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

Wed, 22 Dec 2010 16:10:53 +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/22/t1293034216rz9ihopepw3rb7q.htm/, Retrieved Mon, 06 May 2024 00:39:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114349, Retrieved Mon, 06 May 2024 00:39:57 +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

146

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

-       [(Partial) Autocorrelation Function] [Paper Auto Correl...] [2010-12-22 16:10:53] [f38914513f1f4d866974b642cdd0baea] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

0.504208603
0.457969746
0.509923035
0.606622221
0.626210885
0.626631316
0.676731276
0.613117455
0.486215861
0.452529881
0.467150592
0.494624486
0.444567428
0.478862605
0.544458459
0.628201498
0.672578445
0.652706633
0.645430599
0.576334011
0.618334234
0.639896351
0.72850438
0.694655375
0.689773225
0.712244845
0.760337031
0.837816503
0.90688735
0.976018259
0.962066806
0.837593417
0.767638807
0.580006349
0.387740568
0.331274078
0.345251272
0.380172806
0.399838692
0.425742404
0.524183377
0.597115327
0.541489699
0.615039426
0.547924872
0.574540743
0.603438956
0.577492342
0.614198564
0.584776957
0.62752366
0.676859979
0.645996894
0.596059959
0.585961029
0.607617528
0.598462423
0.638703699
0.64923164

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114349&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114349&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114349&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.420661	3.2037	0.001103
2	0.185354	1.4116	0.081703
3	0.008089	0.0616	0.475546
4	-0.173615	-1.3222	0.095643
5	-0.249457	-1.8998	0.031217
6	-0.361662	-2.7543	0.003921
7	-0.207587	-1.5809	0.059665
8	-0.14243	-1.0847	0.141269
9	-0.121996	-0.9291	0.178346
10	-0.002934	-0.0223	0.491126
11	0.165566	1.2609	0.106195
12	0.040571	0.309	0.379223
13	-7.6e-05	-6e-04	0.49977
14	0.06488	0.4941	0.311546
15	0.014649	0.1116	0.455777
16	-0.018527	-0.1411	0.44414
17	-0.16041	-1.2216	0.113392

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.420661 & 3.2037 & 0.001103 \tabularnewline
2 & 0.185354 & 1.4116 & 0.081703 \tabularnewline
3 & 0.008089 & 0.0616 & 0.475546 \tabularnewline
4 & -0.173615 & -1.3222 & 0.095643 \tabularnewline
5 & -0.249457 & -1.8998 & 0.031217 \tabularnewline
6 & -0.361662 & -2.7543 & 0.003921 \tabularnewline
7 & -0.207587 & -1.5809 & 0.059665 \tabularnewline
8 & -0.14243 & -1.0847 & 0.141269 \tabularnewline
9 & -0.121996 & -0.9291 & 0.178346 \tabularnewline
10 & -0.002934 & -0.0223 & 0.491126 \tabularnewline
11 & 0.165566 & 1.2609 & 0.106195 \tabularnewline
12 & 0.040571 & 0.309 & 0.379223 \tabularnewline
13 & -7.6e-05 & -6e-04 & 0.49977 \tabularnewline
14 & 0.06488 & 0.4941 & 0.311546 \tabularnewline
15 & 0.014649 & 0.1116 & 0.455777 \tabularnewline
16 & -0.018527 & -0.1411 & 0.44414 \tabularnewline
17 & -0.16041 & -1.2216 & 0.113392 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114349&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]0.420661[/C][C]3.2037[/C][C]0.001103[/C][/ROW]
[ROW][C]2[/C][C]0.185354[/C][C]1.4116[/C][C]0.081703[/C][/ROW]
[ROW][C]3[/C][C]0.008089[/C][C]0.0616[/C][C]0.475546[/C][/ROW]
[ROW][C]4[/C][C]-0.173615[/C][C]-1.3222[/C][C]0.095643[/C][/ROW]
[ROW][C]5[/C][C]-0.249457[/C][C]-1.8998[/C][C]0.031217[/C][/ROW]
[ROW][C]6[/C][C]-0.361662[/C][C]-2.7543[/C][C]0.003921[/C][/ROW]
[ROW][C]7[/C][C]-0.207587[/C][C]-1.5809[/C][C]0.059665[/C][/ROW]
[ROW][C]8[/C][C]-0.14243[/C][C]-1.0847[/C][C]0.141269[/C][/ROW]
[ROW][C]9[/C][C]-0.121996[/C][C]-0.9291[/C][C]0.178346[/C][/ROW]
[ROW][C]10[/C][C]-0.002934[/C][C]-0.0223[/C][C]0.491126[/C][/ROW]
[ROW][C]11[/C][C]0.165566[/C][C]1.2609[/C][C]0.106195[/C][/ROW]
[ROW][C]12[/C][C]0.040571[/C][C]0.309[/C][C]0.379223[/C][/ROW]
[ROW][C]13[/C][C]-7.6e-05[/C][C]-6e-04[/C][C]0.49977[/C][/ROW]
[ROW][C]14[/C][C]0.06488[/C][C]0.4941[/C][C]0.311546[/C][/ROW]
[ROW][C]15[/C][C]0.014649[/C][C]0.1116[/C][C]0.455777[/C][/ROW]
[ROW][C]16[/C][C]-0.018527[/C][C]-0.1411[/C][C]0.44414[/C][/ROW]
[ROW][C]17[/C][C]-0.16041[/C][C]-1.2216[/C][C]0.113392[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114349&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114349&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	0.420661	3.2037	0.001103
2	0.185354	1.4116	0.081703
3	0.008089	0.0616	0.475546
4	-0.173615	-1.3222	0.095643
5	-0.249457	-1.8998	0.031217
6	-0.361662	-2.7543	0.003921
7	-0.207587	-1.5809	0.059665
8	-0.14243	-1.0847	0.141269
9	-0.121996	-0.9291	0.178346
10	-0.002934	-0.0223	0.491126
11	0.165566	1.2609	0.106195
12	0.040571	0.309	0.379223
13	-7.6e-05	-6e-04	0.49977
14	0.06488	0.4941	0.311546
15	0.014649	0.1116	0.455777
16	-0.018527	-0.1411	0.44414
17	-0.16041	-1.2216	0.113392

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.420661	3.2037	0.001103
2	0.010203	0.0777	0.469165
3	-0.089165	-0.6791	0.249901
4	-0.181593	-1.383	0.085988
5	-0.128441	-0.9782	0.166024
6	-0.231593	-1.7638	0.041519
7	0.039357	0.2997	0.382726
8	-0.06932	-0.5279	0.299783
9	-0.123828	-0.943	0.174785
10	-0.018151	-0.1382	0.445268
11	0.130281	0.9922	0.162613
12	-0.224706	-1.7113	0.046184
13	-0.074147	-0.5647	0.287231
14	0.066553	0.5069	0.30709
15	-0.072408	-0.5514	0.291725
16	-0.061739	-0.4702	0.319992
17	-0.1547	-1.1782	0.121772

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.420661 & 3.2037 & 0.001103 \tabularnewline
2 & 0.010203 & 0.0777 & 0.469165 \tabularnewline
3 & -0.089165 & -0.6791 & 0.249901 \tabularnewline
4 & -0.181593 & -1.383 & 0.085988 \tabularnewline
5 & -0.128441 & -0.9782 & 0.166024 \tabularnewline
6 & -0.231593 & -1.7638 & 0.041519 \tabularnewline
7 & 0.039357 & 0.2997 & 0.382726 \tabularnewline
8 & -0.06932 & -0.5279 & 0.299783 \tabularnewline
9 & -0.123828 & -0.943 & 0.174785 \tabularnewline
10 & -0.018151 & -0.1382 & 0.445268 \tabularnewline
11 & 0.130281 & 0.9922 & 0.162613 \tabularnewline
12 & -0.224706 & -1.7113 & 0.046184 \tabularnewline
13 & -0.074147 & -0.5647 & 0.287231 \tabularnewline
14 & 0.066553 & 0.5069 & 0.30709 \tabularnewline
15 & -0.072408 & -0.5514 & 0.291725 \tabularnewline
16 & -0.061739 & -0.4702 & 0.319992 \tabularnewline
17 & -0.1547 & -1.1782 & 0.121772 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114349&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]0.420661[/C][C]3.2037[/C][C]0.001103[/C][/ROW]
[ROW][C]2[/C][C]0.010203[/C][C]0.0777[/C][C]0.469165[/C][/ROW]
[ROW][C]3[/C][C]-0.089165[/C][C]-0.6791[/C][C]0.249901[/C][/ROW]
[ROW][C]4[/C][C]-0.181593[/C][C]-1.383[/C][C]0.085988[/C][/ROW]
[ROW][C]5[/C][C]-0.128441[/C][C]-0.9782[/C][C]0.166024[/C][/ROW]
[ROW][C]6[/C][C]-0.231593[/C][C]-1.7638[/C][C]0.041519[/C][/ROW]
[ROW][C]7[/C][C]0.039357[/C][C]0.2997[/C][C]0.382726[/C][/ROW]
[ROW][C]8[/C][C]-0.06932[/C][C]-0.5279[/C][C]0.299783[/C][/ROW]
[ROW][C]9[/C][C]-0.123828[/C][C]-0.943[/C][C]0.174785[/C][/ROW]
[ROW][C]10[/C][C]-0.018151[/C][C]-0.1382[/C][C]0.445268[/C][/ROW]
[ROW][C]11[/C][C]0.130281[/C][C]0.9922[/C][C]0.162613[/C][/ROW]
[ROW][C]12[/C][C]-0.224706[/C][C]-1.7113[/C][C]0.046184[/C][/ROW]
[ROW][C]13[/C][C]-0.074147[/C][C]-0.5647[/C][C]0.287231[/C][/ROW]
[ROW][C]14[/C][C]0.066553[/C][C]0.5069[/C][C]0.30709[/C][/ROW]
[ROW][C]15[/C][C]-0.072408[/C][C]-0.5514[/C][C]0.291725[/C][/ROW]
[ROW][C]16[/C][C]-0.061739[/C][C]-0.4702[/C][C]0.319992[/C][/ROW]
[ROW][C]17[/C][C]-0.1547[/C][C]-1.1782[/C][C]0.121772[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114349&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114349&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	0.420661	3.2037	0.001103
2	0.010203	0.0777	0.469165
3	-0.089165	-0.6791	0.249901
4	-0.181593	-1.383	0.085988
5	-0.128441	-0.9782	0.166024
6	-0.231593	-1.7638	0.041519
7	0.039357	0.2997	0.382726
8	-0.06932	-0.5279	0.299783
9	-0.123828	-0.943	0.174785
10	-0.018151	-0.1382	0.445268
11	0.130281	0.9922	0.162613
12	-0.224706	-1.7113	0.046184
13	-0.074147	-0.5647	0.287231
14	0.066553	0.5069	0.30709
15	-0.072408	-0.5514	0.291725
16	-0.061739	-0.4702	0.319992
17	-0.1547	-1.1782	0.121772

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