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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 28 Nov 2007 03:46:36 -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/28/t119624617753nwneesykza495.htm/, Retrieved Thu, 02 May 2024 11:25:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7005, Retrieved Thu, 02 May 2024 11:25:37 +0000

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Estimated Impact

228

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-       [(Partial) Autocorrelation Function] [] [2007-11-28 10:46:36] [00ef4a509c2a49a63e98610ffa741e39] [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=7005&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=7005&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7005&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	0.474628	4.0273	6.9e-05
2	0.016227	0.1377	0.445434
3	-0.09618	-0.8161	0.791436
4	-0.136438	-1.1577	0.874596
5	-0.134632	-1.1424	0.871463
6	-0.196724	-1.6693	0.950296
7	-0.22441	-1.9042	0.969559
8	-0.211869	-1.7978	0.961797
9	-0.166907	-1.4163	0.919493
10	-0.026971	-0.2289	0.590185
11	0.293676	2.4919	0.007504
12	0.549192	4.66	7e-06
13	0.240087	2.0372	0.022653
14	-0.022075	-0.1873	0.574029
15	-0.088261	-0.7489	0.771827
16	-0.167465	-1.421	0.920182
17	-0.146717	-1.2449	0.891404

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & 0.474628 & 4.0273 & 6.9e-05 \tabularnewline
2 & 0.016227 & 0.1377 & 0.445434 \tabularnewline
3 & -0.09618 & -0.8161 & 0.791436 \tabularnewline
4 & -0.136438 & -1.1577 & 0.874596 \tabularnewline
5 & -0.134632 & -1.1424 & 0.871463 \tabularnewline
6 & -0.196724 & -1.6693 & 0.950296 \tabularnewline
7 & -0.22441 & -1.9042 & 0.969559 \tabularnewline
8 & -0.211869 & -1.7978 & 0.961797 \tabularnewline
9 & -0.166907 & -1.4163 & 0.919493 \tabularnewline
10 & -0.026971 & -0.2289 & 0.590185 \tabularnewline
11 & 0.293676 & 2.4919 & 0.007504 \tabularnewline
12 & 0.549192 & 4.66 & 7e-06 \tabularnewline
13 & 0.240087 & 2.0372 & 0.022653 \tabularnewline
14 & -0.022075 & -0.1873 & 0.574029 \tabularnewline
15 & -0.088261 & -0.7489 & 0.771827 \tabularnewline
16 & -0.167465 & -1.421 & 0.920182 \tabularnewline
17 & -0.146717 & -1.2449 & 0.891404 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7005&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]0.474628[/C][C]4.0273[/C][C]6.9e-05[/C][/ROW]
[ROW][C]2[/C][C]0.016227[/C][C]0.1377[/C][C]0.445434[/C][/ROW]
[ROW][C]3[/C][C]-0.09618[/C][C]-0.8161[/C][C]0.791436[/C][/ROW]
[ROW][C]4[/C][C]-0.136438[/C][C]-1.1577[/C][C]0.874596[/C][/ROW]
[ROW][C]5[/C][C]-0.134632[/C][C]-1.1424[/C][C]0.871463[/C][/ROW]
[ROW][C]6[/C][C]-0.196724[/C][C]-1.6693[/C][C]0.950296[/C][/ROW]
[ROW][C]7[/C][C]-0.22441[/C][C]-1.9042[/C][C]0.969559[/C][/ROW]
[ROW][C]8[/C][C]-0.211869[/C][C]-1.7978[/C][C]0.961797[/C][/ROW]
[ROW][C]9[/C][C]-0.166907[/C][C]-1.4163[/C][C]0.919493[/C][/ROW]
[ROW][C]10[/C][C]-0.026971[/C][C]-0.2289[/C][C]0.590185[/C][/ROW]
[ROW][C]11[/C][C]0.293676[/C][C]2.4919[/C][C]0.007504[/C][/ROW]
[ROW][C]12[/C][C]0.549192[/C][C]4.66[/C][C]7e-06[/C][/ROW]
[ROW][C]13[/C][C]0.240087[/C][C]2.0372[/C][C]0.022653[/C][/ROW]
[ROW][C]14[/C][C]-0.022075[/C][C]-0.1873[/C][C]0.574029[/C][/ROW]
[ROW][C]15[/C][C]-0.088261[/C][C]-0.7489[/C][C]0.771827[/C][/ROW]
[ROW][C]16[/C][C]-0.167465[/C][C]-1.421[/C][C]0.920182[/C][/ROW]
[ROW][C]17[/C][C]-0.146717[/C][C]-1.2449[/C][C]0.891404[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7005&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7005&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	0.474628	4.0273	6.9e-05
2	0.016227	0.1377	0.445434
3	-0.09618	-0.8161	0.791436
4	-0.136438	-1.1577	0.874596
5	-0.134632	-1.1424	0.871463
6	-0.196724	-1.6693	0.950296
7	-0.22441	-1.9042	0.969559
8	-0.211869	-1.7978	0.961797
9	-0.166907	-1.4163	0.919493
10	-0.026971	-0.2289	0.590185
11	0.293676	2.4919	0.007504
12	0.549192	4.66	7e-06
13	0.240087	2.0372	0.022653
14	-0.022075	-0.1873	0.574029
15	-0.088261	-0.7489	0.771827
16	-0.167465	-1.421	0.920182
17	-0.146717	-1.2449	0.891404

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.474628	4.0273	6.9e-05
1	-0.269829	-2.2896	0.98751
2	0.030778	0.2612	0.397356
3	-0.122067	-1.0358	0.848113
4	-0.036285	-0.3079	0.620471
5	-0.184608	-1.5664	0.939186
6	-0.095242	-0.8082	0.789168
7	-0.149847	-1.2715	0.896177
8	-0.098194	-0.8332	0.796256
9	0.008244	0.0699	0.472214
10	0.307083	2.6057	0.005567
11	0.325177	2.7592	0.003671
12	-0.256467	-2.1762	0.983589
13	0.034732	0.2947	0.384532
14	-0.099996	-0.8485	0.800512
15	-0.152291	-1.2922	0.899796
16	0.001539	0.0131	0.49481
17	-0.083998	-0.7127	0.760846

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.474628 & 4.0273 & 6.9e-05 \tabularnewline
1 & -0.269829 & -2.2896 & 0.98751 \tabularnewline
2 & 0.030778 & 0.2612 & 0.397356 \tabularnewline
3 & -0.122067 & -1.0358 & 0.848113 \tabularnewline
4 & -0.036285 & -0.3079 & 0.620471 \tabularnewline
5 & -0.184608 & -1.5664 & 0.939186 \tabularnewline
6 & -0.095242 & -0.8082 & 0.789168 \tabularnewline
7 & -0.149847 & -1.2715 & 0.896177 \tabularnewline
8 & -0.098194 & -0.8332 & 0.796256 \tabularnewline
9 & 0.008244 & 0.0699 & 0.472214 \tabularnewline
10 & 0.307083 & 2.6057 & 0.005567 \tabularnewline
11 & 0.325177 & 2.7592 & 0.003671 \tabularnewline
12 & -0.256467 & -2.1762 & 0.983589 \tabularnewline
13 & 0.034732 & 0.2947 & 0.384532 \tabularnewline
14 & -0.099996 & -0.8485 & 0.800512 \tabularnewline
15 & -0.152291 & -1.2922 & 0.899796 \tabularnewline
16 & 0.001539 & 0.0131 & 0.49481 \tabularnewline
17 & -0.083998 & -0.7127 & 0.760846 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7005&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]0.474628[/C][C]4.0273[/C][C]6.9e-05[/C][/ROW]
[ROW][C]1[/C][C]-0.269829[/C][C]-2.2896[/C][C]0.98751[/C][/ROW]
[ROW][C]2[/C][C]0.030778[/C][C]0.2612[/C][C]0.397356[/C][/ROW]
[ROW][C]3[/C][C]-0.122067[/C][C]-1.0358[/C][C]0.848113[/C][/ROW]
[ROW][C]4[/C][C]-0.036285[/C][C]-0.3079[/C][C]0.620471[/C][/ROW]
[ROW][C]5[/C][C]-0.184608[/C][C]-1.5664[/C][C]0.939186[/C][/ROW]
[ROW][C]6[/C][C]-0.095242[/C][C]-0.8082[/C][C]0.789168[/C][/ROW]
[ROW][C]7[/C][C]-0.149847[/C][C]-1.2715[/C][C]0.896177[/C][/ROW]
[ROW][C]8[/C][C]-0.098194[/C][C]-0.8332[/C][C]0.796256[/C][/ROW]
[ROW][C]9[/C][C]0.008244[/C][C]0.0699[/C][C]0.472214[/C][/ROW]
[ROW][C]10[/C][C]0.307083[/C][C]2.6057[/C][C]0.005567[/C][/ROW]
[ROW][C]11[/C][C]0.325177[/C][C]2.7592[/C][C]0.003671[/C][/ROW]
[ROW][C]12[/C][C]-0.256467[/C][C]-2.1762[/C][C]0.983589[/C][/ROW]
[ROW][C]13[/C][C]0.034732[/C][C]0.2947[/C][C]0.384532[/C][/ROW]
[ROW][C]14[/C][C]-0.099996[/C][C]-0.8485[/C][C]0.800512[/C][/ROW]
[ROW][C]15[/C][C]-0.152291[/C][C]-1.2922[/C][C]0.899796[/C][/ROW]
[ROW][C]16[/C][C]0.001539[/C][C]0.0131[/C][C]0.49481[/C][/ROW]
[ROW][C]17[/C][C]-0.083998[/C][C]-0.7127[/C][C]0.760846[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7005&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7005&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	0.474628	4.0273	6.9e-05
1	-0.269829	-2.2896	0.98751
2	0.030778	0.2612	0.397356
3	-0.122067	-1.0358	0.848113
4	-0.036285	-0.3079	0.620471
5	-0.184608	-1.5664	0.939186
6	-0.095242	-0.8082	0.789168
7	-0.149847	-1.2715	0.896177
8	-0.098194	-0.8332	0.796256
9	0.008244	0.0699	0.472214
10	0.307083	2.6057	0.005567
11	0.325177	2.7592	0.003671
12	-0.256467	-2.1762	0.983589
13	0.034732	0.2947	0.384532
14	-0.099996	-0.8485	0.800512
15	-0.152291	-1.2922	0.899796
16	0.001539	0.0131	0.49481
17	-0.083998	-0.7127	0.760846

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 = 0 ; par5 = 12 ;

Parameters (R input):

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