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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 25 Nov 2007 10:47:31 -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/25/t119601235585b8fjpxh3cee6x.htm/, Retrieved Sat, 04 May 2024 07:44:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6508, Retrieved Sat, 04 May 2024 07:44:08 +0000

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No (this computation is public)

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Estimated Impact

190

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

-       [(Partial) Autocorrelation Function] [hde] [2007-11-25 17:47:31] [fa77851485501f69e030fcd6dbd2de67] [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=6508&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=6508&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6508&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	8.3066	0
1	0.923886	7.6744	0
2	0.862105	7.1612	0
3	0.801432	6.6572	0
4	0.730503	6.068	0
5	0.668497	5.553	0
6	0.616719	5.1229	1e-06
7	0.562196	4.67	7e-06
8	0.509365	4.2311	3.5e-05
9	0.459817	3.8195	0.000144
10	0.392355	3.2591	0.000868
11	0.340725	2.8303	0.003043
12	0.294106	2.443	0.008564
13	0.271908	2.2586	0.013535
14	0.252271	2.0955	0.019898
15	0.222195	1.8457	0.034614
16	0.193588	1.6081	0.056194
17	0.165217	1.3724	0.087192
18	0.137915	1.1456	0.127958

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.3066 & 0 \tabularnewline
1 & 0.923886 & 7.6744 & 0 \tabularnewline
2 & 0.862105 & 7.1612 & 0 \tabularnewline
3 & 0.801432 & 6.6572 & 0 \tabularnewline
4 & 0.730503 & 6.068 & 0 \tabularnewline
5 & 0.668497 & 5.553 & 0 \tabularnewline
6 & 0.616719 & 5.1229 & 1e-06 \tabularnewline
7 & 0.562196 & 4.67 & 7e-06 \tabularnewline
8 & 0.509365 & 4.2311 & 3.5e-05 \tabularnewline
9 & 0.459817 & 3.8195 & 0.000144 \tabularnewline
10 & 0.392355 & 3.2591 & 0.000868 \tabularnewline
11 & 0.340725 & 2.8303 & 0.003043 \tabularnewline
12 & 0.294106 & 2.443 & 0.008564 \tabularnewline
13 & 0.271908 & 2.2586 & 0.013535 \tabularnewline
14 & 0.252271 & 2.0955 & 0.019898 \tabularnewline
15 & 0.222195 & 1.8457 & 0.034614 \tabularnewline
16 & 0.193588 & 1.6081 & 0.056194 \tabularnewline
17 & 0.165217 & 1.3724 & 0.087192 \tabularnewline
18 & 0.137915 & 1.1456 & 0.127958 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6508&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]8.3066[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.923886[/C][C]7.6744[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.862105[/C][C]7.1612[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.801432[/C][C]6.6572[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.730503[/C][C]6.068[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.668497[/C][C]5.553[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.616719[/C][C]5.1229[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.562196[/C][C]4.67[/C][C]7e-06[/C][/ROW]
[ROW][C]8[/C][C]0.509365[/C][C]4.2311[/C][C]3.5e-05[/C][/ROW]
[ROW][C]9[/C][C]0.459817[/C][C]3.8195[/C][C]0.000144[/C][/ROW]
[ROW][C]10[/C][C]0.392355[/C][C]3.2591[/C][C]0.000868[/C][/ROW]
[ROW][C]11[/C][C]0.340725[/C][C]2.8303[/C][C]0.003043[/C][/ROW]
[ROW][C]12[/C][C]0.294106[/C][C]2.443[/C][C]0.008564[/C][/ROW]
[ROW][C]13[/C][C]0.271908[/C][C]2.2586[/C][C]0.013535[/C][/ROW]
[ROW][C]14[/C][C]0.252271[/C][C]2.0955[/C][C]0.019898[/C][/ROW]
[ROW][C]15[/C][C]0.222195[/C][C]1.8457[/C][C]0.034614[/C][/ROW]
[ROW][C]16[/C][C]0.193588[/C][C]1.6081[/C][C]0.056194[/C][/ROW]
[ROW][C]17[/C][C]0.165217[/C][C]1.3724[/C][C]0.087192[/C][/ROW]
[ROW][C]18[/C][C]0.137915[/C][C]1.1456[/C][C]0.127958[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6508&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6508&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	8.3066	0
1	0.923886	7.6744	0
2	0.862105	7.1612	0
3	0.801432	6.6572	0
4	0.730503	6.068	0
5	0.668497	5.553	0
6	0.616719	5.1229	1e-06
7	0.562196	4.67	7e-06
8	0.509365	4.2311	3.5e-05
9	0.459817	3.8195	0.000144
10	0.392355	3.2591	0.000868
11	0.340725	2.8303	0.003043
12	0.294106	2.443	0.008564
13	0.271908	2.2586	0.013535
14	0.252271	2.0955	0.019898
15	0.222195	1.8457	0.034614
16	0.193588	1.6081	0.056194
17	0.165217	1.3724	0.087192
18	0.137915	1.1456	0.127958

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.923886	7.6744	0
1	0.058325	0.4845	0.31479
2	-0.017027	-0.1414	0.55603
3	-0.10186	-0.8461	0.799792
4	0.008417	0.0699	0.47223
5	0.041923	0.3482	0.36436
6	-0.033236	-0.2761	0.608345
7	-0.03142	-0.261	0.602562
8	-0.018121	-0.1505	0.559605
9	-0.146815	-1.2195	0.886604
10	0.047008	0.3905	0.348693
11	0.010169	0.0845	0.466462
12	0.161655	1.3428	0.091867
13	0.004439	0.0369	0.485346
14	-0.106017	-0.8806	0.809216
15	-0.041433	-0.3442	0.634118
16	-0.009705	-0.0806	0.532009
17	0.020382	0.1693	0.433026
18	-0.100088	-0.8314	0.79569

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.923886 & 7.6744 & 0 \tabularnewline
1 & 0.058325 & 0.4845 & 0.31479 \tabularnewline
2 & -0.017027 & -0.1414 & 0.55603 \tabularnewline
3 & -0.10186 & -0.8461 & 0.799792 \tabularnewline
4 & 0.008417 & 0.0699 & 0.47223 \tabularnewline
5 & 0.041923 & 0.3482 & 0.36436 \tabularnewline
6 & -0.033236 & -0.2761 & 0.608345 \tabularnewline
7 & -0.03142 & -0.261 & 0.602562 \tabularnewline
8 & -0.018121 & -0.1505 & 0.559605 \tabularnewline
9 & -0.146815 & -1.2195 & 0.886604 \tabularnewline
10 & 0.047008 & 0.3905 & 0.348693 \tabularnewline
11 & 0.010169 & 0.0845 & 0.466462 \tabularnewline
12 & 0.161655 & 1.3428 & 0.091867 \tabularnewline
13 & 0.004439 & 0.0369 & 0.485346 \tabularnewline
14 & -0.106017 & -0.8806 & 0.809216 \tabularnewline
15 & -0.041433 & -0.3442 & 0.634118 \tabularnewline
16 & -0.009705 & -0.0806 & 0.532009 \tabularnewline
17 & 0.020382 & 0.1693 & 0.433026 \tabularnewline
18 & -0.100088 & -0.8314 & 0.79569 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6508&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]0.923886[/C][C]7.6744[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.058325[/C][C]0.4845[/C][C]0.31479[/C][/ROW]
[ROW][C]2[/C][C]-0.017027[/C][C]-0.1414[/C][C]0.55603[/C][/ROW]
[ROW][C]3[/C][C]-0.10186[/C][C]-0.8461[/C][C]0.799792[/C][/ROW]
[ROW][C]4[/C][C]0.008417[/C][C]0.0699[/C][C]0.47223[/C][/ROW]
[ROW][C]5[/C][C]0.041923[/C][C]0.3482[/C][C]0.36436[/C][/ROW]
[ROW][C]6[/C][C]-0.033236[/C][C]-0.2761[/C][C]0.608345[/C][/ROW]
[ROW][C]7[/C][C]-0.03142[/C][C]-0.261[/C][C]0.602562[/C][/ROW]
[ROW][C]8[/C][C]-0.018121[/C][C]-0.1505[/C][C]0.559605[/C][/ROW]
[ROW][C]9[/C][C]-0.146815[/C][C]-1.2195[/C][C]0.886604[/C][/ROW]
[ROW][C]10[/C][C]0.047008[/C][C]0.3905[/C][C]0.348693[/C][/ROW]
[ROW][C]11[/C][C]0.010169[/C][C]0.0845[/C][C]0.466462[/C][/ROW]
[ROW][C]12[/C][C]0.161655[/C][C]1.3428[/C][C]0.091867[/C][/ROW]
[ROW][C]13[/C][C]0.004439[/C][C]0.0369[/C][C]0.485346[/C][/ROW]
[ROW][C]14[/C][C]-0.106017[/C][C]-0.8806[/C][C]0.809216[/C][/ROW]
[ROW][C]15[/C][C]-0.041433[/C][C]-0.3442[/C][C]0.634118[/C][/ROW]
[ROW][C]16[/C][C]-0.009705[/C][C]-0.0806[/C][C]0.532009[/C][/ROW]
[ROW][C]17[/C][C]0.020382[/C][C]0.1693[/C][C]0.433026[/C][/ROW]
[ROW][C]18[/C][C]-0.100088[/C][C]-0.8314[/C][C]0.79569[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6508&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6508&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	0.923886	7.6744	0
1	0.058325	0.4845	0.31479
2	-0.017027	-0.1414	0.55603
3	-0.10186	-0.8461	0.799792
4	0.008417	0.0699	0.47223
5	0.041923	0.3482	0.36436
6	-0.033236	-0.2761	0.608345
7	-0.03142	-0.261	0.602562
8	-0.018121	-0.1505	0.559605
9	-0.146815	-1.2195	0.886604
10	0.047008	0.3905	0.348693
11	0.010169	0.0845	0.466462
12	0.161655	1.3428	0.091867
13	0.004439	0.0369	0.485346
14	-0.106017	-0.8806	0.809216
15	-0.041433	-0.3442	0.634118
16	-0.009705	-0.0806	0.532009
17	0.020382	0.1693	0.433026
18	-0.100088	-0.8314	0.79569

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 = 1 ; par5 = 12 ;

Parameters (R input):

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