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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: Thu, 16 Dec 2010 20:41:50 +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/16/t1292531986g6fxbe5hmfx82na.htm/, Retrieved Thu, 16 Dec 2010 21:39:48 +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/16/t1292531986g6fxbe5hmfx82na.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 «

-820.8 993.3 741.7 603.6 -145.8 -35.1 395.1 523.1 462.3 183.4 791.5 344.8 -217.0 406.7 228.6 -580.1 -1550.4 -1447.5 -40.1 -1033.5 -925.6 -347.8 -447.7 -102.6 -2062.2 -929.7 -720.7 -1541.8 -1432.3 -1216.2 -212.8 -378.2 76.9 -101.3 220.4 495.6 -1035.2 61.8 -734.8 -6.9 -1061.1 -854.6 -186.5 244.0 -992.6 -335.2 316.8 477.6 -572.1 1115.2

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.374794	2.6502	0.005371
2	0.305471	2.16	0.017796
3	0.278184	1.9671	0.027369
4	0.328303	2.3215	0.012189
5	0.136719	0.9667	0.169161
6	-0.075295	-0.5324	0.298399
7	0.06758	0.4779	0.317415
8	0.129032	0.9124	0.182969
9	0.013259	0.0938	0.46284
10	-0.042462	-0.3003	0.382615
11	-0.020887	-0.1477	0.441589
12	0.206544	1.4605	0.075206
13	-0.115563	-0.8172	0.208859
14	-0.187644	-1.3268	0.095294
15	-0.224936	-1.5905	0.059009
16	-0.121535	-0.8594	0.197116
17	-0.125401	-0.8867	0.189737
18	-0.357685	-2.5292	0.007316
19	-0.20429	-1.4445	0.077412
20	-0.094966	-0.6715	0.252494
21	-0.151946	-1.0744	0.143896
22	-0.22811	-1.613	0.056521
23	-0.211153	-1.4931	0.070851
24	0.03127	0.2211	0.412952
25	-0.113264	-0.8009	0.213491
26	-0.1503	-1.0628	0.146494
27	-0.100527	-0.7108	0.240245
28	-0.008555	-0.0605	0.476001
29	0.00117	0.0083	0.496717
30	-0.146127	-1.0333	0.153224
31	-0.032121	-0.2271	0.410626
32	-0.024764	-0.1751	0.430852
33	-0.042029	-0.2972	0.383775
34	-0.051175	-0.3619	0.35949
35	-0.041283	-0.2919	0.385781
36	0.085387	0.6038	0.27436
37	-0.022667	-0.1603	0.436652
38	0.005973	0.0422	0.483239
39	0.019564	0.1383	0.445265
40	0.056854	0.402	0.344691
41	0.064488	0.456	0.325183
42	0.035846	0.2535	0.400472
43	0.006846	0.0484	0.480791
44	0.069688	0.4928	0.312166
45	0.05417	0.383	0.351657
46	0.057357	0.4056	0.343392
47	0.022722	0.1607	0.4365
48	0.072431	0.5122	0.305396

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.374794	2.6502	0.005371
2	0.191966	1.3574	0.090374
3	0.137374	0.9714	0.168018
4	0.189568	1.3404	0.093079
5	-0.097569	-0.6899	0.246717
6	-0.271454	-1.9195	0.03032
7	0.082894	0.5861	0.280206
8	0.143105	1.0119	0.158227
9	-0.022369	-0.1582	0.437479
10	-0.01103	-0.078	0.469071
11	-0.070847	-0.501	0.309297
12	0.200304	1.4164	0.081435
13	-0.245967	-1.7392	0.044073
14	-0.184821	-1.3069	0.098616
15	-0.183271	-1.2959	0.100476
16	-0.01902	-0.1345	0.446777
17	0.180489	1.2763	0.103881
18	-0.142006	-1.0041	0.160074
19	-0.070135	-0.4959	0.311059
20	0.004095	0.029	0.488507
21	-0.070112	-0.4958	0.311117
22	-0.041742	-0.2952	0.384548
23	-0.070384	-0.4977	0.310443
24	0.065507	0.4632	0.322614
25	0.04466	0.3158	0.376736
26	0.02191	0.1549	0.438752
27	0.014694	0.1039	0.45883
28	-0.118243	-0.8361	0.203537
29	-0.081557	-0.5767	0.283367
30	0.00463	0.0327	0.487007
31	-0.002347	-0.0166	0.493414
32	-0.10684	-0.7555	0.226754
33	-0.067056	-0.4742	0.318726
34	0.054131	0.3828	0.351759
35	0.074765	0.5287	0.299687
36	-0.070455	-0.4982	0.310266
37	-0.180791	-1.2784	0.103509
38	-0.006204	-0.0439	0.482592
39	0.067203	0.4752	0.318357
40	0.049325	0.3488	0.36436
41	-0.05599	-0.3959	0.346928
42	0.070496	0.4985	0.310165
43	-0.106954	-0.7563	0.226515
44	0.056259	0.3978	0.346231
45	-8.5e-05	-6e-04	0.499761
46	-0.073759	-0.5216	0.302142
47	-0.03039	-0.2149	0.415363
48	-0.025394	-0.1796	0.42911

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292531986g6fxbe5hmfx82na/1esy31292532107.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292531986g6fxbe5hmfx82na/1esy31292532107.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292531986g6fxbe5hmfx82na/262yo1292532107.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292531986g6fxbe5hmfx82na/262yo1292532107.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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