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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Nov 2007 08:42:24 -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/t1195832021kta1z43u8m8afk0.htm/, Retrieved Mon, 29 Apr 2024 06:56:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6198, Retrieved Mon, 29 Apr 2024 06:56:41 +0000

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No (this computation is public)

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Estimated Impact

159

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

-       [(Partial) Autocorrelation Function] [] [2007-11-23 15:42:24] [a1fadf46580e43815db2830b4560d35f] [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=6198&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=6198&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6198&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	0.358077	2.7504	0.003945
2	0.104072	0.7994	0.213635
3	0.079765	0.6127	0.27122
4	-0.137429	-1.0556	0.852276
5	-0.333937	-2.565	0.99356
6	-0.249986	-1.9202	0.970163
7	-0.294738	-2.2639	0.986365
8	-0.267539	-2.055	0.977843
9	-0.146549	-1.1257	0.867567
10	0.026339	0.2023	0.420183
11	0.133742	1.0273	0.154239
12	0.126518	0.9718	0.167557
13	0.210335	1.6156	0.055756
14	0.221617	1.7023	0.046984
15	-0.056174	-0.4315	0.666154
16	0.045689	0.3509	0.36344

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6811 & 0 \tabularnewline
1 & 0.358077 & 2.7504 & 0.003945 \tabularnewline
2 & 0.104072 & 0.7994 & 0.213635 \tabularnewline
3 & 0.079765 & 0.6127 & 0.27122 \tabularnewline
4 & -0.137429 & -1.0556 & 0.852276 \tabularnewline
5 & -0.333937 & -2.565 & 0.99356 \tabularnewline
6 & -0.249986 & -1.9202 & 0.970163 \tabularnewline
7 & -0.294738 & -2.2639 & 0.986365 \tabularnewline
8 & -0.267539 & -2.055 & 0.977843 \tabularnewline
9 & -0.146549 & -1.1257 & 0.867567 \tabularnewline
10 & 0.026339 & 0.2023 & 0.420183 \tabularnewline
11 & 0.133742 & 1.0273 & 0.154239 \tabularnewline
12 & 0.126518 & 0.9718 & 0.167557 \tabularnewline
13 & 0.210335 & 1.6156 & 0.055756 \tabularnewline
14 & 0.221617 & 1.7023 & 0.046984 \tabularnewline
15 & -0.056174 & -0.4315 & 0.666154 \tabularnewline
16 & 0.045689 & 0.3509 & 0.36344 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6198&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]0.358077[/C][C]2.7504[/C][C]0.003945[/C][/ROW]
[ROW][C]2[/C][C]0.104072[/C][C]0.7994[/C][C]0.213635[/C][/ROW]
[ROW][C]3[/C][C]0.079765[/C][C]0.6127[/C][C]0.27122[/C][/ROW]
[ROW][C]4[/C][C]-0.137429[/C][C]-1.0556[/C][C]0.852276[/C][/ROW]
[ROW][C]5[/C][C]-0.333937[/C][C]-2.565[/C][C]0.99356[/C][/ROW]
[ROW][C]6[/C][C]-0.249986[/C][C]-1.9202[/C][C]0.970163[/C][/ROW]
[ROW][C]7[/C][C]-0.294738[/C][C]-2.2639[/C][C]0.986365[/C][/ROW]
[ROW][C]8[/C][C]-0.267539[/C][C]-2.055[/C][C]0.977843[/C][/ROW]
[ROW][C]9[/C][C]-0.146549[/C][C]-1.1257[/C][C]0.867567[/C][/ROW]
[ROW][C]10[/C][C]0.026339[/C][C]0.2023[/C][C]0.420183[/C][/ROW]
[ROW][C]11[/C][C]0.133742[/C][C]1.0273[/C][C]0.154239[/C][/ROW]
[ROW][C]12[/C][C]0.126518[/C][C]0.9718[/C][C]0.167557[/C][/ROW]
[ROW][C]13[/C][C]0.210335[/C][C]1.6156[/C][C]0.055756[/C][/ROW]
[ROW][C]14[/C][C]0.221617[/C][C]1.7023[/C][C]0.046984[/C][/ROW]
[ROW][C]15[/C][C]-0.056174[/C][C]-0.4315[/C][C]0.666154[/C][/ROW]
[ROW][C]16[/C][C]0.045689[/C][C]0.3509[/C][C]0.36344[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6198&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6198&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	0.358077	2.7504	0.003945
2	0.104072	0.7994	0.213635
3	0.079765	0.6127	0.27122
4	-0.137429	-1.0556	0.852276
5	-0.333937	-2.565	0.99356
6	-0.249986	-1.9202	0.970163
7	-0.294738	-2.2639	0.986365
8	-0.267539	-2.055	0.977843
9	-0.146549	-1.1257	0.867567
10	0.026339	0.2023	0.420183
11	0.133742	1.0273	0.154239
12	0.126518	0.9718	0.167557
13	0.210335	1.6156	0.055756
14	0.221617	1.7023	0.046984
15	-0.056174	-0.4315	0.666154
16	0.045689	0.3509	0.36344

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.358077	2.7504	0.003945
1	-0.027699	-0.2128	0.583875
2	0.058988	0.4531	0.326071
3	-0.210687	-1.6183	0.944536
4	-0.259734	-1.9951	0.974669
5	-0.063452	-0.4874	0.686104
6	-0.198786	-1.5269	0.933936
7	-0.114661	-0.8807	0.808981
8	-0.112321	-0.8628	0.804117
9	0.016191	0.1244	0.450723
10	0.036941	0.2837	0.388798
11	-0.093566	-0.7187	0.762416
12	0.049759	0.3822	0.351841
13	0.020532	0.1577	0.437611
14	-0.245565	-1.8862	0.967905
15	0.127637	0.9804	0.165447
16	-0.178233	-1.369	0.911911

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.358077 & 2.7504 & 0.003945 \tabularnewline
1 & -0.027699 & -0.2128 & 0.583875 \tabularnewline
2 & 0.058988 & 0.4531 & 0.326071 \tabularnewline
3 & -0.210687 & -1.6183 & 0.944536 \tabularnewline
4 & -0.259734 & -1.9951 & 0.974669 \tabularnewline
5 & -0.063452 & -0.4874 & 0.686104 \tabularnewline
6 & -0.198786 & -1.5269 & 0.933936 \tabularnewline
7 & -0.114661 & -0.8807 & 0.808981 \tabularnewline
8 & -0.112321 & -0.8628 & 0.804117 \tabularnewline
9 & 0.016191 & 0.1244 & 0.450723 \tabularnewline
10 & 0.036941 & 0.2837 & 0.388798 \tabularnewline
11 & -0.093566 & -0.7187 & 0.762416 \tabularnewline
12 & 0.049759 & 0.3822 & 0.351841 \tabularnewline
13 & 0.020532 & 0.1577 & 0.437611 \tabularnewline
14 & -0.245565 & -1.8862 & 0.967905 \tabularnewline
15 & 0.127637 & 0.9804 & 0.165447 \tabularnewline
16 & -0.178233 & -1.369 & 0.911911 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6198&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]0.358077[/C][C]2.7504[/C][C]0.003945[/C][/ROW]
[ROW][C]1[/C][C]-0.027699[/C][C]-0.2128[/C][C]0.583875[/C][/ROW]
[ROW][C]2[/C][C]0.058988[/C][C]0.4531[/C][C]0.326071[/C][/ROW]
[ROW][C]3[/C][C]-0.210687[/C][C]-1.6183[/C][C]0.944536[/C][/ROW]
[ROW][C]4[/C][C]-0.259734[/C][C]-1.9951[/C][C]0.974669[/C][/ROW]
[ROW][C]5[/C][C]-0.063452[/C][C]-0.4874[/C][C]0.686104[/C][/ROW]
[ROW][C]6[/C][C]-0.198786[/C][C]-1.5269[/C][C]0.933936[/C][/ROW]
[ROW][C]7[/C][C]-0.114661[/C][C]-0.8807[/C][C]0.808981[/C][/ROW]
[ROW][C]8[/C][C]-0.112321[/C][C]-0.8628[/C][C]0.804117[/C][/ROW]
[ROW][C]9[/C][C]0.016191[/C][C]0.1244[/C][C]0.450723[/C][/ROW]
[ROW][C]10[/C][C]0.036941[/C][C]0.2837[/C][C]0.388798[/C][/ROW]
[ROW][C]11[/C][C]-0.093566[/C][C]-0.7187[/C][C]0.762416[/C][/ROW]
[ROW][C]12[/C][C]0.049759[/C][C]0.3822[/C][C]0.351841[/C][/ROW]
[ROW][C]13[/C][C]0.020532[/C][C]0.1577[/C][C]0.437611[/C][/ROW]
[ROW][C]14[/C][C]-0.245565[/C][C]-1.8862[/C][C]0.967905[/C][/ROW]
[ROW][C]15[/C][C]0.127637[/C][C]0.9804[/C][C]0.165447[/C][/ROW]
[ROW][C]16[/C][C]-0.178233[/C][C]-1.369[/C][C]0.911911[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6198&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6198&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	0.358077	2.7504	0.003945
1	-0.027699	-0.2128	0.583875
2	0.058988	0.4531	0.326071
3	-0.210687	-1.6183	0.944536
4	-0.259734	-1.9951	0.974669
5	-0.063452	-0.4874	0.686104
6	-0.198786	-1.5269	0.933936
7	-0.114661	-0.8807	0.808981
8	-0.112321	-0.8628	0.804117
9	0.016191	0.1244	0.450723
10	0.036941	0.2837	0.388798
11	-0.093566	-0.7187	0.762416
12	0.049759	0.3822	0.351841
13	0.020532	0.1577	0.437611
14	-0.245565	-1.8862	0.967905
15	0.127637	0.9804	0.165447
16	-0.178233	-1.369	0.911911

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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Input Parameters & R Code