Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 28 Mar 2012 07:11:09 -0400

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/2012/Mar/28/t1332933177q0qdjwagq6mua7a.htm/, Retrieved Sun, 05 May 2024 11:25:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=164167, Retrieved Sun, 05 May 2024 11:25:42 +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

KDGP2W12

Estimated Impact

173

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

-       [(Partial) Autocorrelation Function] [IKO opgave 6 bis ...] [2012-03-28 11:11:09] [93d78dde8d64c5a73537ad1fcc88d508] [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	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164167&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164167&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164167&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	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.977655	8.9604	0
2	0.950128	8.7081	0
3	0.921678	8.4473	0
4	0.892459	8.1795	0
5	0.862325	7.9033	0
6	0.832627	7.6312	0
7	0.802277	7.353	0
8	0.773252	7.087	0
9	0.741559	6.7965	0
10	0.710512	6.512	0
11	0.680029	6.2326	0
12	0.646388	5.9242	0
13	0.609049	5.582	0
14	0.567355	5.1999	1e-06
15	0.522635	4.79	4e-06
16	0.477589	4.3772	1.7e-05
17	0.43384	3.9762	7.4e-05
18	0.390877	3.5824	0.000285
19	0.348711	3.196	0.000982

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.977655 & 8.9604 & 0 \tabularnewline
2 & 0.950128 & 8.7081 & 0 \tabularnewline
3 & 0.921678 & 8.4473 & 0 \tabularnewline
4 & 0.892459 & 8.1795 & 0 \tabularnewline
5 & 0.862325 & 7.9033 & 0 \tabularnewline
6 & 0.832627 & 7.6312 & 0 \tabularnewline
7 & 0.802277 & 7.353 & 0 \tabularnewline
8 & 0.773252 & 7.087 & 0 \tabularnewline
9 & 0.741559 & 6.7965 & 0 \tabularnewline
10 & 0.710512 & 6.512 & 0 \tabularnewline
11 & 0.680029 & 6.2326 & 0 \tabularnewline
12 & 0.646388 & 5.9242 & 0 \tabularnewline
13 & 0.609049 & 5.582 & 0 \tabularnewline
14 & 0.567355 & 5.1999 & 1e-06 \tabularnewline
15 & 0.522635 & 4.79 & 4e-06 \tabularnewline
16 & 0.477589 & 4.3772 & 1.7e-05 \tabularnewline
17 & 0.43384 & 3.9762 & 7.4e-05 \tabularnewline
18 & 0.390877 & 3.5824 & 0.000285 \tabularnewline
19 & 0.348711 & 3.196 & 0.000982 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164167&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]0.977655[/C][C]8.9604[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.950128[/C][C]8.7081[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.921678[/C][C]8.4473[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.892459[/C][C]8.1795[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.862325[/C][C]7.9033[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.832627[/C][C]7.6312[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.802277[/C][C]7.353[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.773252[/C][C]7.087[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.741559[/C][C]6.7965[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.710512[/C][C]6.512[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.680029[/C][C]6.2326[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.646388[/C][C]5.9242[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.609049[/C][C]5.582[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.567355[/C][C]5.1999[/C][C]1e-06[/C][/ROW]
[ROW][C]15[/C][C]0.522635[/C][C]4.79[/C][C]4e-06[/C][/ROW]
[ROW][C]16[/C][C]0.477589[/C][C]4.3772[/C][C]1.7e-05[/C][/ROW]
[ROW][C]17[/C][C]0.43384[/C][C]3.9762[/C][C]7.4e-05[/C][/ROW]
[ROW][C]18[/C][C]0.390877[/C][C]3.5824[/C][C]0.000285[/C][/ROW]
[ROW][C]19[/C][C]0.348711[/C][C]3.196[/C][C]0.000982[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164167&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164167&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	0.977655	8.9604	0
2	0.950128	8.7081	0
3	0.921678	8.4473	0
4	0.892459	8.1795	0
5	0.862325	7.9033	0
6	0.832627	7.6312	0
7	0.802277	7.353	0
8	0.773252	7.087	0
9	0.741559	6.7965	0
10	0.710512	6.512	0
11	0.680029	6.2326	0
12	0.646388	5.9242	0
13	0.609049	5.582	0
14	0.567355	5.1999	1e-06
15	0.522635	4.79	4e-06
16	0.477589	4.3772	1.7e-05
17	0.43384	3.9762	7.4e-05
18	0.390877	3.5824	0.000285
19	0.348711	3.196	0.000982

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.977655	8.9604	0
2	-0.12856	-1.1783	0.121007
3	-0.021872	-0.2005	0.420801
4	-0.029291	-0.2685	0.394504
5	-0.032799	-0.3006	0.382229
6	-0.001502	-0.0138	0.494524
7	-0.033378	-0.3059	0.380212
8	0.017558	0.1609	0.436269
9	-0.084856	-0.7777	0.21946
10	0.010699	0.0981	0.46106
11	-0.008909	-0.0817	0.467559
12	-0.094614	-0.8672	0.194164
13	-0.087184	-0.7991	0.213256
14	-0.112458	-1.0307	0.15282
15	-0.073638	-0.6749	0.250796
16	-0.028138	-0.2579	0.398563
17	0.00559	0.0512	0.479631
18	-0.018648	-0.1709	0.432351
19	-0.023534	-0.2157	0.414876

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.977655 & 8.9604 & 0 \tabularnewline
2 & -0.12856 & -1.1783 & 0.121007 \tabularnewline
3 & -0.021872 & -0.2005 & 0.420801 \tabularnewline
4 & -0.029291 & -0.2685 & 0.394504 \tabularnewline
5 & -0.032799 & -0.3006 & 0.382229 \tabularnewline
6 & -0.001502 & -0.0138 & 0.494524 \tabularnewline
7 & -0.033378 & -0.3059 & 0.380212 \tabularnewline
8 & 0.017558 & 0.1609 & 0.436269 \tabularnewline
9 & -0.084856 & -0.7777 & 0.21946 \tabularnewline
10 & 0.010699 & 0.0981 & 0.46106 \tabularnewline
11 & -0.008909 & -0.0817 & 0.467559 \tabularnewline
12 & -0.094614 & -0.8672 & 0.194164 \tabularnewline
13 & -0.087184 & -0.7991 & 0.213256 \tabularnewline
14 & -0.112458 & -1.0307 & 0.15282 \tabularnewline
15 & -0.073638 & -0.6749 & 0.250796 \tabularnewline
16 & -0.028138 & -0.2579 & 0.398563 \tabularnewline
17 & 0.00559 & 0.0512 & 0.479631 \tabularnewline
18 & -0.018648 & -0.1709 & 0.432351 \tabularnewline
19 & -0.023534 & -0.2157 & 0.414876 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164167&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]0.977655[/C][C]8.9604[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.12856[/C][C]-1.1783[/C][C]0.121007[/C][/ROW]
[ROW][C]3[/C][C]-0.021872[/C][C]-0.2005[/C][C]0.420801[/C][/ROW]
[ROW][C]4[/C][C]-0.029291[/C][C]-0.2685[/C][C]0.394504[/C][/ROW]
[ROW][C]5[/C][C]-0.032799[/C][C]-0.3006[/C][C]0.382229[/C][/ROW]
[ROW][C]6[/C][C]-0.001502[/C][C]-0.0138[/C][C]0.494524[/C][/ROW]
[ROW][C]7[/C][C]-0.033378[/C][C]-0.3059[/C][C]0.380212[/C][/ROW]
[ROW][C]8[/C][C]0.017558[/C][C]0.1609[/C][C]0.436269[/C][/ROW]
[ROW][C]9[/C][C]-0.084856[/C][C]-0.7777[/C][C]0.21946[/C][/ROW]
[ROW][C]10[/C][C]0.010699[/C][C]0.0981[/C][C]0.46106[/C][/ROW]
[ROW][C]11[/C][C]-0.008909[/C][C]-0.0817[/C][C]0.467559[/C][/ROW]
[ROW][C]12[/C][C]-0.094614[/C][C]-0.8672[/C][C]0.194164[/C][/ROW]
[ROW][C]13[/C][C]-0.087184[/C][C]-0.7991[/C][C]0.213256[/C][/ROW]
[ROW][C]14[/C][C]-0.112458[/C][C]-1.0307[/C][C]0.15282[/C][/ROW]
[ROW][C]15[/C][C]-0.073638[/C][C]-0.6749[/C][C]0.250796[/C][/ROW]
[ROW][C]16[/C][C]-0.028138[/C][C]-0.2579[/C][C]0.398563[/C][/ROW]
[ROW][C]17[/C][C]0.00559[/C][C]0.0512[/C][C]0.479631[/C][/ROW]
[ROW][C]18[/C][C]-0.018648[/C][C]-0.1709[/C][C]0.432351[/C][/ROW]
[ROW][C]19[/C][C]-0.023534[/C][C]-0.2157[/C][C]0.414876[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164167&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164167&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	0.977655	8.9604	0
2	-0.12856	-1.1783	0.121007
3	-0.021872	-0.2005	0.420801
4	-0.029291	-0.2685	0.394504
5	-0.032799	-0.3006	0.382229
6	-0.001502	-0.0138	0.494524
7	-0.033378	-0.3059	0.380212
8	0.017558	0.1609	0.436269
9	-0.084856	-0.7777	0.21946
10	0.010699	0.0981	0.46106
11	-0.008909	-0.0817	0.467559
12	-0.094614	-0.8672	0.194164
13	-0.087184	-0.7991	0.213256
14	-0.112458	-1.0307	0.15282
15	-0.073638	-0.6749	0.250796
16	-0.028138	-0.2579	0.398563
17	0.00559	0.0512	0.479631
18	-0.018648	-0.1709	0.432351
19	-0.023534	-0.2157	0.414876

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 = 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 ; 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