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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Nov 2007 08:08:18 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/22/t1195743606b8ts7k73fij25r6.htm/, Retrieved Fri, 03 May 2024 00:32:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6040, Retrieved Fri, 03 May 2024 00:32:47 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

W10Q2G7

Estimated Impact

189

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

-       [(Partial) Autocorrelation Function] [autocorrelation f...] [2007-11-22 15:08:18] [65108f21b143a71c6470aac06bd65b08] [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=6040&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=6040&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6040&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	8.4853	0
1	-0.142507	-1.2092	0.884731
2	-0.142638	-1.2103	0.884944
3	-0.030371	-0.2577	0.601316
4	-0.065998	-0.56	0.711396
5	-0.025455	-0.216	0.585197
6	-0.073376	-0.6226	0.732248
7	0.150636	1.2782	0.102644
8	-0.107304	-0.9105	0.817202
9	0.056703	0.4811	0.315938
10	0.052674	0.447	0.328125
11	-0.197889	-1.6791	0.951271
12	-0.021693	-0.1841	0.572763
13	-0.039586	-0.3359	0.631037
14	-0.034904	-0.2962	0.616024
15	0.013957	0.1184	0.453028
16	0.188244	1.5973	0.057289
17	-0.075581	-0.6413	0.738327

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & -0.142507 & -1.2092 & 0.884731 \tabularnewline
2 & -0.142638 & -1.2103 & 0.884944 \tabularnewline
3 & -0.030371 & -0.2577 & 0.601316 \tabularnewline
4 & -0.065998 & -0.56 & 0.711396 \tabularnewline
5 & -0.025455 & -0.216 & 0.585197 \tabularnewline
6 & -0.073376 & -0.6226 & 0.732248 \tabularnewline
7 & 0.150636 & 1.2782 & 0.102644 \tabularnewline
8 & -0.107304 & -0.9105 & 0.817202 \tabularnewline
9 & 0.056703 & 0.4811 & 0.315938 \tabularnewline
10 & 0.052674 & 0.447 & 0.328125 \tabularnewline
11 & -0.197889 & -1.6791 & 0.951271 \tabularnewline
12 & -0.021693 & -0.1841 & 0.572763 \tabularnewline
13 & -0.039586 & -0.3359 & 0.631037 \tabularnewline
14 & -0.034904 & -0.2962 & 0.616024 \tabularnewline
15 & 0.013957 & 0.1184 & 0.453028 \tabularnewline
16 & 0.188244 & 1.5973 & 0.057289 \tabularnewline
17 & -0.075581 & -0.6413 & 0.738327 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6040&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]-0.142507[/C][C]-1.2092[/C][C]0.884731[/C][/ROW]
[ROW][C]2[/C][C]-0.142638[/C][C]-1.2103[/C][C]0.884944[/C][/ROW]
[ROW][C]3[/C][C]-0.030371[/C][C]-0.2577[/C][C]0.601316[/C][/ROW]
[ROW][C]4[/C][C]-0.065998[/C][C]-0.56[/C][C]0.711396[/C][/ROW]
[ROW][C]5[/C][C]-0.025455[/C][C]-0.216[/C][C]0.585197[/C][/ROW]
[ROW][C]6[/C][C]-0.073376[/C][C]-0.6226[/C][C]0.732248[/C][/ROW]
[ROW][C]7[/C][C]0.150636[/C][C]1.2782[/C][C]0.102644[/C][/ROW]
[ROW][C]8[/C][C]-0.107304[/C][C]-0.9105[/C][C]0.817202[/C][/ROW]
[ROW][C]9[/C][C]0.056703[/C][C]0.4811[/C][C]0.315938[/C][/ROW]
[ROW][C]10[/C][C]0.052674[/C][C]0.447[/C][C]0.328125[/C][/ROW]
[ROW][C]11[/C][C]-0.197889[/C][C]-1.6791[/C][C]0.951271[/C][/ROW]
[ROW][C]12[/C][C]-0.021693[/C][C]-0.1841[/C][C]0.572763[/C][/ROW]
[ROW][C]13[/C][C]-0.039586[/C][C]-0.3359[/C][C]0.631037[/C][/ROW]
[ROW][C]14[/C][C]-0.034904[/C][C]-0.2962[/C][C]0.616024[/C][/ROW]
[ROW][C]15[/C][C]0.013957[/C][C]0.1184[/C][C]0.453028[/C][/ROW]
[ROW][C]16[/C][C]0.188244[/C][C]1.5973[/C][C]0.057289[/C][/ROW]
[ROW][C]17[/C][C]-0.075581[/C][C]-0.6413[/C][C]0.738327[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6040&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6040&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	-0.142507	-1.2092	0.884731
2	-0.142638	-1.2103	0.884944
3	-0.030371	-0.2577	0.601316
4	-0.065998	-0.56	0.711396
5	-0.025455	-0.216	0.585197
6	-0.073376	-0.6226	0.732248
7	0.150636	1.2782	0.102644
8	-0.107304	-0.9105	0.817202
9	0.056703	0.4811	0.315938
10	0.052674	0.447	0.328125
11	-0.197889	-1.6791	0.951271
12	-0.021693	-0.1841	0.572763
13	-0.039586	-0.3359	0.631037
14	-0.034904	-0.2962	0.616024
15	0.013957	0.1184	0.453028
16	0.188244	1.5973	0.057289
17	-0.075581	-0.6413	0.738327

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.142507	-1.2092	0.884731
1	-0.166324	-1.4113	0.918769
2	-0.081652	-0.6928	0.754681
3	-0.114933	-0.9752	0.833647
4	-0.080327	-0.6816	0.75116
5	-0.135614	-1.1507	0.873174
6	0.089172	0.7566	0.225865
7	-0.124924	-1.06	0.853659
8	0.042814	0.3633	0.358726
9	0.028143	0.2388	0.405969
10	-0.18358	-1.5577	0.938159
11	-0.092915	-0.7884	0.783476
12	-0.120734	-1.0245	0.845477
13	-0.165408	-1.4035	0.917622
14	-0.079676	-0.6761	0.74942
15	0.092368	0.7838	0.217873
16	-0.126511	-1.0735	0.856679
17	-0.107406	-0.9114	0.81743

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.142507 & -1.2092 & 0.884731 \tabularnewline
1 & -0.166324 & -1.4113 & 0.918769 \tabularnewline
2 & -0.081652 & -0.6928 & 0.754681 \tabularnewline
3 & -0.114933 & -0.9752 & 0.833647 \tabularnewline
4 & -0.080327 & -0.6816 & 0.75116 \tabularnewline
5 & -0.135614 & -1.1507 & 0.873174 \tabularnewline
6 & 0.089172 & 0.7566 & 0.225865 \tabularnewline
7 & -0.124924 & -1.06 & 0.853659 \tabularnewline
8 & 0.042814 & 0.3633 & 0.358726 \tabularnewline
9 & 0.028143 & 0.2388 & 0.405969 \tabularnewline
10 & -0.18358 & -1.5577 & 0.938159 \tabularnewline
11 & -0.092915 & -0.7884 & 0.783476 \tabularnewline
12 & -0.120734 & -1.0245 & 0.845477 \tabularnewline
13 & -0.165408 & -1.4035 & 0.917622 \tabularnewline
14 & -0.079676 & -0.6761 & 0.74942 \tabularnewline
15 & 0.092368 & 0.7838 & 0.217873 \tabularnewline
16 & -0.126511 & -1.0735 & 0.856679 \tabularnewline
17 & -0.107406 & -0.9114 & 0.81743 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6040&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]-0.142507[/C][C]-1.2092[/C][C]0.884731[/C][/ROW]
[ROW][C]1[/C][C]-0.166324[/C][C]-1.4113[/C][C]0.918769[/C][/ROW]
[ROW][C]2[/C][C]-0.081652[/C][C]-0.6928[/C][C]0.754681[/C][/ROW]
[ROW][C]3[/C][C]-0.114933[/C][C]-0.9752[/C][C]0.833647[/C][/ROW]
[ROW][C]4[/C][C]-0.080327[/C][C]-0.6816[/C][C]0.75116[/C][/ROW]
[ROW][C]5[/C][C]-0.135614[/C][C]-1.1507[/C][C]0.873174[/C][/ROW]
[ROW][C]6[/C][C]0.089172[/C][C]0.7566[/C][C]0.225865[/C][/ROW]
[ROW][C]7[/C][C]-0.124924[/C][C]-1.06[/C][C]0.853659[/C][/ROW]
[ROW][C]8[/C][C]0.042814[/C][C]0.3633[/C][C]0.358726[/C][/ROW]
[ROW][C]9[/C][C]0.028143[/C][C]0.2388[/C][C]0.405969[/C][/ROW]
[ROW][C]10[/C][C]-0.18358[/C][C]-1.5577[/C][C]0.938159[/C][/ROW]
[ROW][C]11[/C][C]-0.092915[/C][C]-0.7884[/C][C]0.783476[/C][/ROW]
[ROW][C]12[/C][C]-0.120734[/C][C]-1.0245[/C][C]0.845477[/C][/ROW]
[ROW][C]13[/C][C]-0.165408[/C][C]-1.4035[/C][C]0.917622[/C][/ROW]
[ROW][C]14[/C][C]-0.079676[/C][C]-0.6761[/C][C]0.74942[/C][/ROW]
[ROW][C]15[/C][C]0.092368[/C][C]0.7838[/C][C]0.217873[/C][/ROW]
[ROW][C]16[/C][C]-0.126511[/C][C]-1.0735[/C][C]0.856679[/C][/ROW]
[ROW][C]17[/C][C]-0.107406[/C][C]-0.9114[/C][C]0.81743[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6040&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6040&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	-0.142507	-1.2092	0.884731
1	-0.166324	-1.4113	0.918769
2	-0.081652	-0.6928	0.754681
3	-0.114933	-0.9752	0.833647
4	-0.080327	-0.6816	0.75116
5	-0.135614	-1.1507	0.873174
6	0.089172	0.7566	0.225865
7	-0.124924	-1.06	0.853659
8	0.042814	0.3633	0.358726
9	0.028143	0.2388	0.405969
10	-0.18358	-1.5577	0.938159
11	-0.092915	-0.7884	0.783476
12	-0.120734	-1.0245	0.845477
13	-0.165408	-1.4035	0.917622
14	-0.079676	-0.6761	0.74942
15	0.092368	0.7838	0.217873
16	-0.126511	-1.0735	0.856679
17	-0.107406	-0.9114	0.81743

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 = 0 ; par5 = 12 ;

Parameters (R input):

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