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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 29 Nov 2007 12:50:51 -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/29/t1196365214rakqr5wfjvnyg43.htm/, Retrieved Fri, 03 May 2024 04:20:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7586, Retrieved Fri, 03 May 2024 04:20:02 +0000

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No (this computation is public)

User-defined keywords

Elynne

Estimated Impact

158

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

-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2007-11-29 19:50:51] [c119ddc84594f6b781d845667bf1cf2c] [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=7586&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=7586&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7586&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	0.91036	7.507	0
2	0.775867	6.398	0
3	0.65792	5.4253	0
4	0.572467	4.7207	6e-06
5	0.496163	4.0915	5.8e-05
6	0.448231	3.6962	0.000219
7	0.423145	3.4893	0.000427
8	0.376125	3.1016	0.001401
9	0.309879	2.5553	0.006425
10	0.217395	1.7927	0.038735
11	0.111948	0.9232	0.179596
12	0.001095	0.009	0.496411
13	-0.04936	-0.407	0.657368
14	-0.074474	-0.6141	0.729411
15	-0.094158	-0.7764	0.779911
16	-0.104702	-0.8634	0.804523
17	-0.07798	-0.643	0.738819
18	-0.068388	-0.5639	0.712676

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.2462 & 0 \tabularnewline
1 & 0.91036 & 7.507 & 0 \tabularnewline
2 & 0.775867 & 6.398 & 0 \tabularnewline
3 & 0.65792 & 5.4253 & 0 \tabularnewline
4 & 0.572467 & 4.7207 & 6e-06 \tabularnewline
5 & 0.496163 & 4.0915 & 5.8e-05 \tabularnewline
6 & 0.448231 & 3.6962 & 0.000219 \tabularnewline
7 & 0.423145 & 3.4893 & 0.000427 \tabularnewline
8 & 0.376125 & 3.1016 & 0.001401 \tabularnewline
9 & 0.309879 & 2.5553 & 0.006425 \tabularnewline
10 & 0.217395 & 1.7927 & 0.038735 \tabularnewline
11 & 0.111948 & 0.9232 & 0.179596 \tabularnewline
12 & 0.001095 & 0.009 & 0.496411 \tabularnewline
13 & -0.04936 & -0.407 & 0.657368 \tabularnewline
14 & -0.074474 & -0.6141 & 0.729411 \tabularnewline
15 & -0.094158 & -0.7764 & 0.779911 \tabularnewline
16 & -0.104702 & -0.8634 & 0.804523 \tabularnewline
17 & -0.07798 & -0.643 & 0.738819 \tabularnewline
18 & -0.068388 & -0.5639 & 0.712676 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7586&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]0.91036[/C][C]7.507[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.775867[/C][C]6.398[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.65792[/C][C]5.4253[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.572467[/C][C]4.7207[/C][C]6e-06[/C][/ROW]
[ROW][C]5[/C][C]0.496163[/C][C]4.0915[/C][C]5.8e-05[/C][/ROW]
[ROW][C]6[/C][C]0.448231[/C][C]3.6962[/C][C]0.000219[/C][/ROW]
[ROW][C]7[/C][C]0.423145[/C][C]3.4893[/C][C]0.000427[/C][/ROW]
[ROW][C]8[/C][C]0.376125[/C][C]3.1016[/C][C]0.001401[/C][/ROW]
[ROW][C]9[/C][C]0.309879[/C][C]2.5553[/C][C]0.006425[/C][/ROW]
[ROW][C]10[/C][C]0.217395[/C][C]1.7927[/C][C]0.038735[/C][/ROW]
[ROW][C]11[/C][C]0.111948[/C][C]0.9232[/C][C]0.179596[/C][/ROW]
[ROW][C]12[/C][C]0.001095[/C][C]0.009[/C][C]0.496411[/C][/ROW]
[ROW][C]13[/C][C]-0.04936[/C][C]-0.407[/C][C]0.657368[/C][/ROW]
[ROW][C]14[/C][C]-0.074474[/C][C]-0.6141[/C][C]0.729411[/C][/ROW]
[ROW][C]15[/C][C]-0.094158[/C][C]-0.7764[/C][C]0.779911[/C][/ROW]
[ROW][C]16[/C][C]-0.104702[/C][C]-0.8634[/C][C]0.804523[/C][/ROW]
[ROW][C]17[/C][C]-0.07798[/C][C]-0.643[/C][C]0.738819[/C][/ROW]
[ROW][C]18[/C][C]-0.068388[/C][C]-0.5639[/C][C]0.712676[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7586&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7586&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	0.91036	7.507	0
2	0.775867	6.398	0
3	0.65792	5.4253	0
4	0.572467	4.7207	6e-06
5	0.496163	4.0915	5.8e-05
6	0.448231	3.6962	0.000219
7	0.423145	3.4893	0.000427
8	0.376125	3.1016	0.001401
9	0.309879	2.5553	0.006425
10	0.217395	1.7927	0.038735
11	0.111948	0.9232	0.179596
12	0.001095	0.009	0.496411
13	-0.04936	-0.407	0.657368
14	-0.074474	-0.6141	0.729411
15	-0.094158	-0.7764	0.779911
16	-0.104702	-0.8634	0.804523
17	-0.07798	-0.643	0.738819
18	-0.068388	-0.5639	0.712676

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.91036	7.507	0
1	-0.308849	-2.5468	0.993431
2	0.094378	0.7783	0.219558
3	0.067212	0.5542	0.290614
4	-0.073302	-0.6045	0.726226
5	0.158497	1.307	0.097808
6	0.033982	0.2802	0.390078
7	-0.201162	-1.6588	0.949122
8	0.003564	0.0294	0.488321
9	-0.20304	-1.6743	0.950669
10	-0.119946	-0.9891	0.836941
11	-0.073314	-0.6046	0.72626
12	0.253101	2.0871	0.020314
13	-0.166962	-1.3768	0.913456
14	0.020945	0.1727	0.431694
15	0.103222	0.8512	0.198825
16	0.173249	1.4286	0.078841
17	-0.183483	-1.513	0.932548
18	-0.066033	-0.5445	0.706068

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.91036 & 7.507 & 0 \tabularnewline
1 & -0.308849 & -2.5468 & 0.993431 \tabularnewline
2 & 0.094378 & 0.7783 & 0.219558 \tabularnewline
3 & 0.067212 & 0.5542 & 0.290614 \tabularnewline
4 & -0.073302 & -0.6045 & 0.726226 \tabularnewline
5 & 0.158497 & 1.307 & 0.097808 \tabularnewline
6 & 0.033982 & 0.2802 & 0.390078 \tabularnewline
7 & -0.201162 & -1.6588 & 0.949122 \tabularnewline
8 & 0.003564 & 0.0294 & 0.488321 \tabularnewline
9 & -0.20304 & -1.6743 & 0.950669 \tabularnewline
10 & -0.119946 & -0.9891 & 0.836941 \tabularnewline
11 & -0.073314 & -0.6046 & 0.72626 \tabularnewline
12 & 0.253101 & 2.0871 & 0.020314 \tabularnewline
13 & -0.166962 & -1.3768 & 0.913456 \tabularnewline
14 & 0.020945 & 0.1727 & 0.431694 \tabularnewline
15 & 0.103222 & 0.8512 & 0.198825 \tabularnewline
16 & 0.173249 & 1.4286 & 0.078841 \tabularnewline
17 & -0.183483 & -1.513 & 0.932548 \tabularnewline
18 & -0.066033 & -0.5445 & 0.706068 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7586&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]0.91036[/C][C]7.507[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.308849[/C][C]-2.5468[/C][C]0.993431[/C][/ROW]
[ROW][C]2[/C][C]0.094378[/C][C]0.7783[/C][C]0.219558[/C][/ROW]
[ROW][C]3[/C][C]0.067212[/C][C]0.5542[/C][C]0.290614[/C][/ROW]
[ROW][C]4[/C][C]-0.073302[/C][C]-0.6045[/C][C]0.726226[/C][/ROW]
[ROW][C]5[/C][C]0.158497[/C][C]1.307[/C][C]0.097808[/C][/ROW]
[ROW][C]6[/C][C]0.033982[/C][C]0.2802[/C][C]0.390078[/C][/ROW]
[ROW][C]7[/C][C]-0.201162[/C][C]-1.6588[/C][C]0.949122[/C][/ROW]
[ROW][C]8[/C][C]0.003564[/C][C]0.0294[/C][C]0.488321[/C][/ROW]
[ROW][C]9[/C][C]-0.20304[/C][C]-1.6743[/C][C]0.950669[/C][/ROW]
[ROW][C]10[/C][C]-0.119946[/C][C]-0.9891[/C][C]0.836941[/C][/ROW]
[ROW][C]11[/C][C]-0.073314[/C][C]-0.6046[/C][C]0.72626[/C][/ROW]
[ROW][C]12[/C][C]0.253101[/C][C]2.0871[/C][C]0.020314[/C][/ROW]
[ROW][C]13[/C][C]-0.166962[/C][C]-1.3768[/C][C]0.913456[/C][/ROW]
[ROW][C]14[/C][C]0.020945[/C][C]0.1727[/C][C]0.431694[/C][/ROW]
[ROW][C]15[/C][C]0.103222[/C][C]0.8512[/C][C]0.198825[/C][/ROW]
[ROW][C]16[/C][C]0.173249[/C][C]1.4286[/C][C]0.078841[/C][/ROW]
[ROW][C]17[/C][C]-0.183483[/C][C]-1.513[/C][C]0.932548[/C][/ROW]
[ROW][C]18[/C][C]-0.066033[/C][C]-0.5445[/C][C]0.706068[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7586&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7586&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	0.91036	7.507	0
1	-0.308849	-2.5468	0.993431
2	0.094378	0.7783	0.219558
3	0.067212	0.5542	0.290614
4	-0.073302	-0.6045	0.726226
5	0.158497	1.307	0.097808
6	0.033982	0.2802	0.390078
7	-0.201162	-1.6588	0.949122
8	0.003564	0.0294	0.488321
9	-0.20304	-1.6743	0.950669
10	-0.119946	-0.9891	0.836941
11	-0.073314	-0.6046	0.72626
12	0.253101	2.0871	0.020314
13	-0.166962	-1.3768	0.913456
14	0.020945	0.1727	0.431694
15	0.103222	0.8512	0.198825
16	0.173249	1.4286	0.078841
17	-0.183483	-1.513	0.932548
18	-0.066033	-0.5445	0.706068

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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Dataset

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Input Parameters & R Code