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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: Fri, 27 Nov 2009 10:21:41 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/27/t1259342543bk7odqy3rszrymw.htm/, Retrieved Fri, 27 Nov 2009 18:22:25 +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/2009/Nov/27/t1259342543bk7odqy3rszrymw.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

252.5 251.1 255.1 258.3 255.3 261.1 253.8 252.9 253.9 255.5 262 262.8 263.3 262.5 269.2 270.8 274.1 273 267.3 267.1 268.2 270.2 271.5 281 280.1 281.5 285.9 289.8 292.9 291.2 291.8 289.8 292.5 290.3 297.5 307.5 304.7 304.6 310.7 310.7 315.7 314.7 312.2 312.8 314.3 319.7 319.9 329.5 326.9 329.7 335.7 337.2 339.7 338.3 339.2 342.5 342.2 338.3 339 345.9

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	-0.514831	-3.9208	0.000118
2	0.025944	0.1976	0.422031
3	0.062148	0.4733	0.318887
4	-0.162549	-1.2379	0.110364
5	0.149491	1.1385	0.129798
6	-0.086942	-0.6621	0.255256
7	0.144183	1.0981	0.138357
8	-0.254736	-1.94	0.028623
9	0.257702	1.9626	0.027248
10	-0.233672	-1.7796	0.040191
11	-0.010079	-0.0768	0.469538
12	0.281844	2.1465	0.018015
13	-0.101178	-0.7705	0.222052
14	-0.12097	-0.9213	0.180359
15	0.178124	1.3566	0.09009
16	-0.116845	-0.8899	0.188607
17	-0.070971	-0.5405	0.29546
18	0.169335	1.2896	0.101151
19	-0.164378	-1.2519	0.107822
20	0.06279	0.4782	0.317154
21	0.08799	0.6701	0.252723
22	-0.097954	-0.746	0.229341
23	-0.142052	-1.0818	0.141902
24	0.243551	1.8548	0.034353
25	-0.024499	-0.1866	0.42632
26	-0.069065	-0.526	0.300453
27	0.073356	0.5587	0.289271
28	-0.07624	-0.5806	0.28187
29	-0.035317	-0.269	0.394454
30	0.100245	0.7634	0.224147
31	-0.063061	-0.4803	0.316425
32	-0.063891	-0.4866	0.314195
33	0.212162	1.6158	0.055785
34	-0.274373	-2.0896	0.020527
35	0.143164	1.0903	0.140043
36	0.012627	0.0962	0.461862

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.514831	-3.9208	0.000118
2	-0.325338	-2.4777	0.008079
3	-0.133368	-1.0157	0.156994
4	-0.271598	-2.0684	0.021534
5	-0.121622	-0.9262	0.179079
6	-0.151634	-1.1548	0.126452
7	0.085458	0.6508	0.258862
8	-0.2428	-1.8491	0.03477
9	0.05642	0.4297	0.334509
10	-0.237286	-1.8071	0.037966
11	-0.3203	-2.4393	0.008897
12	-0.066394	-0.5056	0.307512
13	0.218269	1.6623	0.050925
14	-0.152916	-1.1646	0.12448
15	0.207976	1.5839	0.059327
16	0.08559	0.6518	0.258541
17	-0.006438	-0.049	0.480531
18	-0.051861	-0.395	0.34716
19	-0.056385	-0.4294	0.334607
20	-0.133749	-1.0186	0.156312
21	0.110761	0.8435	0.201198
22	0.064783	0.4934	0.311807
23	-0.12373	-0.9423	0.174974
24	-0.114119	-0.8691	0.194186
25	0.090309	0.6878	0.247169
26	0.091289	0.6952	0.244841
27	-0.100555	-0.7658	0.22345
28	0.015759	0.12	0.452441
29	0.017883	0.1362	0.44607
30	0.002028	0.0154	0.493865
31	-0.013229	-0.1007	0.460048
32	-0.038743	-0.2951	0.384502
33	-0.00682	-0.0519	0.479376
34	-0.169751	-1.2928	0.100606
35	0.130645	0.995	0.161944
36	-0.026833	-0.2044	0.419397

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259342543bk7odqy3rszrymw/15bgy1259342499.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259342543bk7odqy3rszrymw/15bgy1259342499.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259342543bk7odqy3rszrymw/2n3tz1259342499.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259342543bk7odqy3rszrymw/2n3tz1259342499.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 2 ; 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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