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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, 29 Dec 2010 12:50:49 +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/29/t1293626919h1qroh7k13oi2fk.htm/, Retrieved Wed, 29 Dec 2010 13:48:40 +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/2010/Dec/29/t1293626919h1qroh7k13oi2fk.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 «

04.031636 03.702076 03.056167 03.280707 02.984728 03.693712 03.226317 02.190349 02.599515 03.080288 02.929672 02.922548 03.234943 02.983081 03.284389 03.806511 03.784579 02.645654 03.092081 03.204859 03.107225 03.466909 02.984404 03.218072 02.827310 03.182049 02.236319 02.033218 01.644804 01.627971 01.677559 02.330828 02.493615 02.257172 02.655517 02.298655 02.600402 03.045230 02.790583 03.227052 02.967479 02.938817 03.277961 03.423985 03.072646 02.754253 02.910431 03.174369 03.068387 03.089543 02.906654 02.931161 03.025660 02.939551 02.691019 03.198120 03.076390 02.863873 03.013802 03.053364 02.864753 03.057062 02.959365 03.252258 03.602988 03.497704 03.296867 03.602417 03.300100 03.401930 03.502591 03.402348 03.498551 03.199823 02.700064 02.801034 02.898628 02.800854 02.399942 02.402724 02.202331 02.102594 01.798293 01.202484 01.400201 01.200832 01.298083 01.099742 01.001377 00.836174

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

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.172704	-1.5155	0.066873
2	-0.018221	-0.1599	0.436694
3	-0.071419	-0.6267	0.266355
4	0.028914	0.2537	0.400196
5	0.103006	0.9039	0.184441
6	0.001735	0.0152	0.493948
7	0.004597	0.0403	0.483963
8	-0.16201	-1.4216	0.079586
9	0.121549	1.0666	0.144745
10	-0.046782	-0.4105	0.341287
11	0.099995	0.8774	0.191486
12	-0.429761	-3.7711	0.000159
13	0.065059	0.5709	0.284869
14	-0.141638	-1.2429	0.108843
15	-0.027745	-0.2435	0.404149
16	0.105394	0.9248	0.178972
17	-0.046806	-0.4107	0.341208
18	0.101031	0.8865	0.189044
19	-0.060612	-0.5319	0.298174
20	0.029434	0.2583	0.398439
21	-0.045762	-0.4016	0.344559
22	0.056427	0.4951	0.310955
23	0.060295	0.5291	0.299135
24	0.111324	0.9769	0.165847
25	-0.008412	-0.0738	0.470674
26	-0.001104	-0.0097	0.496147
27	0.088661	0.778	0.219478
28	0.053766	0.4718	0.319204
29	-0.017853	-0.1567	0.437961
30	-0.080481	-0.7062	0.241092
31	0.012081	0.106	0.457926
32	0.025333	0.2223	0.412337
33	0.062753	0.5507	0.291733
34	0.047213	0.4143	0.339907
35	-0.132884	-1.1661	0.123596
36	-0.06235	-0.5471	0.292939

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.172704	-1.5155	0.066873
2	-0.049525	-0.4346	0.332542
3	-0.086046	-0.7551	0.22626
4	-0.000399	-0.0035	0.498608
5	0.106264	0.9325	0.177007
6	0.037388	0.3281	0.371871
7	0.024272	0.213	0.415949
8	-0.14839	-1.3021	0.098379
9	0.067495	0.5923	0.277705
10	-0.039	-0.3422	0.366558
11	0.07521	0.66	0.255624
12	-0.420107	-3.6864	0.000211
13	-0.043951	-0.3857	0.350403
14	-0.244749	-2.1477	0.017443
15	-0.147323	-1.2928	0.099981
16	0.008065	0.0708	0.471881
17	0.075152	0.6595	0.255786
18	0.150379	1.3196	0.095444
19	0.099227	0.8707	0.193308
20	-0.056411	-0.495	0.311004
21	0.035409	0.3107	0.378428
22	-0.071076	-0.6237	0.267337
23	0.115365	1.0123	0.157278
24	-0.048275	-0.4236	0.336517
25	0.043672	0.3832	0.351305
26	-0.156852	-1.3764	0.086348
27	-0.012246	-0.1075	0.457353
28	0.087984	0.7721	0.221222
29	0.008621	0.0757	0.469947
30	0.080247	0.7042	0.241728
31	0.097929	0.8593	0.196415
32	0.044829	0.3934	0.347566
33	0.105251	0.9236	0.179297
34	0.043486	0.3816	0.351908
35	-0.004226	-0.0371	0.485257
36	-0.067148	-0.5892	0.27872

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293626919h1qroh7k13oi2fk/1pnkd1293627046.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293626919h1qroh7k13oi2fk/1pnkd1293627046.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293626919h1qroh7k13oi2fk/2iejy1293627046.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293626919h1qroh7k13oi2fk/2iejy1293627046.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293626919h1qroh7k13oi2fk/3iejy1293627046.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293626919h1qroh7k13oi2fk/3iejy1293627046.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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 (par8 != '') par8 <- as.numeric(par8)

ox <- x

if (par8 == '') {

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

} else {

x <- log(x,base=par8)

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='picts.png')

op <- par(mfrow=c(2,1))

plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')

if (par8=='') {

mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

} else {

mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

}

plot(x,type='l', main=mytitle,xlab='time',ylab='value')

par(op)

dev.off()

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)

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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