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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 15 Jan 2008 09:51:07 -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/2008/Jan/15/t1200415637pi2i9ocvwmqgcko.htm/, Retrieved Wed, 15 May 2024 10:15:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7963, Retrieved Wed, 15 May 2024 10:15:42 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

auto cor diesel

Estimated Impact

323

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

-       [(Partial) Autocorrelation Function] [s 0650692 paper] [2008-01-15 16:51:07] [011cc8cdd02d5893b5258ac3f5e21d83] [Current]
-  MPD    [(Partial) Autocorrelation Function] [b-r0245787] [2010-12-21 13:15:12] [ebb35fb07def4d07c0eb7ec8d2fd3b0e] 
-           [(Partial) Autocorrelation Function] [b-r0245095] [2010-12-21 13:17:58] [ec8d68d52c1e9c5e97bb689b42436a8c] 
-   P         [(Partial) Autocorrelation Function] [b-r0245095] [2010-12-22 13:10:30] [ec8d68d52c1e9c5e97bb689b42436a8c] 
-   P       [(Partial) Autocorrelation Function] [b-r0245787] [2010-12-22 13:10:36] [ebb35fb07def4d07c0eb7ec8d2fd3b0e] 

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Dataseries X:

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Histogram

Boxplots

0.73
0.74
0.75
0.74
0.76
0.76
0.78
0.79
0.89
0.88
0.88
0.84
0.76
0.77
0.76
0.77
0.78
0.79
0.78
0.76
0.78
0.76
0.74
0.73
0.72
0.71
0.73
0.75
0.75
0.72
0.72
0.72
0.74
0.78
0.74
0.74
0.75
0.78
0.81
0.75
0.7
0.71
0.71
0.73
0.74
0.74
0.75
0.74
0.74
0.73
0.76
0.8
0.83
0.81
0.83
0.88
0.89
0.93
0.91
0.9
0.86
0.88
0.93
0.98
0.97
1.03
1.06
1.06
1.08
1.09
1.04
1

Summary of compuational 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' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7963&T=0

[TABLE]
[ROW][C]Summary of compuational 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' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7963&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7963&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 compuational 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' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.4853	0
1	0.931684	7.9056	0
2	0.838862	7.118	0
3	0.734924	6.236	0
4	0.641528	5.4435	0
5	0.566397	4.806	4e-06
6	0.491001	4.1663	4.2e-05
7	0.42167	3.578	0.000312
8	0.365993	3.1056	0.001358
9	0.326176	2.7677	0.003586
10	0.299593	2.5421	0.006585
11	0.276605	2.3471	0.010838
12	0.240912	2.0442	0.022295
13	0.181971	1.5441	0.063477
14	0.118839	1.0084	0.158325
15	0.052684	0.447	0.328093
16	0.006448	0.0547	0.478259
17	-0.025892	-0.2197	0.586637

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & 0.931684 & 7.9056 & 0 \tabularnewline
2 & 0.838862 & 7.118 & 0 \tabularnewline
3 & 0.734924 & 6.236 & 0 \tabularnewline
4 & 0.641528 & 5.4435 & 0 \tabularnewline
5 & 0.566397 & 4.806 & 4e-06 \tabularnewline
6 & 0.491001 & 4.1663 & 4.2e-05 \tabularnewline
7 & 0.42167 & 3.578 & 0.000312 \tabularnewline
8 & 0.365993 & 3.1056 & 0.001358 \tabularnewline
9 & 0.326176 & 2.7677 & 0.003586 \tabularnewline
10 & 0.299593 & 2.5421 & 0.006585 \tabularnewline
11 & 0.276605 & 2.3471 & 0.010838 \tabularnewline
12 & 0.240912 & 2.0442 & 0.022295 \tabularnewline
13 & 0.181971 & 1.5441 & 0.063477 \tabularnewline
14 & 0.118839 & 1.0084 & 0.158325 \tabularnewline
15 & 0.052684 & 0.447 & 0.328093 \tabularnewline
16 & 0.006448 & 0.0547 & 0.478259 \tabularnewline
17 & -0.025892 & -0.2197 & 0.586637 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7963&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]0[/C][C]1[/C][C]8.4853[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.931684[/C][C]7.9056[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.838862[/C][C]7.118[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.734924[/C][C]6.236[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.641528[/C][C]5.4435[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.566397[/C][C]4.806[/C][C]4e-06[/C][/ROW]
[ROW][C]6[/C][C]0.491001[/C][C]4.1663[/C][C]4.2e-05[/C][/ROW]
[ROW][C]7[/C][C]0.42167[/C][C]3.578[/C][C]0.000312[/C][/ROW]
[ROW][C]8[/C][C]0.365993[/C][C]3.1056[/C][C]0.001358[/C][/ROW]
[ROW][C]9[/C][C]0.326176[/C][C]2.7677[/C][C]0.003586[/C][/ROW]
[ROW][C]10[/C][C]0.299593[/C][C]2.5421[/C][C]0.006585[/C][/ROW]
[ROW][C]11[/C][C]0.276605[/C][C]2.3471[/C][C]0.010838[/C][/ROW]
[ROW][C]12[/C][C]0.240912[/C][C]2.0442[/C][C]0.022295[/C][/ROW]
[ROW][C]13[/C][C]0.181971[/C][C]1.5441[/C][C]0.063477[/C][/ROW]
[ROW][C]14[/C][C]0.118839[/C][C]1.0084[/C][C]0.158325[/C][/ROW]
[ROW][C]15[/C][C]0.052684[/C][C]0.447[/C][C]0.328093[/C][/ROW]
[ROW][C]16[/C][C]0.006448[/C][C]0.0547[/C][C]0.478259[/C][/ROW]
[ROW][C]17[/C][C]-0.025892[/C][C]-0.2197[/C][C]0.586637[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7963&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7963&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
0	1	8.4853	0
1	0.931684	7.9056	0
2	0.838862	7.118	0
3	0.734924	6.236	0
4	0.641528	5.4435	0
5	0.566397	4.806	4e-06
6	0.491001	4.1663	4.2e-05
7	0.42167	3.578	0.000312
8	0.365993	3.1056	0.001358
9	0.326176	2.7677	0.003586
10	0.299593	2.5421	0.006585
11	0.276605	2.3471	0.010838
12	0.240912	2.0442	0.022295
13	0.181971	1.5441	0.063477
14	0.118839	1.0084	0.158325
15	0.052684	0.447	0.328093
16	0.006448	0.0547	0.478259
17	-0.025892	-0.2197	0.586637

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.931684	7.9056	0
1	-0.221067	-1.8758	0.967632
2	-0.107099	-0.9088	0.816747
3	0.047252	0.4009	0.344824
4	0.064264	0.5453	0.293618
5	-0.107801	-0.9147	0.818304
6	-0.006858	-0.0582	0.52312
7	0.073537	0.624	0.267305
8	0.051903	0.4404	0.330479
9	0.011227	0.0953	0.462186
10	-0.018301	-0.1553	0.561486
11	-0.111345	-0.9448	0.826037
12	-0.172187	-1.4611	0.925824
13	0.000402	0.0034	0.498645
14	-0.050521	-0.4287	0.665285
15	0.087394	0.7416	0.230381
16	0.021203	0.1799	0.428864
17	0.034538	0.2931	0.385159

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.931684 & 7.9056 & 0 \tabularnewline
1 & -0.221067 & -1.8758 & 0.967632 \tabularnewline
2 & -0.107099 & -0.9088 & 0.816747 \tabularnewline
3 & 0.047252 & 0.4009 & 0.344824 \tabularnewline
4 & 0.064264 & 0.5453 & 0.293618 \tabularnewline
5 & -0.107801 & -0.9147 & 0.818304 \tabularnewline
6 & -0.006858 & -0.0582 & 0.52312 \tabularnewline
7 & 0.073537 & 0.624 & 0.267305 \tabularnewline
8 & 0.051903 & 0.4404 & 0.330479 \tabularnewline
9 & 0.011227 & 0.0953 & 0.462186 \tabularnewline
10 & -0.018301 & -0.1553 & 0.561486 \tabularnewline
11 & -0.111345 & -0.9448 & 0.826037 \tabularnewline
12 & -0.172187 & -1.4611 & 0.925824 \tabularnewline
13 & 0.000402 & 0.0034 & 0.498645 \tabularnewline
14 & -0.050521 & -0.4287 & 0.665285 \tabularnewline
15 & 0.087394 & 0.7416 & 0.230381 \tabularnewline
16 & 0.021203 & 0.1799 & 0.428864 \tabularnewline
17 & 0.034538 & 0.2931 & 0.385159 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7963&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]0[/C][C]0.931684[/C][C]7.9056[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.221067[/C][C]-1.8758[/C][C]0.967632[/C][/ROW]
[ROW][C]2[/C][C]-0.107099[/C][C]-0.9088[/C][C]0.816747[/C][/ROW]
[ROW][C]3[/C][C]0.047252[/C][C]0.4009[/C][C]0.344824[/C][/ROW]
[ROW][C]4[/C][C]0.064264[/C][C]0.5453[/C][C]0.293618[/C][/ROW]
[ROW][C]5[/C][C]-0.107801[/C][C]-0.9147[/C][C]0.818304[/C][/ROW]
[ROW][C]6[/C][C]-0.006858[/C][C]-0.0582[/C][C]0.52312[/C][/ROW]
[ROW][C]7[/C][C]0.073537[/C][C]0.624[/C][C]0.267305[/C][/ROW]
[ROW][C]8[/C][C]0.051903[/C][C]0.4404[/C][C]0.330479[/C][/ROW]
[ROW][C]9[/C][C]0.011227[/C][C]0.0953[/C][C]0.462186[/C][/ROW]
[ROW][C]10[/C][C]-0.018301[/C][C]-0.1553[/C][C]0.561486[/C][/ROW]
[ROW][C]11[/C][C]-0.111345[/C][C]-0.9448[/C][C]0.826037[/C][/ROW]
[ROW][C]12[/C][C]-0.172187[/C][C]-1.4611[/C][C]0.925824[/C][/ROW]
[ROW][C]13[/C][C]0.000402[/C][C]0.0034[/C][C]0.498645[/C][/ROW]
[ROW][C]14[/C][C]-0.050521[/C][C]-0.4287[/C][C]0.665285[/C][/ROW]
[ROW][C]15[/C][C]0.087394[/C][C]0.7416[/C][C]0.230381[/C][/ROW]
[ROW][C]16[/C][C]0.021203[/C][C]0.1799[/C][C]0.428864[/C][/ROW]
[ROW][C]17[/C][C]0.034538[/C][C]0.2931[/C][C]0.385159[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7963&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7963&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
0	0.931684	7.9056	0
1	-0.221067	-1.8758	0.967632
2	-0.107099	-0.9088	0.816747
3	0.047252	0.4009	0.344824
4	0.064264	0.5453	0.293618
5	-0.107801	-0.9147	0.818304
6	-0.006858	-0.0582	0.52312
7	0.073537	0.624	0.267305
8	0.051903	0.4404	0.330479
9	0.011227	0.0953	0.462186
10	-0.018301	-0.1553	0.561486
11	-0.111345	-0.9448	0.826037
12	-0.172187	-1.4611	0.925824
13	0.000402	0.0034	0.498645
14	-0.050521	-0.4287	0.665285
15	0.087394	0.7416	0.230381
16	0.021203	0.1799	0.428864
17	0.034538	0.2931	0.385159

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code