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

Fri, 02 Dec 2011 10:45:14 -0500

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/2011/Dec/02/t13228407363mqrkl0nghubv1m.htm/, Retrieved Mon, 29 Apr 2024 07:50:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150301, Retrieved Mon, 29 Apr 2024 07:50:49 +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

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

-       [(Partial) Autocorrelation Function] [WS 9 ACF] [2011-12-02 15:45:14] [c98b04636162cea751932dfe577607eb] [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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150301&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150301&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150301&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' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.664088	5.1867	1e-06
2	0.182848	1.4281	0.079183
3	-0.054737	-0.4275	0.335257
4	-0.08022	-0.6265	0.266649
5	0.000268	0.0021	0.499169
6	0.055357	0.4324	0.333504
7	-0.021083	-0.1647	0.434877
8	-0.126485	-0.9879	0.163558
9	-0.110624	-0.864	0.195486
10	0.011011	0.086	0.465876
11	0.278723	2.1769	0.016684
12	0.425422	3.3227	0.000755
13	0.162119	1.2662	0.10513
14	-0.204685	-1.5986	0.057534
15	-0.378975	-2.9599	0.002189
16	-0.374087	-2.9217	0.002438
17	-0.281077	-2.1953	0.015979

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.664088 & 5.1867 & 1e-06 \tabularnewline
2 & 0.182848 & 1.4281 & 0.079183 \tabularnewline
3 & -0.054737 & -0.4275 & 0.335257 \tabularnewline
4 & -0.08022 & -0.6265 & 0.266649 \tabularnewline
5 & 0.000268 & 0.0021 & 0.499169 \tabularnewline
6 & 0.055357 & 0.4324 & 0.333504 \tabularnewline
7 & -0.021083 & -0.1647 & 0.434877 \tabularnewline
8 & -0.126485 & -0.9879 & 0.163558 \tabularnewline
9 & -0.110624 & -0.864 & 0.195486 \tabularnewline
10 & 0.011011 & 0.086 & 0.465876 \tabularnewline
11 & 0.278723 & 2.1769 & 0.016684 \tabularnewline
12 & 0.425422 & 3.3227 & 0.000755 \tabularnewline
13 & 0.162119 & 1.2662 & 0.10513 \tabularnewline
14 & -0.204685 & -1.5986 & 0.057534 \tabularnewline
15 & -0.378975 & -2.9599 & 0.002189 \tabularnewline
16 & -0.374087 & -2.9217 & 0.002438 \tabularnewline
17 & -0.281077 & -2.1953 & 0.015979 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150301&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]0.664088[/C][C]5.1867[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.182848[/C][C]1.4281[/C][C]0.079183[/C][/ROW]
[ROW][C]3[/C][C]-0.054737[/C][C]-0.4275[/C][C]0.335257[/C][/ROW]
[ROW][C]4[/C][C]-0.08022[/C][C]-0.6265[/C][C]0.266649[/C][/ROW]
[ROW][C]5[/C][C]0.000268[/C][C]0.0021[/C][C]0.499169[/C][/ROW]
[ROW][C]6[/C][C]0.055357[/C][C]0.4324[/C][C]0.333504[/C][/ROW]
[ROW][C]7[/C][C]-0.021083[/C][C]-0.1647[/C][C]0.434877[/C][/ROW]
[ROW][C]8[/C][C]-0.126485[/C][C]-0.9879[/C][C]0.163558[/C][/ROW]
[ROW][C]9[/C][C]-0.110624[/C][C]-0.864[/C][C]0.195486[/C][/ROW]
[ROW][C]10[/C][C]0.011011[/C][C]0.086[/C][C]0.465876[/C][/ROW]
[ROW][C]11[/C][C]0.278723[/C][C]2.1769[/C][C]0.016684[/C][/ROW]
[ROW][C]12[/C][C]0.425422[/C][C]3.3227[/C][C]0.000755[/C][/ROW]
[ROW][C]13[/C][C]0.162119[/C][C]1.2662[/C][C]0.10513[/C][/ROW]
[ROW][C]14[/C][C]-0.204685[/C][C]-1.5986[/C][C]0.057534[/C][/ROW]
[ROW][C]15[/C][C]-0.378975[/C][C]-2.9599[/C][C]0.002189[/C][/ROW]
[ROW][C]16[/C][C]-0.374087[/C][C]-2.9217[/C][C]0.002438[/C][/ROW]
[ROW][C]17[/C][C]-0.281077[/C][C]-2.1953[/C][C]0.015979[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150301&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150301&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	0.664088	5.1867	1e-06
2	0.182848	1.4281	0.079183
3	-0.054737	-0.4275	0.335257
4	-0.08022	-0.6265	0.266649
5	0.000268	0.0021	0.499169
6	0.055357	0.4324	0.333504
7	-0.021083	-0.1647	0.434877
8	-0.126485	-0.9879	0.163558
9	-0.110624	-0.864	0.195486
10	0.011011	0.086	0.465876
11	0.278723	2.1769	0.016684
12	0.425422	3.3227	0.000755
13	0.162119	1.2662	0.10513
14	-0.204685	-1.5986	0.057534
15	-0.378975	-2.9599	0.002189
16	-0.374087	-2.9217	0.002438
17	-0.281077	-2.1953	0.015979

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.664088	5.1867	1e-06
2	-0.461845	-3.6071	0.000313
3	0.169325	1.3225	0.095475
4	-0.048565	-0.3793	0.352889
5	0.096475	0.7535	0.227025
6	-0.048135	-0.3759	0.35413
7	-0.145162	-1.1338	0.130668
8	0.00198	0.0155	0.493857
9	0.072355	0.5651	0.287036
10	0.064207	0.5015	0.308922
11	0.413062	3.2261	0.00101
12	-0.125359	-0.9791	0.165702
13	-0.390632	-3.0509	0.001687
14	-0.002953	-0.0231	0.490836
15	-0.181506	-1.4176	0.080697
16	-0.122969	-0.9604	0.170318
17	-0.08424	-0.6579	0.256528

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.664088 & 5.1867 & 1e-06 \tabularnewline
2 & -0.461845 & -3.6071 & 0.000313 \tabularnewline
3 & 0.169325 & 1.3225 & 0.095475 \tabularnewline
4 & -0.048565 & -0.3793 & 0.352889 \tabularnewline
5 & 0.096475 & 0.7535 & 0.227025 \tabularnewline
6 & -0.048135 & -0.3759 & 0.35413 \tabularnewline
7 & -0.145162 & -1.1338 & 0.130668 \tabularnewline
8 & 0.00198 & 0.0155 & 0.493857 \tabularnewline
9 & 0.072355 & 0.5651 & 0.287036 \tabularnewline
10 & 0.064207 & 0.5015 & 0.308922 \tabularnewline
11 & 0.413062 & 3.2261 & 0.00101 \tabularnewline
12 & -0.125359 & -0.9791 & 0.165702 \tabularnewline
13 & -0.390632 & -3.0509 & 0.001687 \tabularnewline
14 & -0.002953 & -0.0231 & 0.490836 \tabularnewline
15 & -0.181506 & -1.4176 & 0.080697 \tabularnewline
16 & -0.122969 & -0.9604 & 0.170318 \tabularnewline
17 & -0.08424 & -0.6579 & 0.256528 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150301&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]0.664088[/C][C]5.1867[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.461845[/C][C]-3.6071[/C][C]0.000313[/C][/ROW]
[ROW][C]3[/C][C]0.169325[/C][C]1.3225[/C][C]0.095475[/C][/ROW]
[ROW][C]4[/C][C]-0.048565[/C][C]-0.3793[/C][C]0.352889[/C][/ROW]
[ROW][C]5[/C][C]0.096475[/C][C]0.7535[/C][C]0.227025[/C][/ROW]
[ROW][C]6[/C][C]-0.048135[/C][C]-0.3759[/C][C]0.35413[/C][/ROW]
[ROW][C]7[/C][C]-0.145162[/C][C]-1.1338[/C][C]0.130668[/C][/ROW]
[ROW][C]8[/C][C]0.00198[/C][C]0.0155[/C][C]0.493857[/C][/ROW]
[ROW][C]9[/C][C]0.072355[/C][C]0.5651[/C][C]0.287036[/C][/ROW]
[ROW][C]10[/C][C]0.064207[/C][C]0.5015[/C][C]0.308922[/C][/ROW]
[ROW][C]11[/C][C]0.413062[/C][C]3.2261[/C][C]0.00101[/C][/ROW]
[ROW][C]12[/C][C]-0.125359[/C][C]-0.9791[/C][C]0.165702[/C][/ROW]
[ROW][C]13[/C][C]-0.390632[/C][C]-3.0509[/C][C]0.001687[/C][/ROW]
[ROW][C]14[/C][C]-0.002953[/C][C]-0.0231[/C][C]0.490836[/C][/ROW]
[ROW][C]15[/C][C]-0.181506[/C][C]-1.4176[/C][C]0.080697[/C][/ROW]
[ROW][C]16[/C][C]-0.122969[/C][C]-0.9604[/C][C]0.170318[/C][/ROW]
[ROW][C]17[/C][C]-0.08424[/C][C]-0.6579[/C][C]0.256528[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150301&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150301&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	0.664088	5.1867	1e-06
2	-0.461845	-3.6071	0.000313
3	0.169325	1.3225	0.095475
4	-0.048565	-0.3793	0.352889
5	0.096475	0.7535	0.227025
6	-0.048135	-0.3759	0.35413
7	-0.145162	-1.1338	0.130668
8	0.00198	0.0155	0.493857
9	0.072355	0.5651	0.287036
10	0.064207	0.5015	0.308922
11	0.413062	3.2261	0.00101
12	-0.125359	-0.9791	0.165702
13	-0.390632	-3.0509	0.001687
14	-0.002953	-0.0231	0.490836
15	-0.181506	-1.4176	0.080697
16	-0.122969	-0.9604	0.170318
17	-0.08424	-0.6579	0.256528

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