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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: Mon, 27 Dec 2010 22:09:23 +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/27/t129348764822q6qx9x0kdcglg.htm/, Retrieved Mon, 27 Dec 2010 23:07:31 +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/27/t129348764822q6qx9x0kdcglg.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 «

110.43 114.77 132.21 122.86 118.5 130.3 113.25 104.54 132.78 122.99 133.14 125.83 122.99 125.7 148.47 120.75 136.7 139.17 123.47 112.76 137.99 139.75 140.22 121.6 132.33 130.34 149.05 130.47 139.29 146.55 137.79 122.95 139.51 155.77 143.95 125.07 142.35 144.34 145.87 156.01 146.74 156.45 152.29 122.56 154.59 149.68 118.75 109.22 104.19 107.33 114.07 107.92 103.53 117.3 112.09 95.08 123.28 121.98 121.74 119.93 115.11

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	-0.412667	-2.859	0.003135
2	0.05479	0.3796	0.352959
3	0.390069	2.7025	0.004744
4	-0.319095	-2.2108	0.015926
5	0.18667	1.2933	0.101051
6	0.125404	0.8688	0.194633
7	-0.374305	-2.5933	0.006283
8	0.250585	1.7361	0.044481
9	-0.112806	-0.7815	0.219161
10	-0.188776	-1.3079	0.098572
11	0.15155	1.05	0.149496
12	-0.175906	-1.2187	0.114455
13	-0.112436	-0.779	0.219908
14	0.085851	0.5948	0.277387
15	-0.052637	-0.3647	0.358475
16	-0.065293	-0.4524	0.326522
17	0.094922	0.6576	0.256955
18	-0.111989	-0.7759	0.220813
19	0.039712	0.2751	0.392199
20	0.083012	0.5751	0.283946
21	-0.072844	-0.5047	0.308046
22	-0.087066	-0.6032	0.274604
23	0.283744	1.9658	0.027558
24	-0.289461	-2.0054	0.025286
25	0.137011	0.9492	0.173626
26	0.072566	0.5028	0.308718
27	-0.19606	-1.3583	0.090352
28	0.194188	1.3454	0.092413
29	-0.036787	-0.2549	0.399957
30	-0.073176	-0.507	0.307246
31	0.153837	1.0658	0.14592
32	-0.126413	-0.8758	0.192746
33	0.029193	0.2023	0.420287
34	0.089148	0.6176	0.269868
35	-0.111122	-0.7699	0.222572
36	0.004657	0.0323	0.487197

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.412667	-2.859	0.003135
2	-0.13921	-0.9645	0.169821
3	0.440471	3.0517	0.001851
4	0.028079	0.1945	0.423288
5	0.020414	0.1414	0.444061
6	0.080736	0.5594	0.28926
7	-0.278553	-1.9299	0.029772
8	-0.133364	-0.924	0.18006
9	-0.085275	-0.5908	0.278711
10	-0.053882	-0.3733	0.355283
11	-0.063285	-0.4385	0.331512
12	-0.027132	-0.188	0.425845
13	-0.123348	-0.8546	0.198515
14	-0.150026	-1.0394	0.151911
15	0.132002	0.9145	0.182504
16	0.039547	0.274	0.392635
17	0.021506	0.149	0.44109
18	-0.100403	-0.6956	0.245012
19	-0.078694	-0.5452	0.294067
20	-0.045817	-0.3174	0.376148
21	0.006132	0.0425	0.483146
22	-0.215181	-1.4908	0.071276
23	0.184618	1.2791	0.10351
24	-0.105373	-0.73	0.234454
25	-0.047285	-0.3276	0.372319
26	-0.066311	-0.4594	0.324003
27	0.011853	0.0821	0.467446
28	0.046197	0.3201	0.375155
29	-0.008863	-0.0614	0.475646
30	0.125271	0.8679	0.194883
31	-0.114538	-0.7935	0.215683
32	-0.083703	-0.5799	0.282342
33	-0.035539	-0.2462	0.403281
34	-0.029495	-0.2044	0.419472
35	0.026131	0.181	0.428548
36	-0.096333	-0.6674	0.253852

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/27/t129348764822q6qx9x0kdcglg/1zxtz1293487760.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t129348764822q6qx9x0kdcglg/1zxtz1293487760.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t129348764822q6qx9x0kdcglg/29ot21293487760.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t129348764822q6qx9x0kdcglg/29ot21293487760.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t129348764822q6qx9x0kdcglg/32gan1293487760.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t129348764822q6qx9x0kdcglg/32gan1293487760.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; 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 (par8 != '') par8 <- as.numeric(par8)

ox <- x

if (par8 == '') {

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

} else {

x <- log(x,base=par8)

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='picts.png')

op <- par(mfrow=c(2,1))

plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')

if (par8=='') {

mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

} else {

mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

}

plot(x,type='l', main=mytitle,xlab='time',ylab='value')

par(op)

dev.off()

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)

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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