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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 17 Dec 2007 15:22:37 -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/Dec/17/t1197929165rjdy7nav55v03tq.htm/, Retrieved Sat, 04 May 2024 01:51:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4439, Retrieved Sat, 04 May 2024 01:51:05 +0000

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Estimated Impact

170

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-       [(Partial) Autocorrelation Function] [] [2007-12-17 22:22:37] [ba3202e2798d2e4685d19d988e9c69df] [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=4439&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=4439&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4439&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	8.4261	0
1	0.108576	0.9149	0.181677
2	-0.053514	-0.4509	0.673288
3	0.131815	1.1107	0.135223
4	-0.023439	-0.1975	0.578
5	-0.149072	-1.2561	0.893401
6	-0.007258	-0.0612	0.524296
7	-0.045352	-0.3821	0.648253
8	0.121053	1.02	0.155593
9	0.008751	0.0737	0.470712
10	0.114326	0.9633	0.169326
11	0.237904	2.0046	0.024409
12	0.02433	0.205	0.419077
13	-0.191852	-1.6166	0.944797
14	-0.005117	-0.0431	0.517137
15	-0.226312	-1.9069	0.969712
16	-0.152848	-1.2879	0.899023
17	-0.128316	-1.0812	0.858369

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4261 & 0 \tabularnewline
1 & 0.108576 & 0.9149 & 0.181677 \tabularnewline
2 & -0.053514 & -0.4509 & 0.673288 \tabularnewline
3 & 0.131815 & 1.1107 & 0.135223 \tabularnewline
4 & -0.023439 & -0.1975 & 0.578 \tabularnewline
5 & -0.149072 & -1.2561 & 0.893401 \tabularnewline
6 & -0.007258 & -0.0612 & 0.524296 \tabularnewline
7 & -0.045352 & -0.3821 & 0.648253 \tabularnewline
8 & 0.121053 & 1.02 & 0.155593 \tabularnewline
9 & 0.008751 & 0.0737 & 0.470712 \tabularnewline
10 & 0.114326 & 0.9633 & 0.169326 \tabularnewline
11 & 0.237904 & 2.0046 & 0.024409 \tabularnewline
12 & 0.02433 & 0.205 & 0.419077 \tabularnewline
13 & -0.191852 & -1.6166 & 0.944797 \tabularnewline
14 & -0.005117 & -0.0431 & 0.517137 \tabularnewline
15 & -0.226312 & -1.9069 & 0.969712 \tabularnewline
16 & -0.152848 & -1.2879 & 0.899023 \tabularnewline
17 & -0.128316 & -1.0812 & 0.858369 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4439&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]8.4261[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.108576[/C][C]0.9149[/C][C]0.181677[/C][/ROW]
[ROW][C]2[/C][C]-0.053514[/C][C]-0.4509[/C][C]0.673288[/C][/ROW]
[ROW][C]3[/C][C]0.131815[/C][C]1.1107[/C][C]0.135223[/C][/ROW]
[ROW][C]4[/C][C]-0.023439[/C][C]-0.1975[/C][C]0.578[/C][/ROW]
[ROW][C]5[/C][C]-0.149072[/C][C]-1.2561[/C][C]0.893401[/C][/ROW]
[ROW][C]6[/C][C]-0.007258[/C][C]-0.0612[/C][C]0.524296[/C][/ROW]
[ROW][C]7[/C][C]-0.045352[/C][C]-0.3821[/C][C]0.648253[/C][/ROW]
[ROW][C]8[/C][C]0.121053[/C][C]1.02[/C][C]0.155593[/C][/ROW]
[ROW][C]9[/C][C]0.008751[/C][C]0.0737[/C][C]0.470712[/C][/ROW]
[ROW][C]10[/C][C]0.114326[/C][C]0.9633[/C][C]0.169326[/C][/ROW]
[ROW][C]11[/C][C]0.237904[/C][C]2.0046[/C][C]0.024409[/C][/ROW]
[ROW][C]12[/C][C]0.02433[/C][C]0.205[/C][C]0.419077[/C][/ROW]
[ROW][C]13[/C][C]-0.191852[/C][C]-1.6166[/C][C]0.944797[/C][/ROW]
[ROW][C]14[/C][C]-0.005117[/C][C]-0.0431[/C][C]0.517137[/C][/ROW]
[ROW][C]15[/C][C]-0.226312[/C][C]-1.9069[/C][C]0.969712[/C][/ROW]
[ROW][C]16[/C][C]-0.152848[/C][C]-1.2879[/C][C]0.899023[/C][/ROW]
[ROW][C]17[/C][C]-0.128316[/C][C]-1.0812[/C][C]0.858369[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4439&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4439&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	8.4261	0
1	0.108576	0.9149	0.181677
2	-0.053514	-0.4509	0.673288
3	0.131815	1.1107	0.135223
4	-0.023439	-0.1975	0.578
5	-0.149072	-1.2561	0.893401
6	-0.007258	-0.0612	0.524296
7	-0.045352	-0.3821	0.648253
8	0.121053	1.02	0.155593
9	0.008751	0.0737	0.470712
10	0.114326	0.9633	0.169326
11	0.237904	2.0046	0.024409
12	0.02433	0.205	0.419077
13	-0.191852	-1.6166	0.944797
14	-0.005117	-0.0431	0.517137
15	-0.226312	-1.9069	0.969712
16	-0.152848	-1.2879	0.899023
17	-0.128316	-1.0812	0.858369

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.108576	0.9149	0.181677
1	-0.066082	-0.5568	0.710297
2	0.147561	1.2434	0.108911
3	-0.062811	-0.5293	0.70086
4	-0.124259	-1.047	0.85068
5	0.002156	0.0182	0.49278
6	-0.055281	-0.4658	0.678609
7	0.180567	1.5215	0.06629
8	-0.049705	-0.4188	0.661695
9	0.147511	1.2429	0.108988
10	0.173011	1.4578	0.07465
11	-0.017905	-0.1509	0.559748
12	-0.174248	-1.4682	0.926772
13	-0.033592	-0.2831	0.611021
14	-0.223528	-1.8835	0.968135
15	-0.028782	-0.2425	0.595464
16	-0.159161	-1.3411	0.907921
17	0.085465	0.7201	0.236901

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.108576 & 0.9149 & 0.181677 \tabularnewline
1 & -0.066082 & -0.5568 & 0.710297 \tabularnewline
2 & 0.147561 & 1.2434 & 0.108911 \tabularnewline
3 & -0.062811 & -0.5293 & 0.70086 \tabularnewline
4 & -0.124259 & -1.047 & 0.85068 \tabularnewline
5 & 0.002156 & 0.0182 & 0.49278 \tabularnewline
6 & -0.055281 & -0.4658 & 0.678609 \tabularnewline
7 & 0.180567 & 1.5215 & 0.06629 \tabularnewline
8 & -0.049705 & -0.4188 & 0.661695 \tabularnewline
9 & 0.147511 & 1.2429 & 0.108988 \tabularnewline
10 & 0.173011 & 1.4578 & 0.07465 \tabularnewline
11 & -0.017905 & -0.1509 & 0.559748 \tabularnewline
12 & -0.174248 & -1.4682 & 0.926772 \tabularnewline
13 & -0.033592 & -0.2831 & 0.611021 \tabularnewline
14 & -0.223528 & -1.8835 & 0.968135 \tabularnewline
15 & -0.028782 & -0.2425 & 0.595464 \tabularnewline
16 & -0.159161 & -1.3411 & 0.907921 \tabularnewline
17 & 0.085465 & 0.7201 & 0.236901 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4439&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]0.108576[/C][C]0.9149[/C][C]0.181677[/C][/ROW]
[ROW][C]1[/C][C]-0.066082[/C][C]-0.5568[/C][C]0.710297[/C][/ROW]
[ROW][C]2[/C][C]0.147561[/C][C]1.2434[/C][C]0.108911[/C][/ROW]
[ROW][C]3[/C][C]-0.062811[/C][C]-0.5293[/C][C]0.70086[/C][/ROW]
[ROW][C]4[/C][C]-0.124259[/C][C]-1.047[/C][C]0.85068[/C][/ROW]
[ROW][C]5[/C][C]0.002156[/C][C]0.0182[/C][C]0.49278[/C][/ROW]
[ROW][C]6[/C][C]-0.055281[/C][C]-0.4658[/C][C]0.678609[/C][/ROW]
[ROW][C]7[/C][C]0.180567[/C][C]1.5215[/C][C]0.06629[/C][/ROW]
[ROW][C]8[/C][C]-0.049705[/C][C]-0.4188[/C][C]0.661695[/C][/ROW]
[ROW][C]9[/C][C]0.147511[/C][C]1.2429[/C][C]0.108988[/C][/ROW]
[ROW][C]10[/C][C]0.173011[/C][C]1.4578[/C][C]0.07465[/C][/ROW]
[ROW][C]11[/C][C]-0.017905[/C][C]-0.1509[/C][C]0.559748[/C][/ROW]
[ROW][C]12[/C][C]-0.174248[/C][C]-1.4682[/C][C]0.926772[/C][/ROW]
[ROW][C]13[/C][C]-0.033592[/C][C]-0.2831[/C][C]0.611021[/C][/ROW]
[ROW][C]14[/C][C]-0.223528[/C][C]-1.8835[/C][C]0.968135[/C][/ROW]
[ROW][C]15[/C][C]-0.028782[/C][C]-0.2425[/C][C]0.595464[/C][/ROW]
[ROW][C]16[/C][C]-0.159161[/C][C]-1.3411[/C][C]0.907921[/C][/ROW]
[ROW][C]17[/C][C]0.085465[/C][C]0.7201[/C][C]0.236901[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4439&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4439&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	0.108576	0.9149	0.181677
1	-0.066082	-0.5568	0.710297
2	0.147561	1.2434	0.108911
3	-0.062811	-0.5293	0.70086
4	-0.124259	-1.047	0.85068
5	0.002156	0.0182	0.49278
6	-0.055281	-0.4658	0.678609
7	0.180567	1.5215	0.06629
8	-0.049705	-0.4188	0.661695
9	0.147511	1.2429	0.108988
10	0.173011	1.4578	0.07465
11	-0.017905	-0.1509	0.559748
12	-0.174248	-1.4682	0.926772
13	-0.033592	-0.2831	0.611021
14	-0.223528	-1.8835	0.968135
15	-0.028782	-0.2425	0.595464
16	-0.159161	-1.3411	0.907921
17	0.085465	0.7201	0.236901

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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