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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 30 Dec 2007 07:18:50 -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/Dec/30/t1199023073n3vy6muuruzagh2.htm/, Retrieved Sat, 04 May 2024 09:13:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4929, Retrieved Sat, 04 May 2024 09:13:31 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

270

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

-       [(Partial) Autocorrelation Function] [AutoCorrelatie na...] [2007-12-30 14:18:50] [ca5e0f9f346e091f4d0fe7e17f7dba21] [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=4929&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=4929&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4929&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	6.9282	0
1	0.450883	3.1238	0.001512
2	0.390752	2.7072	0.004685
3	0.181628	1.2584	0.107175
4	0.204324	1.4156	0.081674
5	0.171176	1.1859	0.120741
6	0.113943	0.7894	0.216874
7	-0.01572	-0.1089	0.543136
8	-0.183282	-1.2698	0.894864
9	-0.026364	-0.1827	0.572081
10	-0.195718	-1.356	0.909274
11	-0.173171	-1.1998	0.88194
12	-0.290051	-2.0095	0.97494
13	-0.25065	-1.7366	0.95556
14	-0.104402	-0.7233	0.763503
15	-0.107501	-0.7448	0.769984
16	-0.097786	-0.6775	0.749323

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 6.9282 & 0 \tabularnewline
1 & 0.450883 & 3.1238 & 0.001512 \tabularnewline
2 & 0.390752 & 2.7072 & 0.004685 \tabularnewline
3 & 0.181628 & 1.2584 & 0.107175 \tabularnewline
4 & 0.204324 & 1.4156 & 0.081674 \tabularnewline
5 & 0.171176 & 1.1859 & 0.120741 \tabularnewline
6 & 0.113943 & 0.7894 & 0.216874 \tabularnewline
7 & -0.01572 & -0.1089 & 0.543136 \tabularnewline
8 & -0.183282 & -1.2698 & 0.894864 \tabularnewline
9 & -0.026364 & -0.1827 & 0.572081 \tabularnewline
10 & -0.195718 & -1.356 & 0.909274 \tabularnewline
11 & -0.173171 & -1.1998 & 0.88194 \tabularnewline
12 & -0.290051 & -2.0095 & 0.97494 \tabularnewline
13 & -0.25065 & -1.7366 & 0.95556 \tabularnewline
14 & -0.104402 & -0.7233 & 0.763503 \tabularnewline
15 & -0.107501 & -0.7448 & 0.769984 \tabularnewline
16 & -0.097786 & -0.6775 & 0.749323 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4929&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]6.9282[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.450883[/C][C]3.1238[/C][C]0.001512[/C][/ROW]
[ROW][C]2[/C][C]0.390752[/C][C]2.7072[/C][C]0.004685[/C][/ROW]
[ROW][C]3[/C][C]0.181628[/C][C]1.2584[/C][C]0.107175[/C][/ROW]
[ROW][C]4[/C][C]0.204324[/C][C]1.4156[/C][C]0.081674[/C][/ROW]
[ROW][C]5[/C][C]0.171176[/C][C]1.1859[/C][C]0.120741[/C][/ROW]
[ROW][C]6[/C][C]0.113943[/C][C]0.7894[/C][C]0.216874[/C][/ROW]
[ROW][C]7[/C][C]-0.01572[/C][C]-0.1089[/C][C]0.543136[/C][/ROW]
[ROW][C]8[/C][C]-0.183282[/C][C]-1.2698[/C][C]0.894864[/C][/ROW]
[ROW][C]9[/C][C]-0.026364[/C][C]-0.1827[/C][C]0.572081[/C][/ROW]
[ROW][C]10[/C][C]-0.195718[/C][C]-1.356[/C][C]0.909274[/C][/ROW]
[ROW][C]11[/C][C]-0.173171[/C][C]-1.1998[/C][C]0.88194[/C][/ROW]
[ROW][C]12[/C][C]-0.290051[/C][C]-2.0095[/C][C]0.97494[/C][/ROW]
[ROW][C]13[/C][C]-0.25065[/C][C]-1.7366[/C][C]0.95556[/C][/ROW]
[ROW][C]14[/C][C]-0.104402[/C][C]-0.7233[/C][C]0.763503[/C][/ROW]
[ROW][C]15[/C][C]-0.107501[/C][C]-0.7448[/C][C]0.769984[/C][/ROW]
[ROW][C]16[/C][C]-0.097786[/C][C]-0.6775[/C][C]0.749323[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4929&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4929&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	6.9282	0
1	0.450883	3.1238	0.001512
2	0.390752	2.7072	0.004685
3	0.181628	1.2584	0.107175
4	0.204324	1.4156	0.081674
5	0.171176	1.1859	0.120741
6	0.113943	0.7894	0.216874
7	-0.01572	-0.1089	0.543136
8	-0.183282	-1.2698	0.894864
9	-0.026364	-0.1827	0.572081
10	-0.195718	-1.356	0.909274
11	-0.173171	-1.1998	0.88194
12	-0.290051	-2.0095	0.97494
13	-0.25065	-1.7366	0.95556
14	-0.104402	-0.7233	0.763503
15	-0.107501	-0.7448	0.769984
16	-0.097786	-0.6775	0.749323

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.450883	3.1238	0.001512
1	0.235289	1.6301	0.05481
2	-0.078647	-0.5449	0.705822
3	0.09528	0.6601	0.256167
4	0.072309	0.501	0.30934
5	-0.046383	-0.3214	0.625331
6	-0.136886	-0.9484	0.826155
7	-0.222382	-1.5407	0.935023
8	0.187078	1.2961	0.100567
9	-0.194251	-1.3458	0.907657
10	-0.129882	-0.8998	0.813653
11	-0.073965	-0.5124	0.694654
12	-0.021686	-0.1502	0.5594
13	0.195461	1.3542	0.091008
14	-0.100318	-0.695	0.754804
15	-0.061196	-0.424	0.663263
16	0.136573	0.9462	0.174392

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.450883 & 3.1238 & 0.001512 \tabularnewline
1 & 0.235289 & 1.6301 & 0.05481 \tabularnewline
2 & -0.078647 & -0.5449 & 0.705822 \tabularnewline
3 & 0.09528 & 0.6601 & 0.256167 \tabularnewline
4 & 0.072309 & 0.501 & 0.30934 \tabularnewline
5 & -0.046383 & -0.3214 & 0.625331 \tabularnewline
6 & -0.136886 & -0.9484 & 0.826155 \tabularnewline
7 & -0.222382 & -1.5407 & 0.935023 \tabularnewline
8 & 0.187078 & 1.2961 & 0.100567 \tabularnewline
9 & -0.194251 & -1.3458 & 0.907657 \tabularnewline
10 & -0.129882 & -0.8998 & 0.813653 \tabularnewline
11 & -0.073965 & -0.5124 & 0.694654 \tabularnewline
12 & -0.021686 & -0.1502 & 0.5594 \tabularnewline
13 & 0.195461 & 1.3542 & 0.091008 \tabularnewline
14 & -0.100318 & -0.695 & 0.754804 \tabularnewline
15 & -0.061196 & -0.424 & 0.663263 \tabularnewline
16 & 0.136573 & 0.9462 & 0.174392 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4929&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]0.450883[/C][C]3.1238[/C][C]0.001512[/C][/ROW]
[ROW][C]1[/C][C]0.235289[/C][C]1.6301[/C][C]0.05481[/C][/ROW]
[ROW][C]2[/C][C]-0.078647[/C][C]-0.5449[/C][C]0.705822[/C][/ROW]
[ROW][C]3[/C][C]0.09528[/C][C]0.6601[/C][C]0.256167[/C][/ROW]
[ROW][C]4[/C][C]0.072309[/C][C]0.501[/C][C]0.30934[/C][/ROW]
[ROW][C]5[/C][C]-0.046383[/C][C]-0.3214[/C][C]0.625331[/C][/ROW]
[ROW][C]6[/C][C]-0.136886[/C][C]-0.9484[/C][C]0.826155[/C][/ROW]
[ROW][C]7[/C][C]-0.222382[/C][C]-1.5407[/C][C]0.935023[/C][/ROW]
[ROW][C]8[/C][C]0.187078[/C][C]1.2961[/C][C]0.100567[/C][/ROW]
[ROW][C]9[/C][C]-0.194251[/C][C]-1.3458[/C][C]0.907657[/C][/ROW]
[ROW][C]10[/C][C]-0.129882[/C][C]-0.8998[/C][C]0.813653[/C][/ROW]
[ROW][C]11[/C][C]-0.073965[/C][C]-0.5124[/C][C]0.694654[/C][/ROW]
[ROW][C]12[/C][C]-0.021686[/C][C]-0.1502[/C][C]0.5594[/C][/ROW]
[ROW][C]13[/C][C]0.195461[/C][C]1.3542[/C][C]0.091008[/C][/ROW]
[ROW][C]14[/C][C]-0.100318[/C][C]-0.695[/C][C]0.754804[/C][/ROW]
[ROW][C]15[/C][C]-0.061196[/C][C]-0.424[/C][C]0.663263[/C][/ROW]
[ROW][C]16[/C][C]0.136573[/C][C]0.9462[/C][C]0.174392[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4929&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4929&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	0.450883	3.1238	0.001512
1	0.235289	1.6301	0.05481
2	-0.078647	-0.5449	0.705822
3	0.09528	0.6601	0.256167
4	0.072309	0.501	0.30934
5	-0.046383	-0.3214	0.625331
6	-0.136886	-0.9484	0.826155
7	-0.222382	-1.5407	0.935023
8	0.187078	1.2961	0.100567
9	-0.194251	-1.3458	0.907657
10	-0.129882	-0.8998	0.813653
11	-0.073965	-0.5124	0.694654
12	-0.021686	-0.1502	0.5594
13	0.195461	1.3542	0.091008
14	-0.100318	-0.695	0.754804
15	-0.061196	-0.424	0.663263
16	0.136573	0.9462	0.174392

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

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code