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, 25 Apr 2012 07:28:23 -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/Apr/25/t1335353322rmqzfqlom1ly872.htm/, Retrieved Tue, 07 May 2024 01:43:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=164816, Retrieved Tue, 07 May 2024 01:43:50 +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

131

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

-       [(Partial) Autocorrelation Function] [] [2012-04-25 11:28:23] [7e303677a10d2f0ca36d048a9aad5f48] [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=164816&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=164816&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164816&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	0.959062	8.1379	0
2	0.911981	7.7384	0
3	0.863033	7.3231	0
4	0.813862	6.9058	0
5	0.764677	6.4885	0
6	0.713687	6.0558	0
7	0.661021	5.6089	0
8	0.608431	5.1627	1e-06
9	0.559965	4.7515	5e-06
10	0.512207	4.3462	2.2e-05
11	0.464354	3.9402	9.3e-05
12	0.415086	3.5221	0.000374
13	0.363448	3.084	0.001448
14	0.308378	2.6167	0.005407
15	0.269125	2.2836	0.012674
16	0.240102	2.0373	0.022646
17	0.216616	1.838	0.03509
18	0.192811	1.6361	0.053096

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.959062 & 8.1379 & 0 \tabularnewline
2 & 0.911981 & 7.7384 & 0 \tabularnewline
3 & 0.863033 & 7.3231 & 0 \tabularnewline
4 & 0.813862 & 6.9058 & 0 \tabularnewline
5 & 0.764677 & 6.4885 & 0 \tabularnewline
6 & 0.713687 & 6.0558 & 0 \tabularnewline
7 & 0.661021 & 5.6089 & 0 \tabularnewline
8 & 0.608431 & 5.1627 & 1e-06 \tabularnewline
9 & 0.559965 & 4.7515 & 5e-06 \tabularnewline
10 & 0.512207 & 4.3462 & 2.2e-05 \tabularnewline
11 & 0.464354 & 3.9402 & 9.3e-05 \tabularnewline
12 & 0.415086 & 3.5221 & 0.000374 \tabularnewline
13 & 0.363448 & 3.084 & 0.001448 \tabularnewline
14 & 0.308378 & 2.6167 & 0.005407 \tabularnewline
15 & 0.269125 & 2.2836 & 0.012674 \tabularnewline
16 & 0.240102 & 2.0373 & 0.022646 \tabularnewline
17 & 0.216616 & 1.838 & 0.03509 \tabularnewline
18 & 0.192811 & 1.6361 & 0.053096 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164816&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]0.959062[/C][C]8.1379[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.911981[/C][C]7.7384[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.863033[/C][C]7.3231[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.813862[/C][C]6.9058[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.764677[/C][C]6.4885[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.713687[/C][C]6.0558[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.661021[/C][C]5.6089[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.608431[/C][C]5.1627[/C][C]1e-06[/C][/ROW]
[ROW][C]9[/C][C]0.559965[/C][C]4.7515[/C][C]5e-06[/C][/ROW]
[ROW][C]10[/C][C]0.512207[/C][C]4.3462[/C][C]2.2e-05[/C][/ROW]
[ROW][C]11[/C][C]0.464354[/C][C]3.9402[/C][C]9.3e-05[/C][/ROW]
[ROW][C]12[/C][C]0.415086[/C][C]3.5221[/C][C]0.000374[/C][/ROW]
[ROW][C]13[/C][C]0.363448[/C][C]3.084[/C][C]0.001448[/C][/ROW]
[ROW][C]14[/C][C]0.308378[/C][C]2.6167[/C][C]0.005407[/C][/ROW]
[ROW][C]15[/C][C]0.269125[/C][C]2.2836[/C][C]0.012674[/C][/ROW]
[ROW][C]16[/C][C]0.240102[/C][C]2.0373[/C][C]0.022646[/C][/ROW]
[ROW][C]17[/C][C]0.216616[/C][C]1.838[/C][C]0.03509[/C][/ROW]
[ROW][C]18[/C][C]0.192811[/C][C]1.6361[/C][C]0.053096[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164816&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164816&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	0.959062	8.1379	0
2	0.911981	7.7384	0
3	0.863033	7.3231	0
4	0.813862	6.9058	0
5	0.764677	6.4885	0
6	0.713687	6.0558	0
7	0.661021	5.6089	0
8	0.608431	5.1627	1e-06
9	0.559965	4.7515	5e-06
10	0.512207	4.3462	2.2e-05
11	0.464354	3.9402	9.3e-05
12	0.415086	3.5221	0.000374
13	0.363448	3.084	0.001448
14	0.308378	2.6167	0.005407
15	0.269125	2.2836	0.012674
16	0.240102	2.0373	0.022646
17	0.216616	1.838	0.03509
18	0.192811	1.6361	0.053096

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.959062	8.1379	0
2	-0.097509	-0.8274	0.205375
3	-0.042571	-0.3612	0.359494
4	-0.026201	-0.2223	0.412345
5	-0.026731	-0.2268	0.410602
6	-0.050649	-0.4298	0.334323
7	-0.047894	-0.4064	0.342828
8	-0.027318	-0.2318	0.408676
9	0.019953	0.1693	0.433014
10	-0.029408	-0.2495	0.401829
11	-0.035121	-0.298	0.383275
12	-0.049843	-0.4229	0.336804
13	-0.062079	-0.5268	0.299992
14	-0.079586	-0.6753	0.250821
15	0.165894	1.4077	0.081768
16	0.075787	0.6431	0.26111
17	0.026039	0.2209	0.412879
18	-0.040567	-0.3442	0.365841

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.959062 & 8.1379 & 0 \tabularnewline
2 & -0.097509 & -0.8274 & 0.205375 \tabularnewline
3 & -0.042571 & -0.3612 & 0.359494 \tabularnewline
4 & -0.026201 & -0.2223 & 0.412345 \tabularnewline
5 & -0.026731 & -0.2268 & 0.410602 \tabularnewline
6 & -0.050649 & -0.4298 & 0.334323 \tabularnewline
7 & -0.047894 & -0.4064 & 0.342828 \tabularnewline
8 & -0.027318 & -0.2318 & 0.408676 \tabularnewline
9 & 0.019953 & 0.1693 & 0.433014 \tabularnewline
10 & -0.029408 & -0.2495 & 0.401829 \tabularnewline
11 & -0.035121 & -0.298 & 0.383275 \tabularnewline
12 & -0.049843 & -0.4229 & 0.336804 \tabularnewline
13 & -0.062079 & -0.5268 & 0.299992 \tabularnewline
14 & -0.079586 & -0.6753 & 0.250821 \tabularnewline
15 & 0.165894 & 1.4077 & 0.081768 \tabularnewline
16 & 0.075787 & 0.6431 & 0.26111 \tabularnewline
17 & 0.026039 & 0.2209 & 0.412879 \tabularnewline
18 & -0.040567 & -0.3442 & 0.365841 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164816&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]0.959062[/C][C]8.1379[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.097509[/C][C]-0.8274[/C][C]0.205375[/C][/ROW]
[ROW][C]3[/C][C]-0.042571[/C][C]-0.3612[/C][C]0.359494[/C][/ROW]
[ROW][C]4[/C][C]-0.026201[/C][C]-0.2223[/C][C]0.412345[/C][/ROW]
[ROW][C]5[/C][C]-0.026731[/C][C]-0.2268[/C][C]0.410602[/C][/ROW]
[ROW][C]6[/C][C]-0.050649[/C][C]-0.4298[/C][C]0.334323[/C][/ROW]
[ROW][C]7[/C][C]-0.047894[/C][C]-0.4064[/C][C]0.342828[/C][/ROW]
[ROW][C]8[/C][C]-0.027318[/C][C]-0.2318[/C][C]0.408676[/C][/ROW]
[ROW][C]9[/C][C]0.019953[/C][C]0.1693[/C][C]0.433014[/C][/ROW]
[ROW][C]10[/C][C]-0.029408[/C][C]-0.2495[/C][C]0.401829[/C][/ROW]
[ROW][C]11[/C][C]-0.035121[/C][C]-0.298[/C][C]0.383275[/C][/ROW]
[ROW][C]12[/C][C]-0.049843[/C][C]-0.4229[/C][C]0.336804[/C][/ROW]
[ROW][C]13[/C][C]-0.062079[/C][C]-0.5268[/C][C]0.299992[/C][/ROW]
[ROW][C]14[/C][C]-0.079586[/C][C]-0.6753[/C][C]0.250821[/C][/ROW]
[ROW][C]15[/C][C]0.165894[/C][C]1.4077[/C][C]0.081768[/C][/ROW]
[ROW][C]16[/C][C]0.075787[/C][C]0.6431[/C][C]0.26111[/C][/ROW]
[ROW][C]17[/C][C]0.026039[/C][C]0.2209[/C][C]0.412879[/C][/ROW]
[ROW][C]18[/C][C]-0.040567[/C][C]-0.3442[/C][C]0.365841[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164816&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164816&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	0.959062	8.1379	0
2	-0.097509	-0.8274	0.205375
3	-0.042571	-0.3612	0.359494
4	-0.026201	-0.2223	0.412345
5	-0.026731	-0.2268	0.410602
6	-0.050649	-0.4298	0.334323
7	-0.047894	-0.4064	0.342828
8	-0.027318	-0.2318	0.408676
9	0.019953	0.1693	0.433014
10	-0.029408	-0.2495	0.401829
11	-0.035121	-0.298	0.383275
12	-0.049843	-0.4229	0.336804
13	-0.062079	-0.5268	0.299992
14	-0.079586	-0.6753	0.250821
15	0.165894	1.4077	0.081768
16	0.075787	0.6431	0.26111
17	0.026039	0.2209	0.412879
18	-0.040567	-0.3442	0.365841

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '1'
par2 <- '1'
par1 <- 'Default'
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