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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: Wed, 15 Dec 2010 16:49:37 +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/15/t129243166774n3if6lzeeohsv.htm/, Retrieved Wed, 15 Dec 2010 17:47:49 +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/15/t129243166774n3if6lzeeohsv.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 «

46 62 66 59 58 61 41 27 58 70 49 59 44 36 72 45 56 54 53 35 61 52 47 51 52 63 74 45 51 64 36 30 55 64 39 40 63 45 59 55 40 64 27 28 45 57 45 69 60 56 58 50 51 53 37 22 55 70 62 58 39 49 58 47 42 62 39 40 72 70 54 65

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.047793	-0.3311	0.370998
2	0.033962	0.2353	0.407489
3	-0.043016	-0.298	0.383485
4	-0.005729	-0.0397	0.484251
5	-0.095004	-0.6582	0.256776
6	-0.029796	-0.2064	0.418664
7	0.030275	0.2098	0.417375
8	0.096671	0.6698	0.253112
9	-0.059499	-0.4122	0.341005
10	-0.048032	-0.3328	0.370377
11	0.120509	0.8349	0.203952
12	-0.498852	-3.4561	0.000578
13	-0.09624	-0.6668	0.254056
14	0.041545	0.2878	0.387356
15	-0.043148	-0.2989	0.38314
16	-0.025227	-0.1748	0.430994
17	-0.121968	-0.845	0.201146
18	0.051287	0.3553	0.361952
19	-0.036223	-0.251	0.401458
20	-0.141102	-0.9776	0.16659
21	0.083836	0.5808	0.282035
22	0.174289	1.2075	0.116576
23	0.017321	0.12	0.452492
24	0.113883	0.789	0.216995
25	0.145074	1.0051	0.159944
26	-0.158436	-1.0977	0.138911
27	0.050976	0.3532	0.362752
28	-0.055989	-0.3879	0.349902
29	0.192754	1.3354	0.094016
30	-0.055034	-0.3813	0.352336
31	0.020056	0.1389	0.445036
32	0.127572	0.8838	0.190594
33	0.066548	0.4611	0.323421
34	-0.101325	-0.702	0.243035
35	-0.101014	-0.6998	0.243701
36	-0.0631	-0.4372	0.331973
37	-0.118339	-0.8199	0.20817
38	0.085223	0.5904	0.278833
39	-0.036929	-0.2559	0.399579
40	0.077777	0.5389	0.296238
41	-0.065893	-0.4565	0.325037
42	0.068832	0.4769	0.317804
43	0.00938	0.065	0.474229
44	-0.017944	-0.1243	0.45079
45	-0.085121	-0.5897	0.279068
46	0.034882	0.2417	0.405032
47	0.008102	0.0561	0.477734
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.047793	-0.3311	0.370998
2	0.031751	0.22	0.413411
3	-0.040059	-0.2775	0.39128
4	-0.010647	-0.0738	0.470752
5	-0.093564	-0.6482	0.259962
6	-0.040194	-0.2785	0.390923
7	0.032226	0.2233	0.412136
8	0.095525	0.6618	0.255627
9	-0.057885	-0.401	0.345087
10	-0.068996	-0.478	0.317404
11	0.123978	0.8589	0.19732
12	-0.504425	-3.4948	0.000516
13	-0.145394	-1.0073	0.159416
14	0.10493	0.727	0.235386
15	-0.154956	-1.0736	0.144192
16	-0.056963	-0.3946	0.347425
17	-0.231854	-1.6063	0.057381
18	-0.05817	-0.403	0.344363
19	-0.07351	-0.5093	0.30644
20	-0.156118	-1.0816	0.142413
21	0.028158	0.1951	0.423074
22	0.058279	0.4038	0.344088
23	0.156096	1.0815	0.142448
24	-0.192499	-1.3337	0.094303
25	0.026728	0.1852	0.426935
26	-0.150963	-1.0459	0.150423
27	-0.032244	-0.2234	0.412088
28	-0.00932	-0.0646	0.474393
29	-0.080866	-0.5603	0.288955
30	-0.074125	-0.5136	0.30496
31	-0.0786	-0.5446	0.294291
32	-0.026991	-0.187	0.426225
33	0.036767	0.2547	0.40001
34	0.073592	0.5099	0.306243
35	-0.060522	-0.4193	0.338431
36	-0.165526	-1.1468	0.128575
37	-0.021392	-0.1482	0.4414
38	-0.023689	-0.1641	0.435162
39	-0.011681	-0.0809	0.467917
40	0.023055	0.1597	0.436882
41	0.028817	0.1997	0.421298
42	0.139968	0.9697	0.168523
43	-0.089978	-0.6234	0.267992
44	0.061822	0.4283	0.335168
45	0.013347	0.0925	0.463354
46	0.073546	0.5095	0.306354
47	-0.045375	-0.3144	0.377301
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t129243166774n3if6lzeeohsv/1yx5n1292431774.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t129243166774n3if6lzeeohsv/1yx5n1292431774.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t129243166774n3if6lzeeohsv/2yx5n1292431774.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t129243166774n3if6lzeeohsv/2yx5n1292431774.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 2 ; 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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