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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 24 Nov 2007 07:20:26 -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/2007/Nov/24/t1195913523aljpsqv0d3fwwtm.htm/, Retrieved Fri, 03 May 2024 12:20:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6311, Retrieved Fri, 03 May 2024 12:20:13 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

195

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

-       [(Partial) Autocorrelation Function] [Partial Autocorre...] [2007-11-24 14:20:26] [6b5c00822e2ce0f7cf73539c28d95782] [Current]

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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=6311&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=6311&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6311&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	7.746	0
1	0.953261	7.3839	0
2	0.902707	6.9923	0
3	0.853038	6.6076	0
4	0.806346	6.2459	0
5	0.759939	5.8865	0
6	0.712422	5.5184	0
7	0.660498	5.1162	2e-06
8	0.605124	4.6873	8e-06
9	0.55498	4.2989	3.2e-05
10	0.511418	3.9614	1e-04
11	0.467048	3.6177	0.000305
12	0.419703	3.251	0.000944
13	0.367736	2.8485	0.003004
14	0.313477	2.4282	0.009095
15	0.265078	2.0533	0.022206
16	0.221004	1.7119	0.046041

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.953261 & 7.3839 & 0 \tabularnewline
2 & 0.902707 & 6.9923 & 0 \tabularnewline
3 & 0.853038 & 6.6076 & 0 \tabularnewline
4 & 0.806346 & 6.2459 & 0 \tabularnewline
5 & 0.759939 & 5.8865 & 0 \tabularnewline
6 & 0.712422 & 5.5184 & 0 \tabularnewline
7 & 0.660498 & 5.1162 & 2e-06 \tabularnewline
8 & 0.605124 & 4.6873 & 8e-06 \tabularnewline
9 & 0.55498 & 4.2989 & 3.2e-05 \tabularnewline
10 & 0.511418 & 3.9614 & 1e-04 \tabularnewline
11 & 0.467048 & 3.6177 & 0.000305 \tabularnewline
12 & 0.419703 & 3.251 & 0.000944 \tabularnewline
13 & 0.367736 & 2.8485 & 0.003004 \tabularnewline
14 & 0.313477 & 2.4282 & 0.009095 \tabularnewline
15 & 0.265078 & 2.0533 & 0.022206 \tabularnewline
16 & 0.221004 & 1.7119 & 0.046041 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6311&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.953261[/C][C]7.3839[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.902707[/C][C]6.9923[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.853038[/C][C]6.6076[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.806346[/C][C]6.2459[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.759939[/C][C]5.8865[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.712422[/C][C]5.5184[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.660498[/C][C]5.1162[/C][C]2e-06[/C][/ROW]
[ROW][C]8[/C][C]0.605124[/C][C]4.6873[/C][C]8e-06[/C][/ROW]
[ROW][C]9[/C][C]0.55498[/C][C]4.2989[/C][C]3.2e-05[/C][/ROW]
[ROW][C]10[/C][C]0.511418[/C][C]3.9614[/C][C]1e-04[/C][/ROW]
[ROW][C]11[/C][C]0.467048[/C][C]3.6177[/C][C]0.000305[/C][/ROW]
[ROW][C]12[/C][C]0.419703[/C][C]3.251[/C][C]0.000944[/C][/ROW]
[ROW][C]13[/C][C]0.367736[/C][C]2.8485[/C][C]0.003004[/C][/ROW]
[ROW][C]14[/C][C]0.313477[/C][C]2.4282[/C][C]0.009095[/C][/ROW]
[ROW][C]15[/C][C]0.265078[/C][C]2.0533[/C][C]0.022206[/C][/ROW]
[ROW][C]16[/C][C]0.221004[/C][C]1.7119[/C][C]0.046041[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6311&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6311&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	7.746	0
1	0.953261	7.3839	0
2	0.902707	6.9923	0
3	0.853038	6.6076	0
4	0.806346	6.2459	0
5	0.759939	5.8865	0
6	0.712422	5.5184	0
7	0.660498	5.1162	2e-06
8	0.605124	4.6873	8e-06
9	0.55498	4.2989	3.2e-05
10	0.511418	3.9614	1e-04
11	0.467048	3.6177	0.000305
12	0.419703	3.251	0.000944
13	0.367736	2.8485	0.003004
14	0.313477	2.4282	0.009095
15	0.265078	2.0533	0.022206
16	0.221004	1.7119	0.046041

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.953261	7.3839	0
1	-0.065723	-0.5091	0.69372
2	-0.015203	-0.1178	0.546675
3	0.005119	0.0397	0.48425
4	-0.025211	-0.1953	0.577084
5	-0.038206	-0.2959	0.615851
6	-0.074387	-0.5762	0.716683
7	-0.065876	-0.5103	0.694134
8	0.024798	0.1921	0.424162
9	0.03304	0.2559	0.399442
10	-0.044751	-0.3466	0.634961
11	-0.057927	-0.4487	0.672368
12	-0.076245	-0.5906	0.721494
13	-0.058675	-0.4545	0.674444
14	0.019957	0.1546	0.438833
15	-0.006293	-0.0487	0.519359
16	-0.001502	-0.0116	0.504622

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.953261 & 7.3839 & 0 \tabularnewline
1 & -0.065723 & -0.5091 & 0.69372 \tabularnewline
2 & -0.015203 & -0.1178 & 0.546675 \tabularnewline
3 & 0.005119 & 0.0397 & 0.48425 \tabularnewline
4 & -0.025211 & -0.1953 & 0.577084 \tabularnewline
5 & -0.038206 & -0.2959 & 0.615851 \tabularnewline
6 & -0.074387 & -0.5762 & 0.716683 \tabularnewline
7 & -0.065876 & -0.5103 & 0.694134 \tabularnewline
8 & 0.024798 & 0.1921 & 0.424162 \tabularnewline
9 & 0.03304 & 0.2559 & 0.399442 \tabularnewline
10 & -0.044751 & -0.3466 & 0.634961 \tabularnewline
11 & -0.057927 & -0.4487 & 0.672368 \tabularnewline
12 & -0.076245 & -0.5906 & 0.721494 \tabularnewline
13 & -0.058675 & -0.4545 & 0.674444 \tabularnewline
14 & 0.019957 & 0.1546 & 0.438833 \tabularnewline
15 & -0.006293 & -0.0487 & 0.519359 \tabularnewline
16 & -0.001502 & -0.0116 & 0.504622 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6311&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]0.953261[/C][C]7.3839[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.065723[/C][C]-0.5091[/C][C]0.69372[/C][/ROW]
[ROW][C]2[/C][C]-0.015203[/C][C]-0.1178[/C][C]0.546675[/C][/ROW]
[ROW][C]3[/C][C]0.005119[/C][C]0.0397[/C][C]0.48425[/C][/ROW]
[ROW][C]4[/C][C]-0.025211[/C][C]-0.1953[/C][C]0.577084[/C][/ROW]
[ROW][C]5[/C][C]-0.038206[/C][C]-0.2959[/C][C]0.615851[/C][/ROW]
[ROW][C]6[/C][C]-0.074387[/C][C]-0.5762[/C][C]0.716683[/C][/ROW]
[ROW][C]7[/C][C]-0.065876[/C][C]-0.5103[/C][C]0.694134[/C][/ROW]
[ROW][C]8[/C][C]0.024798[/C][C]0.1921[/C][C]0.424162[/C][/ROW]
[ROW][C]9[/C][C]0.03304[/C][C]0.2559[/C][C]0.399442[/C][/ROW]
[ROW][C]10[/C][C]-0.044751[/C][C]-0.3466[/C][C]0.634961[/C][/ROW]
[ROW][C]11[/C][C]-0.057927[/C][C]-0.4487[/C][C]0.672368[/C][/ROW]
[ROW][C]12[/C][C]-0.076245[/C][C]-0.5906[/C][C]0.721494[/C][/ROW]
[ROW][C]13[/C][C]-0.058675[/C][C]-0.4545[/C][C]0.674444[/C][/ROW]
[ROW][C]14[/C][C]0.019957[/C][C]0.1546[/C][C]0.438833[/C][/ROW]
[ROW][C]15[/C][C]-0.006293[/C][C]-0.0487[/C][C]0.519359[/C][/ROW]
[ROW][C]16[/C][C]-0.001502[/C][C]-0.0116[/C][C]0.504622[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6311&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6311&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	0.953261	7.3839	0
1	-0.065723	-0.5091	0.69372
2	-0.015203	-0.1178	0.546675
3	0.005119	0.0397	0.48425
4	-0.025211	-0.1953	0.577084
5	-0.038206	-0.2959	0.615851
6	-0.074387	-0.5762	0.716683
7	-0.065876	-0.5103	0.694134
8	0.024798	0.1921	0.424162
9	0.03304	0.2559	0.399442
10	-0.044751	-0.3466	0.634961
11	-0.057927	-0.4487	0.672368
12	-0.076245	-0.5906	0.721494
13	-0.058675	-0.4545	0.674444
14	0.019957	0.1546	0.438833
15	-0.006293	-0.0487	0.519359
16	-0.001502	-0.0116	0.504622

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')

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Dataset

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Input Parameters & R Code