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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Nov 2007 09:48:49 -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/23/t11958360280hhm1lu2604by38.htm/, Retrieved Sun, 28 Apr 2024 21:29:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6229, Retrieved Sun, 28 Apr 2024 21:29:20 +0000

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No (this computation is public)

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Estimated Impact

201

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

-       [(Partial) Autocorrelation Function] [autocorrelatie we...] [2007-11-23 16:48:49] [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=6229&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=6229&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6229&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	7.6811	0
1	0.158225	1.2153	0.114537
2	-0.042724	-0.3282	0.628028
3	-0.181625	-1.3951	0.915891
4	0.038531	0.296	0.384148
5	0.114102	0.8764	0.192174
6	-0.048886	-0.3755	0.645682
7	0.007204	0.0553	0.478031
8	0.113495	0.8718	0.193434
9	0.242558	1.8631	0.033712
10	-0.084648	-0.6502	0.740955
11	-0.095256	-0.7317	0.766367
12	-0.196681	-1.5107	0.931903
13	0.122293	0.9394	0.17569
14	0.295601	2.2706	0.01342
15	0.095815	0.736	0.232332
16	0.021631	0.1662	0.434303
17	-0.138201	-1.0615	0.853616

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6811 & 0 \tabularnewline
1 & 0.158225 & 1.2153 & 0.114537 \tabularnewline
2 & -0.042724 & -0.3282 & 0.628028 \tabularnewline
3 & -0.181625 & -1.3951 & 0.915891 \tabularnewline
4 & 0.038531 & 0.296 & 0.384148 \tabularnewline
5 & 0.114102 & 0.8764 & 0.192174 \tabularnewline
6 & -0.048886 & -0.3755 & 0.645682 \tabularnewline
7 & 0.007204 & 0.0553 & 0.478031 \tabularnewline
8 & 0.113495 & 0.8718 & 0.193434 \tabularnewline
9 & 0.242558 & 1.8631 & 0.033712 \tabularnewline
10 & -0.084648 & -0.6502 & 0.740955 \tabularnewline
11 & -0.095256 & -0.7317 & 0.766367 \tabularnewline
12 & -0.196681 & -1.5107 & 0.931903 \tabularnewline
13 & 0.122293 & 0.9394 & 0.17569 \tabularnewline
14 & 0.295601 & 2.2706 & 0.01342 \tabularnewline
15 & 0.095815 & 0.736 & 0.232332 \tabularnewline
16 & 0.021631 & 0.1662 & 0.434303 \tabularnewline
17 & -0.138201 & -1.0615 & 0.853616 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6229&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]7.6811[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.158225[/C][C]1.2153[/C][C]0.114537[/C][/ROW]
[ROW][C]2[/C][C]-0.042724[/C][C]-0.3282[/C][C]0.628028[/C][/ROW]
[ROW][C]3[/C][C]-0.181625[/C][C]-1.3951[/C][C]0.915891[/C][/ROW]
[ROW][C]4[/C][C]0.038531[/C][C]0.296[/C][C]0.384148[/C][/ROW]
[ROW][C]5[/C][C]0.114102[/C][C]0.8764[/C][C]0.192174[/C][/ROW]
[ROW][C]6[/C][C]-0.048886[/C][C]-0.3755[/C][C]0.645682[/C][/ROW]
[ROW][C]7[/C][C]0.007204[/C][C]0.0553[/C][C]0.478031[/C][/ROW]
[ROW][C]8[/C][C]0.113495[/C][C]0.8718[/C][C]0.193434[/C][/ROW]
[ROW][C]9[/C][C]0.242558[/C][C]1.8631[/C][C]0.033712[/C][/ROW]
[ROW][C]10[/C][C]-0.084648[/C][C]-0.6502[/C][C]0.740955[/C][/ROW]
[ROW][C]11[/C][C]-0.095256[/C][C]-0.7317[/C][C]0.766367[/C][/ROW]
[ROW][C]12[/C][C]-0.196681[/C][C]-1.5107[/C][C]0.931903[/C][/ROW]
[ROW][C]13[/C][C]0.122293[/C][C]0.9394[/C][C]0.17569[/C][/ROW]
[ROW][C]14[/C][C]0.295601[/C][C]2.2706[/C][C]0.01342[/C][/ROW]
[ROW][C]15[/C][C]0.095815[/C][C]0.736[/C][C]0.232332[/C][/ROW]
[ROW][C]16[/C][C]0.021631[/C][C]0.1662[/C][C]0.434303[/C][/ROW]
[ROW][C]17[/C][C]-0.138201[/C][C]-1.0615[/C][C]0.853616[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6229&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6229&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	7.6811	0
1	0.158225	1.2153	0.114537
2	-0.042724	-0.3282	0.628028
3	-0.181625	-1.3951	0.915891
4	0.038531	0.296	0.384148
5	0.114102	0.8764	0.192174
6	-0.048886	-0.3755	0.645682
7	0.007204	0.0553	0.478031
8	0.113495	0.8718	0.193434
9	0.242558	1.8631	0.033712
10	-0.084648	-0.6502	0.740955
11	-0.095256	-0.7317	0.766367
12	-0.196681	-1.5107	0.931903
13	0.122293	0.9394	0.17569
14	0.295601	2.2706	0.01342
15	0.095815	0.736	0.232332
16	0.021631	0.1662	0.434303
17	-0.138201	-1.0615	0.853616

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.158225	1.2153	0.114537
1	-0.069499	-0.5338	0.702269
2	-0.168408	-1.2936	0.899572
3	0.097625	0.7499	0.228155
4	0.082871	0.6365	0.263443
5	-0.117922	-0.9058	0.81563
6	0.068478	0.526	0.300433
7	0.146844	1.1279	0.131957
8	0.171867	1.3201	0.095944
9	-0.162576	-1.2488	0.89166
10	0.010897	0.0837	0.466789
11	-0.142668	-1.0959	0.861202
12	0.106178	0.8156	0.209015
13	0.261034	2.005	0.024777
14	0.008431	0.0648	0.474293
15	0.023819	0.183	0.427728
16	-0.107293	-0.8241	0.793408
17	0.073639	0.5656	0.286894

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.158225 & 1.2153 & 0.114537 \tabularnewline
1 & -0.069499 & -0.5338 & 0.702269 \tabularnewline
2 & -0.168408 & -1.2936 & 0.899572 \tabularnewline
3 & 0.097625 & 0.7499 & 0.228155 \tabularnewline
4 & 0.082871 & 0.6365 & 0.263443 \tabularnewline
5 & -0.117922 & -0.9058 & 0.81563 \tabularnewline
6 & 0.068478 & 0.526 & 0.300433 \tabularnewline
7 & 0.146844 & 1.1279 & 0.131957 \tabularnewline
8 & 0.171867 & 1.3201 & 0.095944 \tabularnewline
9 & -0.162576 & -1.2488 & 0.89166 \tabularnewline
10 & 0.010897 & 0.0837 & 0.466789 \tabularnewline
11 & -0.142668 & -1.0959 & 0.861202 \tabularnewline
12 & 0.106178 & 0.8156 & 0.209015 \tabularnewline
13 & 0.261034 & 2.005 & 0.024777 \tabularnewline
14 & 0.008431 & 0.0648 & 0.474293 \tabularnewline
15 & 0.023819 & 0.183 & 0.427728 \tabularnewline
16 & -0.107293 & -0.8241 & 0.793408 \tabularnewline
17 & 0.073639 & 0.5656 & 0.286894 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6229&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]0.158225[/C][C]1.2153[/C][C]0.114537[/C][/ROW]
[ROW][C]1[/C][C]-0.069499[/C][C]-0.5338[/C][C]0.702269[/C][/ROW]
[ROW][C]2[/C][C]-0.168408[/C][C]-1.2936[/C][C]0.899572[/C][/ROW]
[ROW][C]3[/C][C]0.097625[/C][C]0.7499[/C][C]0.228155[/C][/ROW]
[ROW][C]4[/C][C]0.082871[/C][C]0.6365[/C][C]0.263443[/C][/ROW]
[ROW][C]5[/C][C]-0.117922[/C][C]-0.9058[/C][C]0.81563[/C][/ROW]
[ROW][C]6[/C][C]0.068478[/C][C]0.526[/C][C]0.300433[/C][/ROW]
[ROW][C]7[/C][C]0.146844[/C][C]1.1279[/C][C]0.131957[/C][/ROW]
[ROW][C]8[/C][C]0.171867[/C][C]1.3201[/C][C]0.095944[/C][/ROW]
[ROW][C]9[/C][C]-0.162576[/C][C]-1.2488[/C][C]0.89166[/C][/ROW]
[ROW][C]10[/C][C]0.010897[/C][C]0.0837[/C][C]0.466789[/C][/ROW]
[ROW][C]11[/C][C]-0.142668[/C][C]-1.0959[/C][C]0.861202[/C][/ROW]
[ROW][C]12[/C][C]0.106178[/C][C]0.8156[/C][C]0.209015[/C][/ROW]
[ROW][C]13[/C][C]0.261034[/C][C]2.005[/C][C]0.024777[/C][/ROW]
[ROW][C]14[/C][C]0.008431[/C][C]0.0648[/C][C]0.474293[/C][/ROW]
[ROW][C]15[/C][C]0.023819[/C][C]0.183[/C][C]0.427728[/C][/ROW]
[ROW][C]16[/C][C]-0.107293[/C][C]-0.8241[/C][C]0.793408[/C][/ROW]
[ROW][C]17[/C][C]0.073639[/C][C]0.5656[/C][C]0.286894[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6229&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6229&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	0.158225	1.2153	0.114537
1	-0.069499	-0.5338	0.702269
2	-0.168408	-1.2936	0.899572
3	0.097625	0.7499	0.228155
4	0.082871	0.6365	0.263443
5	-0.117922	-0.9058	0.81563
6	0.068478	0.526	0.300433
7	0.146844	1.1279	0.131957
8	0.171867	1.3201	0.095944
9	-0.162576	-1.2488	0.89166
10	0.010897	0.0837	0.466789
11	-0.142668	-1.0959	0.861202
12	0.106178	0.8156	0.209015
13	0.261034	2.005	0.024777
14	0.008431	0.0648	0.474293
15	0.023819	0.183	0.427728
16	-0.107293	-0.8241	0.793408
17	0.073639	0.5656	0.286894

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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