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, 20 Oct 2014 19:23:15 +0100

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/2014/Oct/20/t1413829407wqe6d5uhbyub2tc.htm/, Retrieved Sun, 12 May 2024 08:43:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=244213, Retrieved Sun, 12 May 2024 08:43:40 +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] [] [2014-10-20 18:15:32] [deebc1e457a5ecb4dd1aad0be1fbee4a]
-   PD    [(Partial) Autocorrelation Function] [] [2014-10-20 18:23:15] [f2e79deb6e51141b138dd10990a8e48d] [Current]
- R PD      [(Partial) Autocorrelation Function] [] [2014-12-13 15:23:51] [deebc1e457a5ecb4dd1aad0be1fbee4a] 

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

5,06
5,05
5,05
5,04
5,06
5,07
5,09
5,08
5,09
5,09
5,09
5,1
5,12
5,14
5,14
5,14
5,13
5,15
5,16
5,17
5,17
5,18
5,21
5,19
5,22
5,24
5,21
5,24
5,28
5,3
5,32
5,32
5,29
5,3
5,32
5,31
5,35
5,36
5,33
5,35
5,35
5,35
5,37
5,39
5,4
5,39
5,4
5,4
5,4
5,38
5,32
5,36
5,35
5,39
5,4
5,41
5,36
5,38
5,41
5,35
5,4
5,41
5,42
5,41
5,41
5,42
5,4
5,42
5,41
5,34
5,46
5,45
5,47
5,48
5,43
5,5
5,51
5,51
5,52
5,55
5,55
5,48
5,61
5,59
5,68
5,71
5,68
5,7
5,76
5,78
5,77
5,85
5,82
5,84
5,89
5,84

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=244213&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=244213&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=244213&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	0.883945	8.1015	0
2	0.814171	7.462	0
3	0.721284	6.6107	0
4	0.663199	6.0783	0
5	0.604036	5.5361	0
6	0.549325	5.0346	1e-06
7	0.514587	4.7163	5e-06
8	0.4669	4.2792	2.5e-05
9	0.412855	3.7839	0.000144
10	0.3105	2.8458	0.002783
11	0.217326	1.9918	0.02482
12	0.123739	1.1341	0.129992
13	0.122522	1.1229	0.132332
14	0.088587	0.8119	0.209569
15	0.045797	0.4197	0.337876
16	-0.001997	-0.0183	0.492721
17	-0.041475	-0.3801	0.352405
18	-0.081144	-0.7437	0.229567
19	-0.164534	-1.508	0.067656

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.883945 & 8.1015 & 0 \tabularnewline
2 & 0.814171 & 7.462 & 0 \tabularnewline
3 & 0.721284 & 6.6107 & 0 \tabularnewline
4 & 0.663199 & 6.0783 & 0 \tabularnewline
5 & 0.604036 & 5.5361 & 0 \tabularnewline
6 & 0.549325 & 5.0346 & 1e-06 \tabularnewline
7 & 0.514587 & 4.7163 & 5e-06 \tabularnewline
8 & 0.4669 & 4.2792 & 2.5e-05 \tabularnewline
9 & 0.412855 & 3.7839 & 0.000144 \tabularnewline
10 & 0.3105 & 2.8458 & 0.002783 \tabularnewline
11 & 0.217326 & 1.9918 & 0.02482 \tabularnewline
12 & 0.123739 & 1.1341 & 0.129992 \tabularnewline
13 & 0.122522 & 1.1229 & 0.132332 \tabularnewline
14 & 0.088587 & 0.8119 & 0.209569 \tabularnewline
15 & 0.045797 & 0.4197 & 0.337876 \tabularnewline
16 & -0.001997 & -0.0183 & 0.492721 \tabularnewline
17 & -0.041475 & -0.3801 & 0.352405 \tabularnewline
18 & -0.081144 & -0.7437 & 0.229567 \tabularnewline
19 & -0.164534 & -1.508 & 0.067656 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=244213&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]0.883945[/C][C]8.1015[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.814171[/C][C]7.462[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.721284[/C][C]6.6107[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.663199[/C][C]6.0783[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.604036[/C][C]5.5361[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.549325[/C][C]5.0346[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.514587[/C][C]4.7163[/C][C]5e-06[/C][/ROW]
[ROW][C]8[/C][C]0.4669[/C][C]4.2792[/C][C]2.5e-05[/C][/ROW]
[ROW][C]9[/C][C]0.412855[/C][C]3.7839[/C][C]0.000144[/C][/ROW]
[ROW][C]10[/C][C]0.3105[/C][C]2.8458[/C][C]0.002783[/C][/ROW]
[ROW][C]11[/C][C]0.217326[/C][C]1.9918[/C][C]0.02482[/C][/ROW]
[ROW][C]12[/C][C]0.123739[/C][C]1.1341[/C][C]0.129992[/C][/ROW]
[ROW][C]13[/C][C]0.122522[/C][C]1.1229[/C][C]0.132332[/C][/ROW]
[ROW][C]14[/C][C]0.088587[/C][C]0.8119[/C][C]0.209569[/C][/ROW]
[ROW][C]15[/C][C]0.045797[/C][C]0.4197[/C][C]0.337876[/C][/ROW]
[ROW][C]16[/C][C]-0.001997[/C][C]-0.0183[/C][C]0.492721[/C][/ROW]
[ROW][C]17[/C][C]-0.041475[/C][C]-0.3801[/C][C]0.352405[/C][/ROW]
[ROW][C]18[/C][C]-0.081144[/C][C]-0.7437[/C][C]0.229567[/C][/ROW]
[ROW][C]19[/C][C]-0.164534[/C][C]-1.508[/C][C]0.067656[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=244213&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=244213&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	0.883945	8.1015	0
2	0.814171	7.462	0
3	0.721284	6.6107	0
4	0.663199	6.0783	0
5	0.604036	5.5361	0
6	0.549325	5.0346	1e-06
7	0.514587	4.7163	5e-06
8	0.4669	4.2792	2.5e-05
9	0.412855	3.7839	0.000144
10	0.3105	2.8458	0.002783
11	0.217326	1.9918	0.02482
12	0.123739	1.1341	0.129992
13	0.122522	1.1229	0.132332
14	0.088587	0.8119	0.209569
15	0.045797	0.4197	0.337876
16	-0.001997	-0.0183	0.492721
17	-0.041475	-0.3801	0.352405
18	-0.081144	-0.7437	0.229567
19	-0.164534	-1.508	0.067656

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.883945	8.1015	0
2	0.150075	1.3755	0.086323
3	-0.107851	-0.9885	0.162881
4	0.079588	0.7294	0.233881
5	0.014868	0.1363	0.445968
6	-0.028006	-0.2567	0.399025
7	0.078357	0.7182	0.237326
8	-0.0477	-0.4372	0.331551
9	-0.087225	-0.7994	0.213147
10	-0.25183	-2.3081	0.011727
11	-0.109696	-1.0054	0.158801
12	-0.063221	-0.5794	0.281926
13	0.348218	3.1915	0.000996
14	-0.040063	-0.3672	0.357203
15	-0.212555	-1.9481	0.027372
16	-0.066567	-0.6101	0.271724
17	0.03043	0.2789	0.390505
18	0.020343	0.1865	0.42627
19	-0.176063	-1.6136	0.055178

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.883945 & 8.1015 & 0 \tabularnewline
2 & 0.150075 & 1.3755 & 0.086323 \tabularnewline
3 & -0.107851 & -0.9885 & 0.162881 \tabularnewline
4 & 0.079588 & 0.7294 & 0.233881 \tabularnewline
5 & 0.014868 & 0.1363 & 0.445968 \tabularnewline
6 & -0.028006 & -0.2567 & 0.399025 \tabularnewline
7 & 0.078357 & 0.7182 & 0.237326 \tabularnewline
8 & -0.0477 & -0.4372 & 0.331551 \tabularnewline
9 & -0.087225 & -0.7994 & 0.213147 \tabularnewline
10 & -0.25183 & -2.3081 & 0.011727 \tabularnewline
11 & -0.109696 & -1.0054 & 0.158801 \tabularnewline
12 & -0.063221 & -0.5794 & 0.281926 \tabularnewline
13 & 0.348218 & 3.1915 & 0.000996 \tabularnewline
14 & -0.040063 & -0.3672 & 0.357203 \tabularnewline
15 & -0.212555 & -1.9481 & 0.027372 \tabularnewline
16 & -0.066567 & -0.6101 & 0.271724 \tabularnewline
17 & 0.03043 & 0.2789 & 0.390505 \tabularnewline
18 & 0.020343 & 0.1865 & 0.42627 \tabularnewline
19 & -0.176063 & -1.6136 & 0.055178 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=244213&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]0.883945[/C][C]8.1015[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.150075[/C][C]1.3755[/C][C]0.086323[/C][/ROW]
[ROW][C]3[/C][C]-0.107851[/C][C]-0.9885[/C][C]0.162881[/C][/ROW]
[ROW][C]4[/C][C]0.079588[/C][C]0.7294[/C][C]0.233881[/C][/ROW]
[ROW][C]5[/C][C]0.014868[/C][C]0.1363[/C][C]0.445968[/C][/ROW]
[ROW][C]6[/C][C]-0.028006[/C][C]-0.2567[/C][C]0.399025[/C][/ROW]
[ROW][C]7[/C][C]0.078357[/C][C]0.7182[/C][C]0.237326[/C][/ROW]
[ROW][C]8[/C][C]-0.0477[/C][C]-0.4372[/C][C]0.331551[/C][/ROW]
[ROW][C]9[/C][C]-0.087225[/C][C]-0.7994[/C][C]0.213147[/C][/ROW]
[ROW][C]10[/C][C]-0.25183[/C][C]-2.3081[/C][C]0.011727[/C][/ROW]
[ROW][C]11[/C][C]-0.109696[/C][C]-1.0054[/C][C]0.158801[/C][/ROW]
[ROW][C]12[/C][C]-0.063221[/C][C]-0.5794[/C][C]0.281926[/C][/ROW]
[ROW][C]13[/C][C]0.348218[/C][C]3.1915[/C][C]0.000996[/C][/ROW]
[ROW][C]14[/C][C]-0.040063[/C][C]-0.3672[/C][C]0.357203[/C][/ROW]
[ROW][C]15[/C][C]-0.212555[/C][C]-1.9481[/C][C]0.027372[/C][/ROW]
[ROW][C]16[/C][C]-0.066567[/C][C]-0.6101[/C][C]0.271724[/C][/ROW]
[ROW][C]17[/C][C]0.03043[/C][C]0.2789[/C][C]0.390505[/C][/ROW]
[ROW][C]18[/C][C]0.020343[/C][C]0.1865[/C][C]0.42627[/C][/ROW]
[ROW][C]19[/C][C]-0.176063[/C][C]-1.6136[/C][C]0.055178[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=244213&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=244213&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	0.883945	8.1015	0
2	0.150075	1.3755	0.086323
3	-0.107851	-0.9885	0.162881
4	0.079588	0.7294	0.233881
5	0.014868	0.1363	0.445968
6	-0.028006	-0.2567	0.399025
7	0.078357	0.7182	0.237326
8	-0.0477	-0.4372	0.331551
9	-0.087225	-0.7994	0.213147
10	-0.25183	-2.3081	0.011727
11	-0.109696	-1.0054	0.158801
12	-0.063221	-0.5794	0.281926
13	0.348218	3.1915	0.000996
14	-0.040063	-0.3672	0.357203
15	-0.212555	-1.9481	0.027372
16	-0.066567	-0.6101	0.271724
17	0.03043	0.2789	0.390505
18	0.020343	0.1865	0.42627
19	-0.176063	-1.6136	0.055178

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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