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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 16 Dec 2007 03:14:03 -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/16/t11977994958b4zwyi1j0rd233.htm/, Retrieved Thu, 02 May 2024 10:07:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4122, Retrieved Thu, 02 May 2024 10:07:51 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

226

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

-       [(Partial) Autocorrelation Function] [autocorrelatie jo...] [2007-12-16 10:14:03] [bd02e85be52eb1cb060a2c60779eb820] [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=4122&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=4122&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4122&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	0.014976	0.115	0.454406
2	-0.135073	-1.0375	0.848136
3	-0.212316	-1.6308	0.945873
4	0.020168	0.1549	0.43871
5	0.10726	0.8239	0.206663
6	0.092626	0.7115	0.239797
7	0.190296	1.4617	0.074566
8	-0.05709	-0.4385	0.668692
9	-0.048956	-0.376	0.645882
10	-0.173615	-1.3336	0.906263
11	0.045201	0.3472	0.36484
12	-0.014864	-0.1142	0.545256
13	0.061556	0.4728	0.319043
14	0.093795	0.7205	0.237046
15	0.029516	0.2267	0.410714
16	-0.226978	-1.7434	0.956768
17	-0.064847	-0.4981	0.689868

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6811 & 0 \tabularnewline
1 & 0.014976 & 0.115 & 0.454406 \tabularnewline
2 & -0.135073 & -1.0375 & 0.848136 \tabularnewline
3 & -0.212316 & -1.6308 & 0.945873 \tabularnewline
4 & 0.020168 & 0.1549 & 0.43871 \tabularnewline
5 & 0.10726 & 0.8239 & 0.206663 \tabularnewline
6 & 0.092626 & 0.7115 & 0.239797 \tabularnewline
7 & 0.190296 & 1.4617 & 0.074566 \tabularnewline
8 & -0.05709 & -0.4385 & 0.668692 \tabularnewline
9 & -0.048956 & -0.376 & 0.645882 \tabularnewline
10 & -0.173615 & -1.3336 & 0.906263 \tabularnewline
11 & 0.045201 & 0.3472 & 0.36484 \tabularnewline
12 & -0.014864 & -0.1142 & 0.545256 \tabularnewline
13 & 0.061556 & 0.4728 & 0.319043 \tabularnewline
14 & 0.093795 & 0.7205 & 0.237046 \tabularnewline
15 & 0.029516 & 0.2267 & 0.410714 \tabularnewline
16 & -0.226978 & -1.7434 & 0.956768 \tabularnewline
17 & -0.064847 & -0.4981 & 0.689868 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4122&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]0.014976[/C][C]0.115[/C][C]0.454406[/C][/ROW]
[ROW][C]2[/C][C]-0.135073[/C][C]-1.0375[/C][C]0.848136[/C][/ROW]
[ROW][C]3[/C][C]-0.212316[/C][C]-1.6308[/C][C]0.945873[/C][/ROW]
[ROW][C]4[/C][C]0.020168[/C][C]0.1549[/C][C]0.43871[/C][/ROW]
[ROW][C]5[/C][C]0.10726[/C][C]0.8239[/C][C]0.206663[/C][/ROW]
[ROW][C]6[/C][C]0.092626[/C][C]0.7115[/C][C]0.239797[/C][/ROW]
[ROW][C]7[/C][C]0.190296[/C][C]1.4617[/C][C]0.074566[/C][/ROW]
[ROW][C]8[/C][C]-0.05709[/C][C]-0.4385[/C][C]0.668692[/C][/ROW]
[ROW][C]9[/C][C]-0.048956[/C][C]-0.376[/C][C]0.645882[/C][/ROW]
[ROW][C]10[/C][C]-0.173615[/C][C]-1.3336[/C][C]0.906263[/C][/ROW]
[ROW][C]11[/C][C]0.045201[/C][C]0.3472[/C][C]0.36484[/C][/ROW]
[ROW][C]12[/C][C]-0.014864[/C][C]-0.1142[/C][C]0.545256[/C][/ROW]
[ROW][C]13[/C][C]0.061556[/C][C]0.4728[/C][C]0.319043[/C][/ROW]
[ROW][C]14[/C][C]0.093795[/C][C]0.7205[/C][C]0.237046[/C][/ROW]
[ROW][C]15[/C][C]0.029516[/C][C]0.2267[/C][C]0.410714[/C][/ROW]
[ROW][C]16[/C][C]-0.226978[/C][C]-1.7434[/C][C]0.956768[/C][/ROW]
[ROW][C]17[/C][C]-0.064847[/C][C]-0.4981[/C][C]0.689868[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4122&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4122&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	0.014976	0.115	0.454406
2	-0.135073	-1.0375	0.848136
3	-0.212316	-1.6308	0.945873
4	0.020168	0.1549	0.43871
5	0.10726	0.8239	0.206663
6	0.092626	0.7115	0.239797
7	0.190296	1.4617	0.074566
8	-0.05709	-0.4385	0.668692
9	-0.048956	-0.376	0.645882
10	-0.173615	-1.3336	0.906263
11	0.045201	0.3472	0.36484
12	-0.014864	-0.1142	0.545256
13	0.061556	0.4728	0.319043
14	0.093795	0.7205	0.237046
15	0.029516	0.2267	0.410714
16	-0.226978	-1.7434	0.956768
17	-0.064847	-0.4981	0.689868

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.014976	0.115	0.454406
1	-0.135328	-1.0395	0.848587
2	-0.211921	-1.6278	0.945551
3	0.003275	0.0252	0.490009
4	0.05434	0.4174	0.338954
5	0.056148	0.4313	0.333917
6	0.233146	1.7908	0.039225
7	0.002757	0.0212	0.491588
8	0.033405	0.2566	0.399195
9	-0.124852	-0.959	0.829265
10	-0.005413	-0.0416	0.516513
11	-0.115807	-0.8895	0.811334
12	-0.018628	-0.1431	0.556644
13	0.074284	0.5706	0.285224
14	0.075224	0.5778	0.282796
15	-0.186985	-1.4363	0.921895
16	0.048465	0.3723	0.355513
17	-0.092068	-0.7072	0.758884

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.014976 & 0.115 & 0.454406 \tabularnewline
1 & -0.135328 & -1.0395 & 0.848587 \tabularnewline
2 & -0.211921 & -1.6278 & 0.945551 \tabularnewline
3 & 0.003275 & 0.0252 & 0.490009 \tabularnewline
4 & 0.05434 & 0.4174 & 0.338954 \tabularnewline
5 & 0.056148 & 0.4313 & 0.333917 \tabularnewline
6 & 0.233146 & 1.7908 & 0.039225 \tabularnewline
7 & 0.002757 & 0.0212 & 0.491588 \tabularnewline
8 & 0.033405 & 0.2566 & 0.399195 \tabularnewline
9 & -0.124852 & -0.959 & 0.829265 \tabularnewline
10 & -0.005413 & -0.0416 & 0.516513 \tabularnewline
11 & -0.115807 & -0.8895 & 0.811334 \tabularnewline
12 & -0.018628 & -0.1431 & 0.556644 \tabularnewline
13 & 0.074284 & 0.5706 & 0.285224 \tabularnewline
14 & 0.075224 & 0.5778 & 0.282796 \tabularnewline
15 & -0.186985 & -1.4363 & 0.921895 \tabularnewline
16 & 0.048465 & 0.3723 & 0.355513 \tabularnewline
17 & -0.092068 & -0.7072 & 0.758884 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4122&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]0.014976[/C][C]0.115[/C][C]0.454406[/C][/ROW]
[ROW][C]1[/C][C]-0.135328[/C][C]-1.0395[/C][C]0.848587[/C][/ROW]
[ROW][C]2[/C][C]-0.211921[/C][C]-1.6278[/C][C]0.945551[/C][/ROW]
[ROW][C]3[/C][C]0.003275[/C][C]0.0252[/C][C]0.490009[/C][/ROW]
[ROW][C]4[/C][C]0.05434[/C][C]0.4174[/C][C]0.338954[/C][/ROW]
[ROW][C]5[/C][C]0.056148[/C][C]0.4313[/C][C]0.333917[/C][/ROW]
[ROW][C]6[/C][C]0.233146[/C][C]1.7908[/C][C]0.039225[/C][/ROW]
[ROW][C]7[/C][C]0.002757[/C][C]0.0212[/C][C]0.491588[/C][/ROW]
[ROW][C]8[/C][C]0.033405[/C][C]0.2566[/C][C]0.399195[/C][/ROW]
[ROW][C]9[/C][C]-0.124852[/C][C]-0.959[/C][C]0.829265[/C][/ROW]
[ROW][C]10[/C][C]-0.005413[/C][C]-0.0416[/C][C]0.516513[/C][/ROW]
[ROW][C]11[/C][C]-0.115807[/C][C]-0.8895[/C][C]0.811334[/C][/ROW]
[ROW][C]12[/C][C]-0.018628[/C][C]-0.1431[/C][C]0.556644[/C][/ROW]
[ROW][C]13[/C][C]0.074284[/C][C]0.5706[/C][C]0.285224[/C][/ROW]
[ROW][C]14[/C][C]0.075224[/C][C]0.5778[/C][C]0.282796[/C][/ROW]
[ROW][C]15[/C][C]-0.186985[/C][C]-1.4363[/C][C]0.921895[/C][/ROW]
[ROW][C]16[/C][C]0.048465[/C][C]0.3723[/C][C]0.355513[/C][/ROW]
[ROW][C]17[/C][C]-0.092068[/C][C]-0.7072[/C][C]0.758884[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4122&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4122&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	0.014976	0.115	0.454406
1	-0.135328	-1.0395	0.848587
2	-0.211921	-1.6278	0.945551
3	0.003275	0.0252	0.490009
4	0.05434	0.4174	0.338954
5	0.056148	0.4313	0.333917
6	0.233146	1.7908	0.039225
7	0.002757	0.0212	0.491588
8	0.033405	0.2566	0.399195
9	-0.124852	-0.959	0.829265
10	-0.005413	-0.0416	0.516513
11	-0.115807	-0.8895	0.811334
12	-0.018628	-0.1431	0.556644
13	0.074284	0.5706	0.285224
14	0.075224	0.5778	0.282796
15	-0.186985	-1.4363	0.921895
16	0.048465	0.3723	0.355513
17	-0.092068	-0.7072	0.758884

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 = 1 ; par5 = 12 ;

Parameters (R input):

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