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

Thu, 26 Nov 2009 03:14:07 -0700

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/2009/Nov/26/t1259230515ymgsnpbpag6lnw3.htm/, Retrieved Sun, 28 Apr 2024 22:00:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59775, Retrieved Sun, 28 Apr 2024 22:00:12 +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

178

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

-       [(Partial) Autocorrelation Function] [] [2009-11-26 10:14:07] [a5b01ef1969ffd97a40c5fefe56a50d0] [Current]
-   P     [(Partial) Autocorrelation Function] [] [2009-12-03 08:28:18] [2f674a53c3d7aaa1bcf80e66074d3c9b] 

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

1.8
1.6
1.9
1.7
1.6
1.3
1.1
1.9
2.6
2.3
2.4
2.2
2
2.9
2.6
2.3
2.3
2.6
3.1
2.8
2.5
2.9
3.1
3.1
3.2
2.5
2.6
2.9
2.6
2.4
1.7
2
2.2
1.9
1.6
1.6
1.2
1.2
1.5
1.6
1.7
1.8
1.8
1.8
1.3
1.3
1.4
1.1
1.5
2.2
2.9
3.1
3.5
3.6
4.4
4.2
5.2
5.8
5.9
5.4
5.5

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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59775&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59775&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59775&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.079789	0.618	0.269443
2	-0.073334	-0.568	0.286063
3	0.010733	0.0831	0.467009
4	0.065322	0.506	0.307363
5	0.207598	1.608	0.056538
6	0.110256	0.854	0.198241
7	-0.171652	-1.3296	0.09434
8	0.092366	0.7155	0.238548
9	-0.012728	-0.0986	0.460896
10	0.04272	0.3309	0.370934
11	0.185855	1.4396	0.077585
12	-0.315496	-2.4438	0.008745
13	-0.090613	-0.7019	0.242732
14	0.182783	1.4158	0.080997
15	-0.01069	-0.0828	0.467141
16	-0.005512	-0.0427	0.483043
17	-0.118284	-0.9162	0.181608

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.079789 & 0.618 & 0.269443 \tabularnewline
2 & -0.073334 & -0.568 & 0.286063 \tabularnewline
3 & 0.010733 & 0.0831 & 0.467009 \tabularnewline
4 & 0.065322 & 0.506 & 0.307363 \tabularnewline
5 & 0.207598 & 1.608 & 0.056538 \tabularnewline
6 & 0.110256 & 0.854 & 0.198241 \tabularnewline
7 & -0.171652 & -1.3296 & 0.09434 \tabularnewline
8 & 0.092366 & 0.7155 & 0.238548 \tabularnewline
9 & -0.012728 & -0.0986 & 0.460896 \tabularnewline
10 & 0.04272 & 0.3309 & 0.370934 \tabularnewline
11 & 0.185855 & 1.4396 & 0.077585 \tabularnewline
12 & -0.315496 & -2.4438 & 0.008745 \tabularnewline
13 & -0.090613 & -0.7019 & 0.242732 \tabularnewline
14 & 0.182783 & 1.4158 & 0.080997 \tabularnewline
15 & -0.01069 & -0.0828 & 0.467141 \tabularnewline
16 & -0.005512 & -0.0427 & 0.483043 \tabularnewline
17 & -0.118284 & -0.9162 & 0.181608 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59775&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]0.079789[/C][C]0.618[/C][C]0.269443[/C][/ROW]
[ROW][C]2[/C][C]-0.073334[/C][C]-0.568[/C][C]0.286063[/C][/ROW]
[ROW][C]3[/C][C]0.010733[/C][C]0.0831[/C][C]0.467009[/C][/ROW]
[ROW][C]4[/C][C]0.065322[/C][C]0.506[/C][C]0.307363[/C][/ROW]
[ROW][C]5[/C][C]0.207598[/C][C]1.608[/C][C]0.056538[/C][/ROW]
[ROW][C]6[/C][C]0.110256[/C][C]0.854[/C][C]0.198241[/C][/ROW]
[ROW][C]7[/C][C]-0.171652[/C][C]-1.3296[/C][C]0.09434[/C][/ROW]
[ROW][C]8[/C][C]0.092366[/C][C]0.7155[/C][C]0.238548[/C][/ROW]
[ROW][C]9[/C][C]-0.012728[/C][C]-0.0986[/C][C]0.460896[/C][/ROW]
[ROW][C]10[/C][C]0.04272[/C][C]0.3309[/C][C]0.370934[/C][/ROW]
[ROW][C]11[/C][C]0.185855[/C][C]1.4396[/C][C]0.077585[/C][/ROW]
[ROW][C]12[/C][C]-0.315496[/C][C]-2.4438[/C][C]0.008745[/C][/ROW]
[ROW][C]13[/C][C]-0.090613[/C][C]-0.7019[/C][C]0.242732[/C][/ROW]
[ROW][C]14[/C][C]0.182783[/C][C]1.4158[/C][C]0.080997[/C][/ROW]
[ROW][C]15[/C][C]-0.01069[/C][C]-0.0828[/C][C]0.467141[/C][/ROW]
[ROW][C]16[/C][C]-0.005512[/C][C]-0.0427[/C][C]0.483043[/C][/ROW]
[ROW][C]17[/C][C]-0.118284[/C][C]-0.9162[/C][C]0.181608[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59775&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59775&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	0.079789	0.618	0.269443
2	-0.073334	-0.568	0.286063
3	0.010733	0.0831	0.467009
4	0.065322	0.506	0.307363
5	0.207598	1.608	0.056538
6	0.110256	0.854	0.198241
7	-0.171652	-1.3296	0.09434
8	0.092366	0.7155	0.238548
9	-0.012728	-0.0986	0.460896
10	0.04272	0.3309	0.370934
11	0.185855	1.4396	0.077585
12	-0.315496	-2.4438	0.008745
13	-0.090613	-0.7019	0.242732
14	0.182783	1.4158	0.080997
15	-0.01069	-0.0828	0.467141
16	-0.005512	-0.0427	0.483043
17	-0.118284	-0.9162	0.181608

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.079789	0.618	0.269443
2	-0.080211	-0.6213	0.268375
3	0.023757	0.184	0.42731
4	0.05721	0.4431	0.329626
5	0.20293	1.5719	0.060618
6	0.091539	0.7091	0.240518
7	-0.166538	-1.29	0.101
8	0.129421	1.0025	0.160066
9	-0.089126	-0.6904	0.246313
10	0.026606	0.2061	0.418709
11	0.166172	1.2872	0.10149
12	-0.3504	-2.7142	0.004331
13	0.017679	0.1369	0.445769
14	0.146458	1.1345	0.130558
15	-0.075128	-0.5819	0.281394
16	-0.013294	-0.103	0.459162
17	-0.028509	-0.2208	0.412987

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.079789 & 0.618 & 0.269443 \tabularnewline
2 & -0.080211 & -0.6213 & 0.268375 \tabularnewline
3 & 0.023757 & 0.184 & 0.42731 \tabularnewline
4 & 0.05721 & 0.4431 & 0.329626 \tabularnewline
5 & 0.20293 & 1.5719 & 0.060618 \tabularnewline
6 & 0.091539 & 0.7091 & 0.240518 \tabularnewline
7 & -0.166538 & -1.29 & 0.101 \tabularnewline
8 & 0.129421 & 1.0025 & 0.160066 \tabularnewline
9 & -0.089126 & -0.6904 & 0.246313 \tabularnewline
10 & 0.026606 & 0.2061 & 0.418709 \tabularnewline
11 & 0.166172 & 1.2872 & 0.10149 \tabularnewline
12 & -0.3504 & -2.7142 & 0.004331 \tabularnewline
13 & 0.017679 & 0.1369 & 0.445769 \tabularnewline
14 & 0.146458 & 1.1345 & 0.130558 \tabularnewline
15 & -0.075128 & -0.5819 & 0.281394 \tabularnewline
16 & -0.013294 & -0.103 & 0.459162 \tabularnewline
17 & -0.028509 & -0.2208 & 0.412987 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59775&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]0.079789[/C][C]0.618[/C][C]0.269443[/C][/ROW]
[ROW][C]2[/C][C]-0.080211[/C][C]-0.6213[/C][C]0.268375[/C][/ROW]
[ROW][C]3[/C][C]0.023757[/C][C]0.184[/C][C]0.42731[/C][/ROW]
[ROW][C]4[/C][C]0.05721[/C][C]0.4431[/C][C]0.329626[/C][/ROW]
[ROW][C]5[/C][C]0.20293[/C][C]1.5719[/C][C]0.060618[/C][/ROW]
[ROW][C]6[/C][C]0.091539[/C][C]0.7091[/C][C]0.240518[/C][/ROW]
[ROW][C]7[/C][C]-0.166538[/C][C]-1.29[/C][C]0.101[/C][/ROW]
[ROW][C]8[/C][C]0.129421[/C][C]1.0025[/C][C]0.160066[/C][/ROW]
[ROW][C]9[/C][C]-0.089126[/C][C]-0.6904[/C][C]0.246313[/C][/ROW]
[ROW][C]10[/C][C]0.026606[/C][C]0.2061[/C][C]0.418709[/C][/ROW]
[ROW][C]11[/C][C]0.166172[/C][C]1.2872[/C][C]0.10149[/C][/ROW]
[ROW][C]12[/C][C]-0.3504[/C][C]-2.7142[/C][C]0.004331[/C][/ROW]
[ROW][C]13[/C][C]0.017679[/C][C]0.1369[/C][C]0.445769[/C][/ROW]
[ROW][C]14[/C][C]0.146458[/C][C]1.1345[/C][C]0.130558[/C][/ROW]
[ROW][C]15[/C][C]-0.075128[/C][C]-0.5819[/C][C]0.281394[/C][/ROW]
[ROW][C]16[/C][C]-0.013294[/C][C]-0.103[/C][C]0.459162[/C][/ROW]
[ROW][C]17[/C][C]-0.028509[/C][C]-0.2208[/C][C]0.412987[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59775&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59775&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	0.079789	0.618	0.269443
2	-0.080211	-0.6213	0.268375
3	0.023757	0.184	0.42731
4	0.05721	0.4431	0.329626
5	0.20293	1.5719	0.060618
6	0.091539	0.7091	0.240518
7	-0.166538	-1.29	0.101
8	0.129421	1.0025	0.160066
9	-0.089126	-0.6904	0.246313
10	0.026606	0.2061	0.418709
11	0.166172	1.2872	0.10149
12	-0.3504	-2.7142	0.004331
13	0.017679	0.1369	0.445769
14	0.146458	1.1345	0.130558
15	-0.075128	-0.5819	0.281394
16	-0.013294	-0.103	0.459162
17	-0.028509	-0.2208	0.412987

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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