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Paper PAC coins

*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, 29 Dec 2010 15:58:07 +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/29/t12936382092gtqluga4ihxozy.htm/, Retrieved Wed, 29 Dec 2010 16:56:49 +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/29/t12936382092gtqluga4ihxozy.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 «

34420 34070 33978 34484 34645 34410 34534 35019 35508 35488 35709 36534 36066 35724 35727 36281 36017 35780 36003 36285 36419 36413 36663 37451 37063 36613 36564 37064 36817 36621 36798 36967 36926 36975 37324 38159 37776 37465 37451 37944 37737 37603 37813 37960 37934 37975 38241 39176 39137 38797 38730 39031 38851 38727 39291 39407 39326 39326 39617 40458 40425 40092 39939 40174 40065 39922 40107 40163 40116 40118 40416 41215 40852 40497 40430 40766 40626 40442 40590 40673 40660 40736 41082 41873 41507 41104 40963 41227 41063 40873 41016 41433 41345 41375 41597 42225 41937 41642 41551 41866 41744 41615 41764 41828 41786 41852 42183 42937 42635 42292 42202 42577 42600 42433 42584 42660 42659 42712 43039 43664 43397 43110 43005 43159 43066 42977 43139 43226 43242 43348 43605 44225 43983 43754 43632 43868 43864 43808 43954 44032 44090 44210 44435 44919 44785 44616 44 etc...

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.983153	14.4159	0
2	0.964671	14.1449	0
3	0.948777	13.9118	0
4	0.934967	13.7093	0
5	0.918797	13.4722	0
6	0.902039	13.2265	0
7	0.888261	13.0245	0
8	0.875661	12.8397	0
9	0.862042	12.64	0
10	0.849103	12.4503	0
11	0.839145	12.3043	0
12	0.830649	12.1797	0
13	0.815195	11.9531	0
14	0.79835	11.7061	0
15	0.784038	11.4963	0
16	0.77187	11.3178	0
17	0.756365	11.0905	0
18	0.740334	10.8554	0
19	0.727501	10.6673	0
20	0.71517	10.4864	0
21	0.700857	10.2766	0
22	0.687102	10.0749	0
23	0.676242	9.9157	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.983153	14.4159	0
2	-0.057447	-0.8423	0.200268
3	0.070653	1.036	0.150688
4	0.04677	0.6858	0.246794
5	-0.078441	-1.1502	0.125676
6	-0.010135	-0.1486	0.441
7	0.076066	1.1153	0.132973
8	0.009526	0.1397	0.444525
9	-0.025331	-0.3714	0.355344
10	0.031952	0.4685	0.319948
11	0.069802	1.0235	0.153613
12	0.025632	0.3758	0.353704
13	-0.198975	-2.9176	0.001951
14	-0.013716	-0.2011	0.420397
15	0.041904	0.6144	0.269789
16	0.020887	0.3063	0.379849
17	-0.078142	-1.1458	0.12658
18	0.015387	0.2256	0.410856
19	0.055586	0.8151	0.207972
20	-0.031145	-0.4567	0.324184
21	-0.036683	-0.5379	0.295609
22	0.035409	0.5192	0.302077
23	0.032298	0.4736	0.318139

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936382092gtqluga4ihxozy/1dt3b1293638284.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936382092gtqluga4ihxozy/1dt3b1293638284.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936382092gtqluga4ihxozy/2o2kw1293638284.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936382092gtqluga4ihxozy/2o2kw1293638284.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936382092gtqluga4ihxozy/3o2kw1293638284.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936382092gtqluga4ihxozy/3o2kw1293638284.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = Default ; 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 (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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