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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 03:24:00 -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/t1195812923an3v5vf6i7px5oh.htm/, Retrieved Mon, 29 Apr 2024 01:12:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6130, Retrieved Mon, 29 Apr 2024 01:12:48 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Q2, groep 1

Estimated Impact

215

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

-       [(Partial) Autocorrelation Function] [Q2, groep 1] [2007-11-23 10:24:00] [ce556af355e2eff84137e549c6ea8397] [Current]
-   PD    [(Partial) Autocorrelation Function] [w8] [2007-12-03 10:45:58] [74be16979710d4c4e7c6647856088456] 
-   PD    [(Partial) Autocorrelation Function] [w8] [2007-12-03 10:47:15] [74be16979710d4c4e7c6647856088456] 

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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=6130&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=6130&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6130&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	8.2462	0
1	0.424939	3.5041	0.000408
2	0.433212	3.5724	0.000328
3	0.50528	4.1666	4.5e-05
4	0.331181	2.731	0.004018
5	0.439445	3.6238	0.000278
6	0.326005	2.6883	0.004511
7	0.130778	1.0784	0.142329
8	0.246198	2.0302	0.023125
9	0.22798	1.88	0.032198
10	0.034638	0.2856	0.388015
11	0.012296	0.1014	0.459766
12	-0.122691	-1.0117	0.842374
13	-0.044929	-0.3705	0.643917
14	-0.005245	-0.0433	0.517187
15	-0.079797	-0.658	0.743627
16	-0.165913	-1.3682	0.912116
17	-0.059546	-0.491	0.687506
18	-0.029259	-0.2413	0.594967

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.2462 & 0 \tabularnewline
1 & 0.424939 & 3.5041 & 0.000408 \tabularnewline
2 & 0.433212 & 3.5724 & 0.000328 \tabularnewline
3 & 0.50528 & 4.1666 & 4.5e-05 \tabularnewline
4 & 0.331181 & 2.731 & 0.004018 \tabularnewline
5 & 0.439445 & 3.6238 & 0.000278 \tabularnewline
6 & 0.326005 & 2.6883 & 0.004511 \tabularnewline
7 & 0.130778 & 1.0784 & 0.142329 \tabularnewline
8 & 0.246198 & 2.0302 & 0.023125 \tabularnewline
9 & 0.22798 & 1.88 & 0.032198 \tabularnewline
10 & 0.034638 & 0.2856 & 0.388015 \tabularnewline
11 & 0.012296 & 0.1014 & 0.459766 \tabularnewline
12 & -0.122691 & -1.0117 & 0.842374 \tabularnewline
13 & -0.044929 & -0.3705 & 0.643917 \tabularnewline
14 & -0.005245 & -0.0433 & 0.517187 \tabularnewline
15 & -0.079797 & -0.658 & 0.743627 \tabularnewline
16 & -0.165913 & -1.3682 & 0.912116 \tabularnewline
17 & -0.059546 & -0.491 & 0.687506 \tabularnewline
18 & -0.029259 & -0.2413 & 0.594967 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6130&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]8.2462[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.424939[/C][C]3.5041[/C][C]0.000408[/C][/ROW]
[ROW][C]2[/C][C]0.433212[/C][C]3.5724[/C][C]0.000328[/C][/ROW]
[ROW][C]3[/C][C]0.50528[/C][C]4.1666[/C][C]4.5e-05[/C][/ROW]
[ROW][C]4[/C][C]0.331181[/C][C]2.731[/C][C]0.004018[/C][/ROW]
[ROW][C]5[/C][C]0.439445[/C][C]3.6238[/C][C]0.000278[/C][/ROW]
[ROW][C]6[/C][C]0.326005[/C][C]2.6883[/C][C]0.004511[/C][/ROW]
[ROW][C]7[/C][C]0.130778[/C][C]1.0784[/C][C]0.142329[/C][/ROW]
[ROW][C]8[/C][C]0.246198[/C][C]2.0302[/C][C]0.023125[/C][/ROW]
[ROW][C]9[/C][C]0.22798[/C][C]1.88[/C][C]0.032198[/C][/ROW]
[ROW][C]10[/C][C]0.034638[/C][C]0.2856[/C][C]0.388015[/C][/ROW]
[ROW][C]11[/C][C]0.012296[/C][C]0.1014[/C][C]0.459766[/C][/ROW]
[ROW][C]12[/C][C]-0.122691[/C][C]-1.0117[/C][C]0.842374[/C][/ROW]
[ROW][C]13[/C][C]-0.044929[/C][C]-0.3705[/C][C]0.643917[/C][/ROW]
[ROW][C]14[/C][C]-0.005245[/C][C]-0.0433[/C][C]0.517187[/C][/ROW]
[ROW][C]15[/C][C]-0.079797[/C][C]-0.658[/C][C]0.743627[/C][/ROW]
[ROW][C]16[/C][C]-0.165913[/C][C]-1.3682[/C][C]0.912116[/C][/ROW]
[ROW][C]17[/C][C]-0.059546[/C][C]-0.491[/C][C]0.687506[/C][/ROW]
[ROW][C]18[/C][C]-0.029259[/C][C]-0.2413[/C][C]0.594967[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6130&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6130&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	8.2462	0
1	0.424939	3.5041	0.000408
2	0.433212	3.5724	0.000328
3	0.50528	4.1666	4.5e-05
4	0.331181	2.731	0.004018
5	0.439445	3.6238	0.000278
6	0.326005	2.6883	0.004511
7	0.130778	1.0784	0.142329
8	0.246198	2.0302	0.023125
9	0.22798	1.88	0.032198
10	0.034638	0.2856	0.388015
11	0.012296	0.1014	0.459766
12	-0.122691	-1.0117	0.842374
13	-0.044929	-0.3705	0.643917
14	-0.005245	-0.0433	0.517187
15	-0.079797	-0.658	0.743627
16	-0.165913	-1.3682	0.912116
17	-0.059546	-0.491	0.687506
18	-0.029259	-0.2413	0.594967

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.424939	3.5041	0.000408
1	0.308311	2.5424	0.006646
2	0.333004	2.746	0.003856
3	0.002844	0.0234	0.49068
4	0.189836	1.5654	0.061062
5	-0.031606	-0.2606	0.602418
6	-0.242502	-1.9997	0.975236
7	-0.010644	-0.0878	0.534842
8	0.104335	0.8604	0.196305
9	-0.17467	-1.4404	0.922824
10	-0.193848	-1.5985	0.942717
11	-0.202423	-1.6692	0.950165
12	0.090529	0.7465	0.228964
13	0.097229	0.8018	0.212739
14	0.144234	1.1894	0.119212
15	-0.064551	-0.5323	0.701873
16	0.103296	0.8518	0.198656
17	0.101031	0.8331	0.203845
18	-0.19347	-1.5954	0.942369

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.424939 & 3.5041 & 0.000408 \tabularnewline
1 & 0.308311 & 2.5424 & 0.006646 \tabularnewline
2 & 0.333004 & 2.746 & 0.003856 \tabularnewline
3 & 0.002844 & 0.0234 & 0.49068 \tabularnewline
4 & 0.189836 & 1.5654 & 0.061062 \tabularnewline
5 & -0.031606 & -0.2606 & 0.602418 \tabularnewline
6 & -0.242502 & -1.9997 & 0.975236 \tabularnewline
7 & -0.010644 & -0.0878 & 0.534842 \tabularnewline
8 & 0.104335 & 0.8604 & 0.196305 \tabularnewline
9 & -0.17467 & -1.4404 & 0.922824 \tabularnewline
10 & -0.193848 & -1.5985 & 0.942717 \tabularnewline
11 & -0.202423 & -1.6692 & 0.950165 \tabularnewline
12 & 0.090529 & 0.7465 & 0.228964 \tabularnewline
13 & 0.097229 & 0.8018 & 0.212739 \tabularnewline
14 & 0.144234 & 1.1894 & 0.119212 \tabularnewline
15 & -0.064551 & -0.5323 & 0.701873 \tabularnewline
16 & 0.103296 & 0.8518 & 0.198656 \tabularnewline
17 & 0.101031 & 0.8331 & 0.203845 \tabularnewline
18 & -0.19347 & -1.5954 & 0.942369 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6130&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]0.424939[/C][C]3.5041[/C][C]0.000408[/C][/ROW]
[ROW][C]1[/C][C]0.308311[/C][C]2.5424[/C][C]0.006646[/C][/ROW]
[ROW][C]2[/C][C]0.333004[/C][C]2.746[/C][C]0.003856[/C][/ROW]
[ROW][C]3[/C][C]0.002844[/C][C]0.0234[/C][C]0.49068[/C][/ROW]
[ROW][C]4[/C][C]0.189836[/C][C]1.5654[/C][C]0.061062[/C][/ROW]
[ROW][C]5[/C][C]-0.031606[/C][C]-0.2606[/C][C]0.602418[/C][/ROW]
[ROW][C]6[/C][C]-0.242502[/C][C]-1.9997[/C][C]0.975236[/C][/ROW]
[ROW][C]7[/C][C]-0.010644[/C][C]-0.0878[/C][C]0.534842[/C][/ROW]
[ROW][C]8[/C][C]0.104335[/C][C]0.8604[/C][C]0.196305[/C][/ROW]
[ROW][C]9[/C][C]-0.17467[/C][C]-1.4404[/C][C]0.922824[/C][/ROW]
[ROW][C]10[/C][C]-0.193848[/C][C]-1.5985[/C][C]0.942717[/C][/ROW]
[ROW][C]11[/C][C]-0.202423[/C][C]-1.6692[/C][C]0.950165[/C][/ROW]
[ROW][C]12[/C][C]0.090529[/C][C]0.7465[/C][C]0.228964[/C][/ROW]
[ROW][C]13[/C][C]0.097229[/C][C]0.8018[/C][C]0.212739[/C][/ROW]
[ROW][C]14[/C][C]0.144234[/C][C]1.1894[/C][C]0.119212[/C][/ROW]
[ROW][C]15[/C][C]-0.064551[/C][C]-0.5323[/C][C]0.701873[/C][/ROW]
[ROW][C]16[/C][C]0.103296[/C][C]0.8518[/C][C]0.198656[/C][/ROW]
[ROW][C]17[/C][C]0.101031[/C][C]0.8331[/C][C]0.203845[/C][/ROW]
[ROW][C]18[/C][C]-0.19347[/C][C]-1.5954[/C][C]0.942369[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6130&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6130&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	0.424939	3.5041	0.000408
1	0.308311	2.5424	0.006646
2	0.333004	2.746	0.003856
3	0.002844	0.0234	0.49068
4	0.189836	1.5654	0.061062
5	-0.031606	-0.2606	0.602418
6	-0.242502	-1.9997	0.975236
7	-0.010644	-0.0878	0.534842
8	0.104335	0.8604	0.196305
9	-0.17467	-1.4404	0.922824
10	-0.193848	-1.5985	0.942717
11	-0.202423	-1.6692	0.950165
12	0.090529	0.7465	0.228964
13	0.097229	0.8018	0.212739
14	0.144234	1.1894	0.119212
15	-0.064551	-0.5323	0.701873
16	0.103296	0.8518	0.198656
17	0.101031	0.8331	0.203845
18	-0.19347	-1.5954	0.942369

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 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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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Figures (Output of Computation)

Input Parameters & R Code