Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 26 Dec 2010 15:37:47 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/26/t1293377755g63m8ovu847j2jk.htm/, Retrieved Mon, 06 May 2024 12:26:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115670, Retrieved Mon, 06 May 2024 12:26:44 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

122

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [paper statistiek 2] [2010-12-26 15:37:47] [f3d6336ce664ba129edd250394d444d3] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115670&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115670&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115670&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

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	-0.146445	-1.1249	0.132601
2	-0.20074	-1.5419	0.06422
3	-0.14458	-1.1105	0.135636
4	0.577601	4.4366	2e-05
5	-0.140411	-1.0785	0.142597
6	-0.228807	-1.7575	0.04201
7	-0.169942	-1.3054	0.098421
8	0.51931	3.9889	9.3e-05
9	-0.185866	-1.4277	0.07933
10	-0.192448	-1.4782	0.072334
11	-0.120587	-0.9262	0.179046
12	0.713165	5.4779	0
13	-0.160559	-1.2333	0.111181
14	-0.224069	-1.7211	0.045236
15	-0.140098	-1.0761	0.14313
16	0.43806	3.3648	0.000676
17	-0.145921	-1.1208	0.133449

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.146445 & -1.1249 & 0.132601 \tabularnewline
2 & -0.20074 & -1.5419 & 0.06422 \tabularnewline
3 & -0.14458 & -1.1105 & 0.135636 \tabularnewline
4 & 0.577601 & 4.4366 & 2e-05 \tabularnewline
5 & -0.140411 & -1.0785 & 0.142597 \tabularnewline
6 & -0.228807 & -1.7575 & 0.04201 \tabularnewline
7 & -0.169942 & -1.3054 & 0.098421 \tabularnewline
8 & 0.51931 & 3.9889 & 9.3e-05 \tabularnewline
9 & -0.185866 & -1.4277 & 0.07933 \tabularnewline
10 & -0.192448 & -1.4782 & 0.072334 \tabularnewline
11 & -0.120587 & -0.9262 & 0.179046 \tabularnewline
12 & 0.713165 & 5.4779 & 0 \tabularnewline
13 & -0.160559 & -1.2333 & 0.111181 \tabularnewline
14 & -0.224069 & -1.7211 & 0.045236 \tabularnewline
15 & -0.140098 & -1.0761 & 0.14313 \tabularnewline
16 & 0.43806 & 3.3648 & 0.000676 \tabularnewline
17 & -0.145921 & -1.1208 & 0.133449 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115670&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]-0.146445[/C][C]-1.1249[/C][C]0.132601[/C][/ROW]
[ROW][C]2[/C][C]-0.20074[/C][C]-1.5419[/C][C]0.06422[/C][/ROW]
[ROW][C]3[/C][C]-0.14458[/C][C]-1.1105[/C][C]0.135636[/C][/ROW]
[ROW][C]4[/C][C]0.577601[/C][C]4.4366[/C][C]2e-05[/C][/ROW]
[ROW][C]5[/C][C]-0.140411[/C][C]-1.0785[/C][C]0.142597[/C][/ROW]
[ROW][C]6[/C][C]-0.228807[/C][C]-1.7575[/C][C]0.04201[/C][/ROW]
[ROW][C]7[/C][C]-0.169942[/C][C]-1.3054[/C][C]0.098421[/C][/ROW]
[ROW][C]8[/C][C]0.51931[/C][C]3.9889[/C][C]9.3e-05[/C][/ROW]
[ROW][C]9[/C][C]-0.185866[/C][C]-1.4277[/C][C]0.07933[/C][/ROW]
[ROW][C]10[/C][C]-0.192448[/C][C]-1.4782[/C][C]0.072334[/C][/ROW]
[ROW][C]11[/C][C]-0.120587[/C][C]-0.9262[/C][C]0.179046[/C][/ROW]
[ROW][C]12[/C][C]0.713165[/C][C]5.4779[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.160559[/C][C]-1.2333[/C][C]0.111181[/C][/ROW]
[ROW][C]14[/C][C]-0.224069[/C][C]-1.7211[/C][C]0.045236[/C][/ROW]
[ROW][C]15[/C][C]-0.140098[/C][C]-1.0761[/C][C]0.14313[/C][/ROW]
[ROW][C]16[/C][C]0.43806[/C][C]3.3648[/C][C]0.000676[/C][/ROW]
[ROW][C]17[/C][C]-0.145921[/C][C]-1.1208[/C][C]0.133449[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115670&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115670&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.146445	-1.1249	0.132601
2	-0.20074	-1.5419	0.06422
3	-0.14458	-1.1105	0.135636
4	0.577601	4.4366	2e-05
5	-0.140411	-1.0785	0.142597
6	-0.228807	-1.7575	0.04201
7	-0.169942	-1.3054	0.098421
8	0.51931	3.9889	9.3e-05
9	-0.185866	-1.4277	0.07933
10	-0.192448	-1.4782	0.072334
11	-0.120587	-0.9262	0.179046
12	0.713165	5.4779	0
13	-0.160559	-1.2333	0.111181
14	-0.224069	-1.7211	0.045236
15	-0.140098	-1.0761	0.14313
16	0.43806	3.3648	0.000676
17	-0.145921	-1.1208	0.133449

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.146445	-1.1249	0.132601
2	-0.227056	-1.744	0.043179
3	-0.230473	-1.7703	0.040922
4	0.519353	3.9892	9.3e-05
5	-0.062647	-0.4812	0.316077
6	-0.132809	-1.0201	0.155916
7	-0.135489	-1.0407	0.151128
8	0.224286	1.7228	0.045084
9	-0.140827	-1.0817	0.14189
10	-0.030282	-0.2326	0.408439
11	0.004731	0.0363	0.485569
12	0.527672	4.0531	7.5e-05
13	0.006887	0.0529	0.478994
14	-0.085489	-0.6567	0.256979
15	-0.088973	-0.6834	0.24851
16	-0.272156	-2.0905	0.020447
17	-0.058972	-0.453	0.326114

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.146445 & -1.1249 & 0.132601 \tabularnewline
2 & -0.227056 & -1.744 & 0.043179 \tabularnewline
3 & -0.230473 & -1.7703 & 0.040922 \tabularnewline
4 & 0.519353 & 3.9892 & 9.3e-05 \tabularnewline
5 & -0.062647 & -0.4812 & 0.316077 \tabularnewline
6 & -0.132809 & -1.0201 & 0.155916 \tabularnewline
7 & -0.135489 & -1.0407 & 0.151128 \tabularnewline
8 & 0.224286 & 1.7228 & 0.045084 \tabularnewline
9 & -0.140827 & -1.0817 & 0.14189 \tabularnewline
10 & -0.030282 & -0.2326 & 0.408439 \tabularnewline
11 & 0.004731 & 0.0363 & 0.485569 \tabularnewline
12 & 0.527672 & 4.0531 & 7.5e-05 \tabularnewline
13 & 0.006887 & 0.0529 & 0.478994 \tabularnewline
14 & -0.085489 & -0.6567 & 0.256979 \tabularnewline
15 & -0.088973 & -0.6834 & 0.24851 \tabularnewline
16 & -0.272156 & -2.0905 & 0.020447 \tabularnewline
17 & -0.058972 & -0.453 & 0.326114 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115670&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]-0.146445[/C][C]-1.1249[/C][C]0.132601[/C][/ROW]
[ROW][C]2[/C][C]-0.227056[/C][C]-1.744[/C][C]0.043179[/C][/ROW]
[ROW][C]3[/C][C]-0.230473[/C][C]-1.7703[/C][C]0.040922[/C][/ROW]
[ROW][C]4[/C][C]0.519353[/C][C]3.9892[/C][C]9.3e-05[/C][/ROW]
[ROW][C]5[/C][C]-0.062647[/C][C]-0.4812[/C][C]0.316077[/C][/ROW]
[ROW][C]6[/C][C]-0.132809[/C][C]-1.0201[/C][C]0.155916[/C][/ROW]
[ROW][C]7[/C][C]-0.135489[/C][C]-1.0407[/C][C]0.151128[/C][/ROW]
[ROW][C]8[/C][C]0.224286[/C][C]1.7228[/C][C]0.045084[/C][/ROW]
[ROW][C]9[/C][C]-0.140827[/C][C]-1.0817[/C][C]0.14189[/C][/ROW]
[ROW][C]10[/C][C]-0.030282[/C][C]-0.2326[/C][C]0.408439[/C][/ROW]
[ROW][C]11[/C][C]0.004731[/C][C]0.0363[/C][C]0.485569[/C][/ROW]
[ROW][C]12[/C][C]0.527672[/C][C]4.0531[/C][C]7.5e-05[/C][/ROW]
[ROW][C]13[/C][C]0.006887[/C][C]0.0529[/C][C]0.478994[/C][/ROW]
[ROW][C]14[/C][C]-0.085489[/C][C]-0.6567[/C][C]0.256979[/C][/ROW]
[ROW][C]15[/C][C]-0.088973[/C][C]-0.6834[/C][C]0.24851[/C][/ROW]
[ROW][C]16[/C][C]-0.272156[/C][C]-2.0905[/C][C]0.020447[/C][/ROW]
[ROW][C]17[/C][C]-0.058972[/C][C]-0.453[/C][C]0.326114[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115670&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115670&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.146445	-1.1249	0.132601
2	-0.227056	-1.744	0.043179
3	-0.230473	-1.7703	0.040922
4	0.519353	3.9892	9.3e-05
5	-0.062647	-0.4812	0.316077
6	-0.132809	-1.0201	0.155916
7	-0.135489	-1.0407	0.151128
8	0.224286	1.7228	0.045084
9	-0.140827	-1.0817	0.14189
10	-0.030282	-0.2326	0.408439
11	0.004731	0.0363	0.485569
12	0.527672	4.0531	7.5e-05
13	0.006887	0.0529	0.478994
14	-0.085489	-0.6567	0.256979
15	-0.088973	-0.6834	0.24851
16	-0.272156	-2.0905	0.020447
17	-0.058972	-0.453	0.326114

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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('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('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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code