0.3863	0.350324
31	-0.082709	-0.646	0.260357
32	-0.109933	-0.8586	0.196961
33	0.081276	0.6348	0.263972
34	-0.109802	-0.8576	0.19724
35	-0.119375	-0.9323	0.177417
36	0.019713	0.154	0.439073

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/25/t1293254213j1euvcb1lhuddyc/1p1m71293254324.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t1293254213j1euvcb1lhuddyc/1p1m71293254324.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t1293254213j1euvcb1lhuddyc/2p1m71293254324.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/25/t1293254213j1euvcb1lhuddyc/2p1m71293254324.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; 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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