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

Mon, 18 Mar 2013 19:01:27 -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/2013/Mar/18/t1363647707faicqjp53nhn5tl.htm/, Retrieved Sat, 27 Apr 2024 05:51:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207872, Retrieved Sat, 27 Apr 2024 05:51:28 +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

151

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

-       [(Partial) Autocorrelation Function] [Opgave 6 bis oefe...] [2013-03-18 23:01:27] [bf566d88435d8cc6ce5d208f6f8dd684] [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	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207872&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207872&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207872&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.865975	7.348	0
2	0.770787	6.5403	0
3	0.76583	6.4983	0
4	0.744498	6.3173	0
5	0.651547	5.5286	0
6	0.576048	4.8879	3e-06
7	0.571246	4.8472	3e-06
8	0.581963	4.9381	2e-06
9	0.519559	4.4086	1.8e-05
10	0.434927	3.6905	0.000216
11	0.468131	3.9722	8.4e-05
12	0.504288	4.279	2.8e-05
13	0.394487	3.3473	0.00065
14	0.30714	2.6062	0.00556
15	0.285586	2.4233	0.008948
16	0.264376	2.2433	0.013977
17	0.184528	1.5658	0.060893
18	0.115175	0.9773	0.165849

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.865975 & 7.348 & 0 \tabularnewline
2 & 0.770787 & 6.5403 & 0 \tabularnewline
3 & 0.76583 & 6.4983 & 0 \tabularnewline
4 & 0.744498 & 6.3173 & 0 \tabularnewline
5 & 0.651547 & 5.5286 & 0 \tabularnewline
6 & 0.576048 & 4.8879 & 3e-06 \tabularnewline
7 & 0.571246 & 4.8472 & 3e-06 \tabularnewline
8 & 0.581963 & 4.9381 & 2e-06 \tabularnewline
9 & 0.519559 & 4.4086 & 1.8e-05 \tabularnewline
10 & 0.434927 & 3.6905 & 0.000216 \tabularnewline
11 & 0.468131 & 3.9722 & 8.4e-05 \tabularnewline
12 & 0.504288 & 4.279 & 2.8e-05 \tabularnewline
13 & 0.394487 & 3.3473 & 0.00065 \tabularnewline
14 & 0.30714 & 2.6062 & 0.00556 \tabularnewline
15 & 0.285586 & 2.4233 & 0.008948 \tabularnewline
16 & 0.264376 & 2.2433 & 0.013977 \tabularnewline
17 & 0.184528 & 1.5658 & 0.060893 \tabularnewline
18 & 0.115175 & 0.9773 & 0.165849 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207872&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]0.865975[/C][C]7.348[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.770787[/C][C]6.5403[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.76583[/C][C]6.4983[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.744498[/C][C]6.3173[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.651547[/C][C]5.5286[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.576048[/C][C]4.8879[/C][C]3e-06[/C][/ROW]
[ROW][C]7[/C][C]0.571246[/C][C]4.8472[/C][C]3e-06[/C][/ROW]
[ROW][C]8[/C][C]0.581963[/C][C]4.9381[/C][C]2e-06[/C][/ROW]
[ROW][C]9[/C][C]0.519559[/C][C]4.4086[/C][C]1.8e-05[/C][/ROW]
[ROW][C]10[/C][C]0.434927[/C][C]3.6905[/C][C]0.000216[/C][/ROW]
[ROW][C]11[/C][C]0.468131[/C][C]3.9722[/C][C]8.4e-05[/C][/ROW]
[ROW][C]12[/C][C]0.504288[/C][C]4.279[/C][C]2.8e-05[/C][/ROW]
[ROW][C]13[/C][C]0.394487[/C][C]3.3473[/C][C]0.00065[/C][/ROW]
[ROW][C]14[/C][C]0.30714[/C][C]2.6062[/C][C]0.00556[/C][/ROW]
[ROW][C]15[/C][C]0.285586[/C][C]2.4233[/C][C]0.008948[/C][/ROW]
[ROW][C]16[/C][C]0.264376[/C][C]2.2433[/C][C]0.013977[/C][/ROW]
[ROW][C]17[/C][C]0.184528[/C][C]1.5658[/C][C]0.060893[/C][/ROW]
[ROW][C]18[/C][C]0.115175[/C][C]0.9773[/C][C]0.165849[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207872&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207872&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	0.865975	7.348	0
2	0.770787	6.5403	0
3	0.76583	6.4983	0
4	0.744498	6.3173	0
5	0.651547	5.5286	0
6	0.576048	4.8879	3e-06
7	0.571246	4.8472	3e-06
8	0.581963	4.9381	2e-06
9	0.519559	4.4086	1.8e-05
10	0.434927	3.6905	0.000216
11	0.468131	3.9722	8.4e-05
12	0.504288	4.279	2.8e-05
13	0.394487	3.3473	0.00065
14	0.30714	2.6062	0.00556
15	0.285586	2.4233	0.008948
16	0.264376	2.2433	0.013977
17	0.184528	1.5658	0.060893
18	0.115175	0.9773	0.165849

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.865975	7.348	0
2	0.083468	0.7082	0.24054
3	0.3293	2.7942	0.003331
4	0.043659	0.3705	0.356063
5	-0.197942	-1.6796	0.048686
6	-0.066406	-0.5635	0.287431
7	0.124814	1.0591	0.146552
8	0.17385	1.4752	0.072264
9	-0.097775	-0.8296	0.204741
10	-0.178936	-1.5183	0.066656
11	0.256196	2.1739	0.016501
12	0.113777	0.9654	0.168781
13	-0.384095	-3.2592	0.000854
14	-0.095432	-0.8098	0.210371
15	-0.107792	-0.9146	0.181715
16	0.032525	0.276	0.391674
17	0.027756	0.2355	0.407238
18	0.015596	0.1323	0.447543

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.865975 & 7.348 & 0 \tabularnewline
2 & 0.083468 & 0.7082 & 0.24054 \tabularnewline
3 & 0.3293 & 2.7942 & 0.003331 \tabularnewline
4 & 0.043659 & 0.3705 & 0.356063 \tabularnewline
5 & -0.197942 & -1.6796 & 0.048686 \tabularnewline
6 & -0.066406 & -0.5635 & 0.287431 \tabularnewline
7 & 0.124814 & 1.0591 & 0.146552 \tabularnewline
8 & 0.17385 & 1.4752 & 0.072264 \tabularnewline
9 & -0.097775 & -0.8296 & 0.204741 \tabularnewline
10 & -0.178936 & -1.5183 & 0.066656 \tabularnewline
11 & 0.256196 & 2.1739 & 0.016501 \tabularnewline
12 & 0.113777 & 0.9654 & 0.168781 \tabularnewline
13 & -0.384095 & -3.2592 & 0.000854 \tabularnewline
14 & -0.095432 & -0.8098 & 0.210371 \tabularnewline
15 & -0.107792 & -0.9146 & 0.181715 \tabularnewline
16 & 0.032525 & 0.276 & 0.391674 \tabularnewline
17 & 0.027756 & 0.2355 & 0.407238 \tabularnewline
18 & 0.015596 & 0.1323 & 0.447543 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207872&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]0.865975[/C][C]7.348[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.083468[/C][C]0.7082[/C][C]0.24054[/C][/ROW]
[ROW][C]3[/C][C]0.3293[/C][C]2.7942[/C][C]0.003331[/C][/ROW]
[ROW][C]4[/C][C]0.043659[/C][C]0.3705[/C][C]0.356063[/C][/ROW]
[ROW][C]5[/C][C]-0.197942[/C][C]-1.6796[/C][C]0.048686[/C][/ROW]
[ROW][C]6[/C][C]-0.066406[/C][C]-0.5635[/C][C]0.287431[/C][/ROW]
[ROW][C]7[/C][C]0.124814[/C][C]1.0591[/C][C]0.146552[/C][/ROW]
[ROW][C]8[/C][C]0.17385[/C][C]1.4752[/C][C]0.072264[/C][/ROW]
[ROW][C]9[/C][C]-0.097775[/C][C]-0.8296[/C][C]0.204741[/C][/ROW]
[ROW][C]10[/C][C]-0.178936[/C][C]-1.5183[/C][C]0.066656[/C][/ROW]
[ROW][C]11[/C][C]0.256196[/C][C]2.1739[/C][C]0.016501[/C][/ROW]
[ROW][C]12[/C][C]0.113777[/C][C]0.9654[/C][C]0.168781[/C][/ROW]
[ROW][C]13[/C][C]-0.384095[/C][C]-3.2592[/C][C]0.000854[/C][/ROW]
[ROW][C]14[/C][C]-0.095432[/C][C]-0.8098[/C][C]0.210371[/C][/ROW]
[ROW][C]15[/C][C]-0.107792[/C][C]-0.9146[/C][C]0.181715[/C][/ROW]
[ROW][C]16[/C][C]0.032525[/C][C]0.276[/C][C]0.391674[/C][/ROW]
[ROW][C]17[/C][C]0.027756[/C][C]0.2355[/C][C]0.407238[/C][/ROW]
[ROW][C]18[/C][C]0.015596[/C][C]0.1323[/C][C]0.447543[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207872&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207872&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	0.865975	7.348	0
2	0.083468	0.7082	0.24054
3	0.3293	2.7942	0.003331
4	0.043659	0.3705	0.356063
5	-0.197942	-1.6796	0.048686
6	-0.066406	-0.5635	0.287431
7	0.124814	1.0591	0.146552
8	0.17385	1.4752	0.072264
9	-0.097775	-0.8296	0.204741
10	-0.178936	-1.5183	0.066656
11	0.256196	2.1739	0.016501
12	0.113777	0.9654	0.168781
13	-0.384095	-3.2592	0.000854
14	-0.095432	-0.8098	0.210371
15	-0.107792	-0.9146	0.181715
16	0.032525	0.276	0.391674
17	0.027756	0.2355	0.407238
18	0.015596	0.1323	0.447543

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