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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: Sat, 12 Dec 2009 06:22:37 -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/Dec/12/t1260624495dnwsspstp5wwmzc.htm/, Retrieved Sat, 12 Dec 2009 14:28:18 +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/Dec/12/t1260624495dnwsspstp5wwmzc.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 «

130.7 117.2 110.8 111.4 108.2 108.8 110.2 109.5 109.5 116 111.2 112.1 114 119.1 114.1 115.1 115.4 110.8 116 119.2 126.5 127.8 131.3 140.3 137.3 143 134.5 139.9 159.3 170.4 175 175.8 180.9 180.3 169.6 172.3 184.8 177.7 184.6 211.4 215.3 215.9 244.7 259.3 289 310.9 321 315.1 333.2 314.1 284.7 273.9 216 196.4 190.9 206.4 196.3 199.5 198.9 214.4

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.399843	-2.7119	0.004689
2	0.120517	0.8174	0.208961
3	-0.09434	-0.6398	0.262725
4	0.116402	0.7895	0.216941
5	-0.174372	-1.1826	0.121513
6	0.123805	0.8397	0.202714
7	0.079361	0.5382	0.2965
8	-0.310185	-2.1038	0.020447
9	0.067047	0.4547	0.325719
10	0.028741	0.1949	0.423152
11	0.044278	0.3003	0.382648
12	-0.197039	-1.3364	0.093999
13	0.084551	0.5735	0.284566
14	-0.131561	-0.8923	0.18844
15	0.033021	0.224	0.411891
16	0.092842	0.6297	0.266008
17	0.177383	1.2031	0.117553
18	-0.187051	-1.2686	0.105476
19	0.058791	0.3987	0.345965
20	0.047006	0.3188	0.375656
21	-0.030281	-0.2054	0.419092
22	-0.043296	-0.2936	0.385175
23	0.057344	0.3889	0.349563
24	-0.042276	-0.2867	0.387804
25	-0.073423	-0.498	0.310437
26	0.161614	1.0961	0.139365
27	-0.055675	-0.3776	0.353731
28	-0.037824	-0.2565	0.39934
29	-0.075314	-0.5108	0.305966
30	0.0326	0.2211	0.412996
31	0.018667	0.1266	0.449903
32	0.006658	0.0452	0.482088
33	0.068669	0.4657	0.321801
34	-0.094187	-0.6388	0.263059
35	0.089546	0.6073	0.27331
36	-0.028304	-0.192	0.424306

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.399843	-2.7119	0.004689
2	-0.046847	-0.3177	0.376063
3	-0.074707	-0.5067	0.307397
4	0.067331	0.4567	0.325032
5	-0.120748	-0.819	0.208517
6	0.007473	0.0507	0.479899
7	0.172887	1.1726	0.123502
8	-0.294737	-1.999	0.025768
9	-0.177509	-1.2039	0.117389
10	0.005659	0.0384	0.484776
11	0.055088	0.3736	0.3552
12	-0.167268	-1.1345	0.131239
13	-0.195531	-1.3262	0.095668
14	-0.153899	-1.0438	0.151017
15	-0.019276	-0.1307	0.448276
16	0.024555	0.1665	0.434231
17	0.184173	1.2491	0.10897
18	-0.017774	-0.1205	0.452286
19	-0.018984	-0.1288	0.449057
20	0.002843	0.0193	0.492348
21	-0.071495	-0.4849	0.315024
22	-0.142551	-0.9668	0.169342
23	-0.082843	-0.5619	0.288466
24	-0.001904	-0.0129	0.494877
25	0.026593	0.1804	0.428829
26	0.058143	0.3943	0.347574
27	-0.021931	-0.1487	0.441204
28	-0.015833	-0.1074	0.457476
29	-0.034953	-0.2371	0.40683
30	-0.093612	-0.6349	0.264316
31	0.076323	0.5177	0.303591
32	0.007293	0.0495	0.480382
33	-0.008656	-0.0587	0.476719
34	-0.086317	-0.5854	0.28056
35	0.061788	0.4191	0.338559
36	0.025214	0.171	0.432482

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260624495dnwsspstp5wwmzc/1fcal1260624155.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260624495dnwsspstp5wwmzc/1fcal1260624155.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260624495dnwsspstp5wwmzc/2s75m1260624155.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260624495dnwsspstp5wwmzc/2s75m1260624155.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 2 ; par4 = 1 ; 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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