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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: Tue, 07 Dec 2010 15:41:58 +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/07/t1291736461f91h6idb08ro8nv.htm/, Retrieved Tue, 07 Dec 2010 16:41:01 +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/07/t1291736461f91h6idb08ro8nv.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 «

31.514 27.071 29.462 26.105 22.397 23.843 21.705 18.089 20.764 25.316 17.704 15.548 28.029 29.383 36.438 32.034 22.679 24.319 18.004 17.537 20.366 22.782 19.169 13.807 29.743 25.591 29.096 26.482 22.405 27.044 17.970 18.730 19.684 19.785 18.479 10.698 31.956 29.506 34.506 27.165 26.736 23.691 18.157 17.328 18.205 20.995 17.382 9.367 31.124 26.551 30.651 25.859 25.100 25.778 20.418 18.688 20.424 24.776 19.814 12.738 31.566 30.111 30.019 31.934 25.826 26.835 20.205 17.789 20.520 22.518 15.572 11.509 25.447 24.090 27.786 26.195 20.516 22.759 19.028 16.971 20.036 22.485 18.730 14.538 27.561 25.985 34.670 32.066 27.186 29.586 21.359 21.553 19.573 24.256

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	0.394187	3.8218	0.000119
2	0.175052	1.6972	0.046485
3	-0.029334	-0.2844	0.388364
4	-0.216516	-2.0992	0.01924
5	-0.280179	-2.7164	0.003927
6	-0.482067	-4.6738	5e-06
7	-0.293832	-2.8488	0.002696
8	-0.2335	-2.2639	0.012941
9	-0.092544	-0.8972	0.185939
10	0.024709	0.2396	0.405596
11	0.226097	2.1921	0.015421
12	0.742837	7.2021	0
13	0.278884	2.7039	0.004068
14	0.124896	1.2109	0.114483
15	-0.029411	-0.2852	0.388077
16	-0.203468	-1.9727	0.025734
17	-0.267059	-2.5892	0.005574
18	-0.472219	-4.5783	7e-06
19	-0.288193	-2.7941	0.003154
20	-0.22251	-2.1573	0.016765
21	-0.089797	-0.8706	0.193092
22	0.04436	0.4301	0.334059
23	0.244507	2.3706	0.009901
24	0.678708	6.5803	0
25	0.308146	2.9876	0.001793
26	0.164195	1.5919	0.057379
27	0.017498	0.1697	0.432824
28	-0.127559	-1.2367	0.109634
29	-0.18678	-1.8109	0.036676
30	-0.379956	-3.6838	0.000192
31	-0.225065	-2.1821	0.015798
32	-0.198279	-1.9224	0.028793
33	-0.113564	-1.101	0.136844
34	0.020182	0.1957	0.422647
35	0.149177	1.4463	0.075707
36	0.525339	5.0934	1e-06
37	0.249709	2.421	0.008699
38	0.130043	1.2608	0.105249
39	0.021769	0.2111	0.416648
40	-0.108252	-1.0495	0.148311
41	-0.165608	-1.6056	0.055855
42	-0.304632	-2.9535	0.001984
43	-0.18461	-1.7899	0.038348
44	-0.178067	-1.7264	0.043778
45	-0.096349	-0.9341	0.176314
46	0.008382	0.0813	0.4677
47	0.109104	1.0578	0.146428
48	0.40826	3.9582	7.3e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.394187	3.8218	0.000119
2	0.023286	0.2258	0.410935
3	-0.125461	-1.2164	0.11344
4	-0.202454	-1.9629	0.026309
5	-0.139482	-1.3523	0.089758
6	-0.371987	-3.6065	0.00025
7	-0.023645	-0.2292	0.409589
8	-0.163917	-1.5892	0.057683
9	-0.093241	-0.904	0.184151
10	-0.129049	-1.2512	0.106987
11	0.109067	1.0574	0.146508
12	0.653869	6.3395	0
13	-0.457434	-4.435	1.2e-05
14	-0.180379	-1.7488	0.041791
15	0.070611	0.6846	0.247641
16	-0.079739	-0.7731	0.220701
17	-0.155869	-1.5112	0.067045
18	-0.096221	-0.9329	0.176632
19	-0.038668	-0.3749	0.354289
20	-0.104458	-1.0128	0.156887
21	-0.038889	-0.377	0.353496
22	0.184292	1.7868	0.038599
23	0.023995	0.2326	0.408275
24	-0.089266	-0.8655	0.194493
25	0.039445	0.3824	0.351501
26	-0.017301	-0.1677	0.433575
27	-0.100449	-0.9739	0.166304
28	0.08612	0.835	0.202928
29	0.099293	0.9627	0.169089
30	-0.01012	-0.0981	0.461024
31	-0.043005	-0.4169	0.338835
32	0.017268	0.1674	0.433699
33	-0.013891	-0.1347	0.446575
34	0.026657	0.2584	0.398313
35	-0.173081	-1.6781	0.048326
36	-0.017712	-0.1717	0.432014
37	0.038921	0.3774	0.353382
38	-0.054725	-0.5306	0.298482
39	0.022751	0.2206	0.412951
40	0.022103	0.2143	0.415391
41	-0.036904	-0.3578	0.360647
42	0.110869	1.0749	0.142583
43	-0.043642	-0.4231	0.336586
44	-0.029581	-0.2868	0.387448
45	0.066827	0.6479	0.25931
46	-0.126544	-1.2269	0.111463
47	0.03735	0.3621	0.359037
48	-0.055224	-0.5354	0.296812

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291736461f91h6idb08ro8nv/18rr21291736515.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291736461f91h6idb08ro8nv/18rr21291736515.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291736461f91h6idb08ro8nv/28rr21291736515.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291736461f91h6idb08ro8nv/28rr21291736515.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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