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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 27 Dec 2007 07:40:44 -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/Dec/27/t119876523095c6qycb5bh4xep.htm/, Retrieved Sat, 27 Apr 2024 21:46:15 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4906, Retrieved Sat, 27 Apr 2024 21:46:15 +0000

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User-defined keywords

Estimated Impact

292

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-       [(Partial) Autocorrelation Function] [s 0650692 paper] [2007-12-27 14:40:44] [011cc8cdd02d5893b5258ac3f5e21d83] [Current]

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Dataseries X:

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Histogram

Boxplots

0,3
2,1
2,5
2,3
2,4
3
1,7
3,5
4
3,7
3,7
3
2,7
2,5
2,2
2,9
3,1
3
2,8
2,5
1,9
1,9
1,8
2
2,6
2,5
2,5
1,6
1,4
0,8
1,1
1,3
1,2
1,3
1,1
1,3
1,2
1,6
1,7
1,5
0,9
1,5
1,4
1,6
1,7
1,4
1,8
1,7
1,4
1,2
1
1,7
2,4
2
2,1
2
1,8
2,7
2,3
1,9
2
2,3
2,8
2,4
2,3
2,7
2,7
2,9
3
2,2
2,3
2,8

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4906&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]2 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=4906&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4906&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	2 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	0.722331	6.1292	0
2	0.585763	4.9704	2e-06
3	0.513133	4.3541	2.2e-05
4	0.413731	3.5106	0.000388
5	0.418788	3.5535	0.000338
6	0.457715	3.8838	0.000113
7	0.344332	2.9218	0.002323
8	0.323384	2.744	0.003828
9	0.271331	2.3023	0.012106
10	0.19074	1.6185	0.054966
11	0.128001	1.0861	0.140524
12	0.018927	0.1606	0.436428
13	0.036748	0.3118	0.378042
14	0.04972	0.4219	0.337182
15	-0.02521	-0.2139	0.584389
16	-0.055801	-0.4735	0.68135
17	-0.138126	-1.172	0.877477

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & 0.722331 & 6.1292 & 0 \tabularnewline
2 & 0.585763 & 4.9704 & 2e-06 \tabularnewline
3 & 0.513133 & 4.3541 & 2.2e-05 \tabularnewline
4 & 0.413731 & 3.5106 & 0.000388 \tabularnewline
5 & 0.418788 & 3.5535 & 0.000338 \tabularnewline
6 & 0.457715 & 3.8838 & 0.000113 \tabularnewline
7 & 0.344332 & 2.9218 & 0.002323 \tabularnewline
8 & 0.323384 & 2.744 & 0.003828 \tabularnewline
9 & 0.271331 & 2.3023 & 0.012106 \tabularnewline
10 & 0.19074 & 1.6185 & 0.054966 \tabularnewline
11 & 0.128001 & 1.0861 & 0.140524 \tabularnewline
12 & 0.018927 & 0.1606 & 0.436428 \tabularnewline
13 & 0.036748 & 0.3118 & 0.378042 \tabularnewline
14 & 0.04972 & 0.4219 & 0.337182 \tabularnewline
15 & -0.02521 & -0.2139 & 0.584389 \tabularnewline
16 & -0.055801 & -0.4735 & 0.68135 \tabularnewline
17 & -0.138126 & -1.172 & 0.877477 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4906&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]0.722331[/C][C]6.1292[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.585763[/C][C]4.9704[/C][C]2e-06[/C][/ROW]
[ROW][C]3[/C][C]0.513133[/C][C]4.3541[/C][C]2.2e-05[/C][/ROW]
[ROW][C]4[/C][C]0.413731[/C][C]3.5106[/C][C]0.000388[/C][/ROW]
[ROW][C]5[/C][C]0.418788[/C][C]3.5535[/C][C]0.000338[/C][/ROW]
[ROW][C]6[/C][C]0.457715[/C][C]3.8838[/C][C]0.000113[/C][/ROW]
[ROW][C]7[/C][C]0.344332[/C][C]2.9218[/C][C]0.002323[/C][/ROW]
[ROW][C]8[/C][C]0.323384[/C][C]2.744[/C][C]0.003828[/C][/ROW]
[ROW][C]9[/C][C]0.271331[/C][C]2.3023[/C][C]0.012106[/C][/ROW]
[ROW][C]10[/C][C]0.19074[/C][C]1.6185[/C][C]0.054966[/C][/ROW]
[ROW][C]11[/C][C]0.128001[/C][C]1.0861[/C][C]0.140524[/C][/ROW]
[ROW][C]12[/C][C]0.018927[/C][C]0.1606[/C][C]0.436428[/C][/ROW]
[ROW][C]13[/C][C]0.036748[/C][C]0.3118[/C][C]0.378042[/C][/ROW]
[ROW][C]14[/C][C]0.04972[/C][C]0.4219[/C][C]0.337182[/C][/ROW]
[ROW][C]15[/C][C]-0.02521[/C][C]-0.2139[/C][C]0.584389[/C][/ROW]
[ROW][C]16[/C][C]-0.055801[/C][C]-0.4735[/C][C]0.68135[/C][/ROW]
[ROW][C]17[/C][C]-0.138126[/C][C]-1.172[/C][C]0.877477[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4906&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4906&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	0.722331	6.1292	0
2	0.585763	4.9704	2e-06
3	0.513133	4.3541	2.2e-05
4	0.413731	3.5106	0.000388
5	0.418788	3.5535	0.000338
6	0.457715	3.8838	0.000113
7	0.344332	2.9218	0.002323
8	0.323384	2.744	0.003828
9	0.271331	2.3023	0.012106
10	0.19074	1.6185	0.054966
11	0.128001	1.0861	0.140524
12	0.018927	0.1606	0.436428
13	0.036748	0.3118	0.378042
14	0.04972	0.4219	0.337182
15	-0.02521	-0.2139	0.584389
16	-0.055801	-0.4735	0.68135
17	-0.138126	-1.172	0.877477

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.722331	6.1292	0
1	0.133826	1.1356	0.129955
2	0.106405	0.9029	0.1848
3	-0.035027	-0.2972	0.61642
4	0.170316	1.4452	0.076373
5	0.17135	1.454	0.075152
6	-0.186868	-1.5856	0.941397
7	0.060449	0.5129	0.304787
8	-0.046516	-0.3947	0.652884
9	-0.052741	-0.4475	0.672079
10	-0.129558	-1.0993	0.862359
11	-0.203268	-1.7248	0.955572
12	0.210433	1.7856	0.039189
13	-0.014938	-0.1267	0.550254
14	-0.158771	-1.3472	0.908932
15	-0.034866	-0.2958	0.615901
16	-0.090916	-0.7715	0.778518
17	0.07417	0.6294	0.265554

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.722331 & 6.1292 & 0 \tabularnewline
1 & 0.133826 & 1.1356 & 0.129955 \tabularnewline
2 & 0.106405 & 0.9029 & 0.1848 \tabularnewline
3 & -0.035027 & -0.2972 & 0.61642 \tabularnewline
4 & 0.170316 & 1.4452 & 0.076373 \tabularnewline
5 & 0.17135 & 1.454 & 0.075152 \tabularnewline
6 & -0.186868 & -1.5856 & 0.941397 \tabularnewline
7 & 0.060449 & 0.5129 & 0.304787 \tabularnewline
8 & -0.046516 & -0.3947 & 0.652884 \tabularnewline
9 & -0.052741 & -0.4475 & 0.672079 \tabularnewline
10 & -0.129558 & -1.0993 & 0.862359 \tabularnewline
11 & -0.203268 & -1.7248 & 0.955572 \tabularnewline
12 & 0.210433 & 1.7856 & 0.039189 \tabularnewline
13 & -0.014938 & -0.1267 & 0.550254 \tabularnewline
14 & -0.158771 & -1.3472 & 0.908932 \tabularnewline
15 & -0.034866 & -0.2958 & 0.615901 \tabularnewline
16 & -0.090916 & -0.7715 & 0.778518 \tabularnewline
17 & 0.07417 & 0.6294 & 0.265554 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4906&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]0.722331[/C][C]6.1292[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.133826[/C][C]1.1356[/C][C]0.129955[/C][/ROW]
[ROW][C]2[/C][C]0.106405[/C][C]0.9029[/C][C]0.1848[/C][/ROW]
[ROW][C]3[/C][C]-0.035027[/C][C]-0.2972[/C][C]0.61642[/C][/ROW]
[ROW][C]4[/C][C]0.170316[/C][C]1.4452[/C][C]0.076373[/C][/ROW]
[ROW][C]5[/C][C]0.17135[/C][C]1.454[/C][C]0.075152[/C][/ROW]
[ROW][C]6[/C][C]-0.186868[/C][C]-1.5856[/C][C]0.941397[/C][/ROW]
[ROW][C]7[/C][C]0.060449[/C][C]0.5129[/C][C]0.304787[/C][/ROW]
[ROW][C]8[/C][C]-0.046516[/C][C]-0.3947[/C][C]0.652884[/C][/ROW]
[ROW][C]9[/C][C]-0.052741[/C][C]-0.4475[/C][C]0.672079[/C][/ROW]
[ROW][C]10[/C][C]-0.129558[/C][C]-1.0993[/C][C]0.862359[/C][/ROW]
[ROW][C]11[/C][C]-0.203268[/C][C]-1.7248[/C][C]0.955572[/C][/ROW]
[ROW][C]12[/C][C]0.210433[/C][C]1.7856[/C][C]0.039189[/C][/ROW]
[ROW][C]13[/C][C]-0.014938[/C][C]-0.1267[/C][C]0.550254[/C][/ROW]
[ROW][C]14[/C][C]-0.158771[/C][C]-1.3472[/C][C]0.908932[/C][/ROW]
[ROW][C]15[/C][C]-0.034866[/C][C]-0.2958[/C][C]0.615901[/C][/ROW]
[ROW][C]16[/C][C]-0.090916[/C][C]-0.7715[/C][C]0.778518[/C][/ROW]
[ROW][C]17[/C][C]0.07417[/C][C]0.6294[/C][C]0.265554[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4906&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4906&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	0.722331	6.1292	0
1	0.133826	1.1356	0.129955
2	0.106405	0.9029	0.1848
3	-0.035027	-0.2972	0.61642
4	0.170316	1.4452	0.076373
5	0.17135	1.454	0.075152
6	-0.186868	-1.5856	0.941397
7	0.060449	0.5129	0.304787
8	-0.046516	-0.3947	0.652884
9	-0.052741	-0.4475	0.672079
10	-0.129558	-1.0993	0.862359
11	-0.203268	-1.7248	0.955572
12	0.210433	1.7856	0.039189
13	-0.014938	-0.1267	0.550254
14	-0.158771	-1.3472	0.908932
15	-0.034866	-0.2958	0.615901
16	-0.090916	-0.7715	0.778518
17	0.07417	0.6294	0.265554

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code