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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 06 Dec 2007 07:31:24 -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/Dec/06/t1196950702y3825fgtig21zi5.htm/, Retrieved Fri, 03 May 2024 09:09:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2626, Retrieved Fri, 03 May 2024 09:09:42 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

177

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

-       [(Partial) Autocorrelation Function] [WS4: Q2 inflatie] [2007-12-06 14:31:24] [9b75aacdafaeee3fe66fbd4de075ccd6] [Current]

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Dataseries X:

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Boxplots

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
2.8
2.8
2.2
2.6
2.8
2.5
2.4
2.3
1.9
1.7
2
2.1
1.7
1.8
1.8
1.8
1.3
1.3
1.3
1.2
1.4
2.2

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=2626&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=2626&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2626&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	7.746	0
1	0.768821	5.9553	0
2	0.609399	4.7204	7e-06
3	0.576111	4.4625	1.8e-05
4	0.562693	4.3586	2.6e-05
5	0.586342	4.5418	1.4e-05
6	0.496858	3.8486	0.000145
7	0.362507	2.808	0.003359
8	0.350834	2.7176	0.004292
9	0.318251	2.4652	0.008287
10	0.333321	2.5819	0.006143
11	0.226195	1.7521	0.042433
12	-0.010816	-0.0838	0.533244
13	-0.014094	-0.1092	0.543285
14	0.022481	0.1741	0.431173
15	-0.05263	-0.4077	0.657516
16	-0.148093	-1.1471	0.872058

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.768821 & 5.9553 & 0 \tabularnewline
2 & 0.609399 & 4.7204 & 7e-06 \tabularnewline
3 & 0.576111 & 4.4625 & 1.8e-05 \tabularnewline
4 & 0.562693 & 4.3586 & 2.6e-05 \tabularnewline
5 & 0.586342 & 4.5418 & 1.4e-05 \tabularnewline
6 & 0.496858 & 3.8486 & 0.000145 \tabularnewline
7 & 0.362507 & 2.808 & 0.003359 \tabularnewline
8 & 0.350834 & 2.7176 & 0.004292 \tabularnewline
9 & 0.318251 & 2.4652 & 0.008287 \tabularnewline
10 & 0.333321 & 2.5819 & 0.006143 \tabularnewline
11 & 0.226195 & 1.7521 & 0.042433 \tabularnewline
12 & -0.010816 & -0.0838 & 0.533244 \tabularnewline
13 & -0.014094 & -0.1092 & 0.543285 \tabularnewline
14 & 0.022481 & 0.1741 & 0.431173 \tabularnewline
15 & -0.05263 & -0.4077 & 0.657516 \tabularnewline
16 & -0.148093 & -1.1471 & 0.872058 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2626&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.768821[/C][C]5.9553[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.609399[/C][C]4.7204[/C][C]7e-06[/C][/ROW]
[ROW][C]3[/C][C]0.576111[/C][C]4.4625[/C][C]1.8e-05[/C][/ROW]
[ROW][C]4[/C][C]0.562693[/C][C]4.3586[/C][C]2.6e-05[/C][/ROW]
[ROW][C]5[/C][C]0.586342[/C][C]4.5418[/C][C]1.4e-05[/C][/ROW]
[ROW][C]6[/C][C]0.496858[/C][C]3.8486[/C][C]0.000145[/C][/ROW]
[ROW][C]7[/C][C]0.362507[/C][C]2.808[/C][C]0.003359[/C][/ROW]
[ROW][C]8[/C][C]0.350834[/C][C]2.7176[/C][C]0.004292[/C][/ROW]
[ROW][C]9[/C][C]0.318251[/C][C]2.4652[/C][C]0.008287[/C][/ROW]
[ROW][C]10[/C][C]0.333321[/C][C]2.5819[/C][C]0.006143[/C][/ROW]
[ROW][C]11[/C][C]0.226195[/C][C]1.7521[/C][C]0.042433[/C][/ROW]
[ROW][C]12[/C][C]-0.010816[/C][C]-0.0838[/C][C]0.533244[/C][/ROW]
[ROW][C]13[/C][C]-0.014094[/C][C]-0.1092[/C][C]0.543285[/C][/ROW]
[ROW][C]14[/C][C]0.022481[/C][C]0.1741[/C][C]0.431173[/C][/ROW]
[ROW][C]15[/C][C]-0.05263[/C][C]-0.4077[/C][C]0.657516[/C][/ROW]
[ROW][C]16[/C][C]-0.148093[/C][C]-1.1471[/C][C]0.872058[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2626&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2626&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	7.746	0
1	0.768821	5.9553	0
2	0.609399	4.7204	7e-06
3	0.576111	4.4625	1.8e-05
4	0.562693	4.3586	2.6e-05
5	0.586342	4.5418	1.4e-05
6	0.496858	3.8486	0.000145
7	0.362507	2.808	0.003359
8	0.350834	2.7176	0.004292
9	0.318251	2.4652	0.008287
10	0.333321	2.5819	0.006143
11	0.226195	1.7521	0.042433
12	-0.010816	-0.0838	0.533244
13	-0.014094	-0.1092	0.543285
14	0.022481	0.1741	0.431173
15	-0.05263	-0.4077	0.657516
16	-0.148093	-1.1471	0.872058

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.768821	5.9553	0
1	0.044786	0.3469	0.364935
2	0.230687	1.7869	0.039503
3	0.114258	0.885	0.189834
4	0.208055	1.6116	0.05615
5	-0.160226	-1.2411	0.890301
6	-0.150187	-1.1633	0.875352
7	0.094778	0.7341	0.23286
8	-0.093247	-0.7223	0.763538
9	0.140611	1.0892	0.140218
10	-0.27769	-2.151	0.982242
11	-0.391647	-3.0337	0.998216
12	0.200549	1.5534	0.062788
13	0.010059	0.0779	0.469077
14	-0.210037	-1.6269	0.945505
15	-0.135024	-1.0459	0.850096
16	-0.094813	-0.7344	0.767222

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.768821 & 5.9553 & 0 \tabularnewline
1 & 0.044786 & 0.3469 & 0.364935 \tabularnewline
2 & 0.230687 & 1.7869 & 0.039503 \tabularnewline
3 & 0.114258 & 0.885 & 0.189834 \tabularnewline
4 & 0.208055 & 1.6116 & 0.05615 \tabularnewline
5 & -0.160226 & -1.2411 & 0.890301 \tabularnewline
6 & -0.150187 & -1.1633 & 0.875352 \tabularnewline
7 & 0.094778 & 0.7341 & 0.23286 \tabularnewline
8 & -0.093247 & -0.7223 & 0.763538 \tabularnewline
9 & 0.140611 & 1.0892 & 0.140218 \tabularnewline
10 & -0.27769 & -2.151 & 0.982242 \tabularnewline
11 & -0.391647 & -3.0337 & 0.998216 \tabularnewline
12 & 0.200549 & 1.5534 & 0.062788 \tabularnewline
13 & 0.010059 & 0.0779 & 0.469077 \tabularnewline
14 & -0.210037 & -1.6269 & 0.945505 \tabularnewline
15 & -0.135024 & -1.0459 & 0.850096 \tabularnewline
16 & -0.094813 & -0.7344 & 0.767222 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2626&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]0.768821[/C][C]5.9553[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.044786[/C][C]0.3469[/C][C]0.364935[/C][/ROW]
[ROW][C]2[/C][C]0.230687[/C][C]1.7869[/C][C]0.039503[/C][/ROW]
[ROW][C]3[/C][C]0.114258[/C][C]0.885[/C][C]0.189834[/C][/ROW]
[ROW][C]4[/C][C]0.208055[/C][C]1.6116[/C][C]0.05615[/C][/ROW]
[ROW][C]5[/C][C]-0.160226[/C][C]-1.2411[/C][C]0.890301[/C][/ROW]
[ROW][C]6[/C][C]-0.150187[/C][C]-1.1633[/C][C]0.875352[/C][/ROW]
[ROW][C]7[/C][C]0.094778[/C][C]0.7341[/C][C]0.23286[/C][/ROW]
[ROW][C]8[/C][C]-0.093247[/C][C]-0.7223[/C][C]0.763538[/C][/ROW]
[ROW][C]9[/C][C]0.140611[/C][C]1.0892[/C][C]0.140218[/C][/ROW]
[ROW][C]10[/C][C]-0.27769[/C][C]-2.151[/C][C]0.982242[/C][/ROW]
[ROW][C]11[/C][C]-0.391647[/C][C]-3.0337[/C][C]0.998216[/C][/ROW]
[ROW][C]12[/C][C]0.200549[/C][C]1.5534[/C][C]0.062788[/C][/ROW]
[ROW][C]13[/C][C]0.010059[/C][C]0.0779[/C][C]0.469077[/C][/ROW]
[ROW][C]14[/C][C]-0.210037[/C][C]-1.6269[/C][C]0.945505[/C][/ROW]
[ROW][C]15[/C][C]-0.135024[/C][C]-1.0459[/C][C]0.850096[/C][/ROW]
[ROW][C]16[/C][C]-0.094813[/C][C]-0.7344[/C][C]0.767222[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2626&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2626&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	0.768821	5.9553	0
1	0.044786	0.3469	0.364935
2	0.230687	1.7869	0.039503
3	0.114258	0.885	0.189834
4	0.208055	1.6116	0.05615
5	-0.160226	-1.2411	0.890301
6	-0.150187	-1.1633	0.875352
7	0.094778	0.7341	0.23286
8	-0.093247	-0.7223	0.763538
9	0.140611	1.0892	0.140218
10	-0.27769	-2.151	0.982242
11	-0.391647	-3.0337	0.998216
12	0.200549	1.5534	0.062788
13	0.010059	0.0779	0.469077
14	-0.210037	-1.6269	0.945505
15	-0.135024	-1.0459	0.850096
16	-0.094813	-0.7344	0.767222

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

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Input Parameters & R Code