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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 01 Dec 2007 05:04:37 -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/Dec/01/t11965100550nc355zvd6mwr8q.htm/, Retrieved Sun, 19 May 2024 19:42:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2221, Retrieved Sun, 19 May 2024 19:42:21 +0000

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No (this computation is public)

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Estimated Impact

227

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-       [(Partial) Autocorrelation Function] [autocorrelation w...] [2007-12-01 12:04:37] [bd02e85be52eb1cb060a2c60779eb820] [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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2221&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2221&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2221&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	9.7468	0
1	-0.012567	-0.1225	0.548615
2	-0.061289	-0.5974	0.724161
3	-0.128984	-1.2572	0.894115
4	0.095799	0.9337	0.176404
5	0.109096	1.0633	0.145163
6	0.105261	1.026	0.153758
7	0.141355	1.3778	0.085757
8	-0.083572	-0.8146	0.79132
9	0.142649	1.3904	0.083833
10	-0.097527	-0.9506	0.827883
11	-0.028744	-0.2802	0.610017
12	-0.03493	-0.3405	0.632869
13	0.073839	0.7197	0.236739
14	0.173552	1.6916	0.047002
15	-0.018319	-0.1786	0.570666
16	-0.02953	-0.2878	0.612944
17	-0.051872	-0.5056	0.692842
18	-0.030809	-0.3003	0.617693
19	-0.096064	-0.9363	0.824258

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 9.7468 & 0 \tabularnewline
1 & -0.012567 & -0.1225 & 0.548615 \tabularnewline
2 & -0.061289 & -0.5974 & 0.724161 \tabularnewline
3 & -0.128984 & -1.2572 & 0.894115 \tabularnewline
4 & 0.095799 & 0.9337 & 0.176404 \tabularnewline
5 & 0.109096 & 1.0633 & 0.145163 \tabularnewline
6 & 0.105261 & 1.026 & 0.153758 \tabularnewline
7 & 0.141355 & 1.3778 & 0.085757 \tabularnewline
8 & -0.083572 & -0.8146 & 0.79132 \tabularnewline
9 & 0.142649 & 1.3904 & 0.083833 \tabularnewline
10 & -0.097527 & -0.9506 & 0.827883 \tabularnewline
11 & -0.028744 & -0.2802 & 0.610017 \tabularnewline
12 & -0.03493 & -0.3405 & 0.632869 \tabularnewline
13 & 0.073839 & 0.7197 & 0.236739 \tabularnewline
14 & 0.173552 & 1.6916 & 0.047002 \tabularnewline
15 & -0.018319 & -0.1786 & 0.570666 \tabularnewline
16 & -0.02953 & -0.2878 & 0.612944 \tabularnewline
17 & -0.051872 & -0.5056 & 0.692842 \tabularnewline
18 & -0.030809 & -0.3003 & 0.617693 \tabularnewline
19 & -0.096064 & -0.9363 & 0.824258 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2221&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]9.7468[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.012567[/C][C]-0.1225[/C][C]0.548615[/C][/ROW]
[ROW][C]2[/C][C]-0.061289[/C][C]-0.5974[/C][C]0.724161[/C][/ROW]
[ROW][C]3[/C][C]-0.128984[/C][C]-1.2572[/C][C]0.894115[/C][/ROW]
[ROW][C]4[/C][C]0.095799[/C][C]0.9337[/C][C]0.176404[/C][/ROW]
[ROW][C]5[/C][C]0.109096[/C][C]1.0633[/C][C]0.145163[/C][/ROW]
[ROW][C]6[/C][C]0.105261[/C][C]1.026[/C][C]0.153758[/C][/ROW]
[ROW][C]7[/C][C]0.141355[/C][C]1.3778[/C][C]0.085757[/C][/ROW]
[ROW][C]8[/C][C]-0.083572[/C][C]-0.8146[/C][C]0.79132[/C][/ROW]
[ROW][C]9[/C][C]0.142649[/C][C]1.3904[/C][C]0.083833[/C][/ROW]
[ROW][C]10[/C][C]-0.097527[/C][C]-0.9506[/C][C]0.827883[/C][/ROW]
[ROW][C]11[/C][C]-0.028744[/C][C]-0.2802[/C][C]0.610017[/C][/ROW]
[ROW][C]12[/C][C]-0.03493[/C][C]-0.3405[/C][C]0.632869[/C][/ROW]
[ROW][C]13[/C][C]0.073839[/C][C]0.7197[/C][C]0.236739[/C][/ROW]
[ROW][C]14[/C][C]0.173552[/C][C]1.6916[/C][C]0.047002[/C][/ROW]
[ROW][C]15[/C][C]-0.018319[/C][C]-0.1786[/C][C]0.570666[/C][/ROW]
[ROW][C]16[/C][C]-0.02953[/C][C]-0.2878[/C][C]0.612944[/C][/ROW]
[ROW][C]17[/C][C]-0.051872[/C][C]-0.5056[/C][C]0.692842[/C][/ROW]
[ROW][C]18[/C][C]-0.030809[/C][C]-0.3003[/C][C]0.617693[/C][/ROW]
[ROW][C]19[/C][C]-0.096064[/C][C]-0.9363[/C][C]0.824258[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2221&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2221&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	9.7468	0
1	-0.012567	-0.1225	0.548615
2	-0.061289	-0.5974	0.724161
3	-0.128984	-1.2572	0.894115
4	0.095799	0.9337	0.176404
5	0.109096	1.0633	0.145163
6	0.105261	1.026	0.153758
7	0.141355	1.3778	0.085757
8	-0.083572	-0.8146	0.79132
9	0.142649	1.3904	0.083833
10	-0.097527	-0.9506	0.827883
11	-0.028744	-0.2802	0.610017
12	-0.03493	-0.3405	0.632869
13	0.073839	0.7197	0.236739
14	0.173552	1.6916	0.047002
15	-0.018319	-0.1786	0.570666
16	-0.02953	-0.2878	0.612944
17	-0.051872	-0.5056	0.692842
18	-0.030809	-0.3003	0.617693
19	-0.096064	-0.9363	0.824258

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.012567	-0.1225	0.548615
1	-0.061457	-0.599	0.724704
2	-0.13109	-1.2777	0.897766
3	0.0894	0.8714	0.192876
4	0.098654	0.9616	0.169356
5	0.106502	1.0381	0.15094
6	0.19005	1.8524	0.033538
7	-0.046281	-0.4511	0.673525
8	0.17883	1.743	0.042283
9	-0.099465	-0.9695	0.832612
10	-0.092765	-0.9042	0.815903
11	-0.054289	-0.5291	0.70103
12	-0.026908	-0.2623	0.603159
13	0.152425	1.4857	0.070341
14	0.005518	0.0538	0.478609
15	-0.001637	-0.016	0.506347
16	0.063936	0.6232	0.267334
17	-0.109626	-1.0685	0.855999
18	-0.12809	-1.2485	0.892537
19	-0.061413	-0.5986	0.724561

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.012567 & -0.1225 & 0.548615 \tabularnewline
1 & -0.061457 & -0.599 & 0.724704 \tabularnewline
2 & -0.13109 & -1.2777 & 0.897766 \tabularnewline
3 & 0.0894 & 0.8714 & 0.192876 \tabularnewline
4 & 0.098654 & 0.9616 & 0.169356 \tabularnewline
5 & 0.106502 & 1.0381 & 0.15094 \tabularnewline
6 & 0.19005 & 1.8524 & 0.033538 \tabularnewline
7 & -0.046281 & -0.4511 & 0.673525 \tabularnewline
8 & 0.17883 & 1.743 & 0.042283 \tabularnewline
9 & -0.099465 & -0.9695 & 0.832612 \tabularnewline
10 & -0.092765 & -0.9042 & 0.815903 \tabularnewline
11 & -0.054289 & -0.5291 & 0.70103 \tabularnewline
12 & -0.026908 & -0.2623 & 0.603159 \tabularnewline
13 & 0.152425 & 1.4857 & 0.070341 \tabularnewline
14 & 0.005518 & 0.0538 & 0.478609 \tabularnewline
15 & -0.001637 & -0.016 & 0.506347 \tabularnewline
16 & 0.063936 & 0.6232 & 0.267334 \tabularnewline
17 & -0.109626 & -1.0685 & 0.855999 \tabularnewline
18 & -0.12809 & -1.2485 & 0.892537 \tabularnewline
19 & -0.061413 & -0.5986 & 0.724561 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2221&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]-0.012567[/C][C]-0.1225[/C][C]0.548615[/C][/ROW]
[ROW][C]1[/C][C]-0.061457[/C][C]-0.599[/C][C]0.724704[/C][/ROW]
[ROW][C]2[/C][C]-0.13109[/C][C]-1.2777[/C][C]0.897766[/C][/ROW]
[ROW][C]3[/C][C]0.0894[/C][C]0.8714[/C][C]0.192876[/C][/ROW]
[ROW][C]4[/C][C]0.098654[/C][C]0.9616[/C][C]0.169356[/C][/ROW]
[ROW][C]5[/C][C]0.106502[/C][C]1.0381[/C][C]0.15094[/C][/ROW]
[ROW][C]6[/C][C]0.19005[/C][C]1.8524[/C][C]0.033538[/C][/ROW]
[ROW][C]7[/C][C]-0.046281[/C][C]-0.4511[/C][C]0.673525[/C][/ROW]
[ROW][C]8[/C][C]0.17883[/C][C]1.743[/C][C]0.042283[/C][/ROW]
[ROW][C]9[/C][C]-0.099465[/C][C]-0.9695[/C][C]0.832612[/C][/ROW]
[ROW][C]10[/C][C]-0.092765[/C][C]-0.9042[/C][C]0.815903[/C][/ROW]
[ROW][C]11[/C][C]-0.054289[/C][C]-0.5291[/C][C]0.70103[/C][/ROW]
[ROW][C]12[/C][C]-0.026908[/C][C]-0.2623[/C][C]0.603159[/C][/ROW]
[ROW][C]13[/C][C]0.152425[/C][C]1.4857[/C][C]0.070341[/C][/ROW]
[ROW][C]14[/C][C]0.005518[/C][C]0.0538[/C][C]0.478609[/C][/ROW]
[ROW][C]15[/C][C]-0.001637[/C][C]-0.016[/C][C]0.506347[/C][/ROW]
[ROW][C]16[/C][C]0.063936[/C][C]0.6232[/C][C]0.267334[/C][/ROW]
[ROW][C]17[/C][C]-0.109626[/C][C]-1.0685[/C][C]0.855999[/C][/ROW]
[ROW][C]18[/C][C]-0.12809[/C][C]-1.2485[/C][C]0.892537[/C][/ROW]
[ROW][C]19[/C][C]-0.061413[/C][C]-0.5986[/C][C]0.724561[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2221&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2221&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	-0.012567	-0.1225	0.548615
1	-0.061457	-0.599	0.724704
2	-0.13109	-1.2777	0.897766
3	0.0894	0.8714	0.192876
4	0.098654	0.9616	0.169356
5	0.106502	1.0381	0.15094
6	0.19005	1.8524	0.033538
7	-0.046281	-0.4511	0.673525
8	0.17883	1.743	0.042283
9	-0.099465	-0.9695	0.832612
10	-0.092765	-0.9042	0.815903
11	-0.054289	-0.5291	0.70103
12	-0.026908	-0.2623	0.603159
13	0.152425	1.4857	0.070341
14	0.005518	0.0538	0.478609
15	-0.001637	-0.016	0.506347
16	0.063936	0.6232	0.267334
17	-0.109626	-1.0685	0.855999
18	-0.12809	-1.2485	0.892537
19	-0.061413	-0.5986	0.724561

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code