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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 26 Nov 2007 11:16:50 -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/26/t1196100418o7tcgsvcan40uzs.htm/, Retrieved Fri, 03 May 2024 02:41:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6609, Retrieved Fri, 03 May 2024 02:41:14 +0000

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No (this computation is public)

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Estimated Impact

200

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

-       [(Partial) Autocorrelation Function] [] [2007-11-26 18:16:50] [7c5f7a910a5108d789a748f71ee8daf4] [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=6609&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=6609&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6609&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	6.8557	0
1	-0.43127	-2.9566	0.997574
2	-0.158641	-1.0876	0.858839
3	0.172944	1.1856	0.120861
4	-0.080051	-0.5488	0.70713
5	-0.063258	-0.4337	0.666746
6	0.224908	1.5419	0.064903
7	-0.230714	-1.5817	0.939787
8	0.002789	0.0191	0.492412
9	0.253341	1.7368	0.044485
10	-0.197625	-1.3548	0.909028
11	0.044562	0.3055	0.380666
12	-0.064926	-0.4451	0.670858
13	-0.050452	-0.3459	0.634513
14	0.21115	1.4476	0.077187
15	-0.116791	-0.8007	0.786328
16	-0.168764	-1.157	0.873439

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 6.8557 & 0 \tabularnewline
1 & -0.43127 & -2.9566 & 0.997574 \tabularnewline
2 & -0.158641 & -1.0876 & 0.858839 \tabularnewline
3 & 0.172944 & 1.1856 & 0.120861 \tabularnewline
4 & -0.080051 & -0.5488 & 0.70713 \tabularnewline
5 & -0.063258 & -0.4337 & 0.666746 \tabularnewline
6 & 0.224908 & 1.5419 & 0.064903 \tabularnewline
7 & -0.230714 & -1.5817 & 0.939787 \tabularnewline
8 & 0.002789 & 0.0191 & 0.492412 \tabularnewline
9 & 0.253341 & 1.7368 & 0.044485 \tabularnewline
10 & -0.197625 & -1.3548 & 0.909028 \tabularnewline
11 & 0.044562 & 0.3055 & 0.380666 \tabularnewline
12 & -0.064926 & -0.4451 & 0.670858 \tabularnewline
13 & -0.050452 & -0.3459 & 0.634513 \tabularnewline
14 & 0.21115 & 1.4476 & 0.077187 \tabularnewline
15 & -0.116791 & -0.8007 & 0.786328 \tabularnewline
16 & -0.168764 & -1.157 & 0.873439 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6609&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]6.8557[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.43127[/C][C]-2.9566[/C][C]0.997574[/C][/ROW]
[ROW][C]2[/C][C]-0.158641[/C][C]-1.0876[/C][C]0.858839[/C][/ROW]
[ROW][C]3[/C][C]0.172944[/C][C]1.1856[/C][C]0.120861[/C][/ROW]
[ROW][C]4[/C][C]-0.080051[/C][C]-0.5488[/C][C]0.70713[/C][/ROW]
[ROW][C]5[/C][C]-0.063258[/C][C]-0.4337[/C][C]0.666746[/C][/ROW]
[ROW][C]6[/C][C]0.224908[/C][C]1.5419[/C][C]0.064903[/C][/ROW]
[ROW][C]7[/C][C]-0.230714[/C][C]-1.5817[/C][C]0.939787[/C][/ROW]
[ROW][C]8[/C][C]0.002789[/C][C]0.0191[/C][C]0.492412[/C][/ROW]
[ROW][C]9[/C][C]0.253341[/C][C]1.7368[/C][C]0.044485[/C][/ROW]
[ROW][C]10[/C][C]-0.197625[/C][C]-1.3548[/C][C]0.909028[/C][/ROW]
[ROW][C]11[/C][C]0.044562[/C][C]0.3055[/C][C]0.380666[/C][/ROW]
[ROW][C]12[/C][C]-0.064926[/C][C]-0.4451[/C][C]0.670858[/C][/ROW]
[ROW][C]13[/C][C]-0.050452[/C][C]-0.3459[/C][C]0.634513[/C][/ROW]
[ROW][C]14[/C][C]0.21115[/C][C]1.4476[/C][C]0.077187[/C][/ROW]
[ROW][C]15[/C][C]-0.116791[/C][C]-0.8007[/C][C]0.786328[/C][/ROW]
[ROW][C]16[/C][C]-0.168764[/C][C]-1.157[/C][C]0.873439[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6609&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6609&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	6.8557	0
1	-0.43127	-2.9566	0.997574
2	-0.158641	-1.0876	0.858839
3	0.172944	1.1856	0.120861
4	-0.080051	-0.5488	0.70713
5	-0.063258	-0.4337	0.666746
6	0.224908	1.5419	0.064903
7	-0.230714	-1.5817	0.939787
8	0.002789	0.0191	0.492412
9	0.253341	1.7368	0.044485
10	-0.197625	-1.3548	0.909028
11	0.044562	0.3055	0.380666
12	-0.064926	-0.4451	0.670858
13	-0.050452	-0.3459	0.634513
14	0.21115	1.4476	0.077187
15	-0.116791	-0.8007	0.786328
16	-0.168764	-1.157	0.873439

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.43127	-2.9566	0.997574
1	-0.423382	-2.9026	0.99719
2	-0.160205	-1.0983	0.861168
3	-0.175153	-1.2008	0.882075
4	-0.212268	-1.4552	0.923875
5	0.085403	0.5855	0.280508
6	-0.130213	-0.8927	0.811715
7	-0.139851	-0.9588	0.82871
8	0.132005	0.905	0.185046
9	0.027753	0.1903	0.424962
10	0.12385	0.8491	0.200072
11	-0.138683	-0.9508	0.826706
12	-0.163896	-1.1236	0.866558
13	0.094132	0.6453	0.260923
14	-0.083497	-0.5724	0.715121
15	-0.203485	-1.395	0.915217
16	0.016552	0.1135	0.455069

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.43127 & -2.9566 & 0.997574 \tabularnewline
1 & -0.423382 & -2.9026 & 0.99719 \tabularnewline
2 & -0.160205 & -1.0983 & 0.861168 \tabularnewline
3 & -0.175153 & -1.2008 & 0.882075 \tabularnewline
4 & -0.212268 & -1.4552 & 0.923875 \tabularnewline
5 & 0.085403 & 0.5855 & 0.280508 \tabularnewline
6 & -0.130213 & -0.8927 & 0.811715 \tabularnewline
7 & -0.139851 & -0.9588 & 0.82871 \tabularnewline
8 & 0.132005 & 0.905 & 0.185046 \tabularnewline
9 & 0.027753 & 0.1903 & 0.424962 \tabularnewline
10 & 0.12385 & 0.8491 & 0.200072 \tabularnewline
11 & -0.138683 & -0.9508 & 0.826706 \tabularnewline
12 & -0.163896 & -1.1236 & 0.866558 \tabularnewline
13 & 0.094132 & 0.6453 & 0.260923 \tabularnewline
14 & -0.083497 & -0.5724 & 0.715121 \tabularnewline
15 & -0.203485 & -1.395 & 0.915217 \tabularnewline
16 & 0.016552 & 0.1135 & 0.455069 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6609&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]-0.43127[/C][C]-2.9566[/C][C]0.997574[/C][/ROW]
[ROW][C]1[/C][C]-0.423382[/C][C]-2.9026[/C][C]0.99719[/C][/ROW]
[ROW][C]2[/C][C]-0.160205[/C][C]-1.0983[/C][C]0.861168[/C][/ROW]
[ROW][C]3[/C][C]-0.175153[/C][C]-1.2008[/C][C]0.882075[/C][/ROW]
[ROW][C]4[/C][C]-0.212268[/C][C]-1.4552[/C][C]0.923875[/C][/ROW]
[ROW][C]5[/C][C]0.085403[/C][C]0.5855[/C][C]0.280508[/C][/ROW]
[ROW][C]6[/C][C]-0.130213[/C][C]-0.8927[/C][C]0.811715[/C][/ROW]
[ROW][C]7[/C][C]-0.139851[/C][C]-0.9588[/C][C]0.82871[/C][/ROW]
[ROW][C]8[/C][C]0.132005[/C][C]0.905[/C][C]0.185046[/C][/ROW]
[ROW][C]9[/C][C]0.027753[/C][C]0.1903[/C][C]0.424962[/C][/ROW]
[ROW][C]10[/C][C]0.12385[/C][C]0.8491[/C][C]0.200072[/C][/ROW]
[ROW][C]11[/C][C]-0.138683[/C][C]-0.9508[/C][C]0.826706[/C][/ROW]
[ROW][C]12[/C][C]-0.163896[/C][C]-1.1236[/C][C]0.866558[/C][/ROW]
[ROW][C]13[/C][C]0.094132[/C][C]0.6453[/C][C]0.260923[/C][/ROW]
[ROW][C]14[/C][C]-0.083497[/C][C]-0.5724[/C][C]0.715121[/C][/ROW]
[ROW][C]15[/C][C]-0.203485[/C][C]-1.395[/C][C]0.915217[/C][/ROW]
[ROW][C]16[/C][C]0.016552[/C][C]0.1135[/C][C]0.455069[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6609&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6609&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	-0.43127	-2.9566	0.997574
1	-0.423382	-2.9026	0.99719
2	-0.160205	-1.0983	0.861168
3	-0.175153	-1.2008	0.882075
4	-0.212268	-1.4552	0.923875
5	0.085403	0.5855	0.280508
6	-0.130213	-0.8927	0.811715
7	-0.139851	-0.9588	0.82871
8	0.132005	0.905	0.185046
9	0.027753	0.1903	0.424962
10	0.12385	0.8491	0.200072
11	-0.138683	-0.9508	0.826706
12	-0.163896	-1.1236	0.866558
13	0.094132	0.6453	0.260923
14	-0.083497	-0.5724	0.715121
15	-0.203485	-1.395	0.915217
16	0.016552	0.1135	0.455069

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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Figures (Output of Computation)

Input Parameters & R Code