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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 25 Nov 2014 21:27:51 +0000

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/2014/Nov/25/t1416950906tf2o5847ruk7jvv.htm/, Retrieved Tue, 28 May 2024 20:13:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=258826, Retrieved Tue, 28 May 2024 20:13:00 +0000

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Original text written by user:

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User-defined keywords

Estimated Impact

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

-     [Mean Plot] [Autocorrelation w...] [2014-10-19 21:29:37] [b1f04123d82573d686ac8c7adc52feaa]
- RM      [(Partial) Autocorrelation Function] [] [2014-11-25 21:27:51] [c260288012d574817ee98c3ddd4d9474] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258826&T=0

[TABLE]
[ROW][C]Summary of computational 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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258826&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258826&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 computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.809504	7.4192	0
2	0.536089	4.9133	2e-06
3	0.392854	3.6006	0.000268
4	0.372431	3.4134	0.000495
5	0.429697	3.9382	8.4e-05
6	0.450124	4.1255	4.3e-05
7	0.360501	3.304	0.000701
8	0.22192	2.0339	0.022557
9	0.143933	1.3192	0.095348
10	0.186508	1.7094	0.045537
11	0.352375	3.2296	0.000885
12	0.438718	4.0209	6.3e-05
13	0.252239	2.3118	0.011618
14	0.001775	0.0163	0.493528
15	-0.13256	-1.2149	0.113897
16	-0.149072	-1.3663	0.087751
17	-0.094382	-0.865	0.194745
18	-0.064086	-0.5874	0.279269
19	-0.118764	-1.0885	0.139746

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.809504 & 7.4192 & 0 \tabularnewline
2 & 0.536089 & 4.9133 & 2e-06 \tabularnewline
3 & 0.392854 & 3.6006 & 0.000268 \tabularnewline
4 & 0.372431 & 3.4134 & 0.000495 \tabularnewline
5 & 0.429697 & 3.9382 & 8.4e-05 \tabularnewline
6 & 0.450124 & 4.1255 & 4.3e-05 \tabularnewline
7 & 0.360501 & 3.304 & 0.000701 \tabularnewline
8 & 0.22192 & 2.0339 & 0.022557 \tabularnewline
9 & 0.143933 & 1.3192 & 0.095348 \tabularnewline
10 & 0.186508 & 1.7094 & 0.045537 \tabularnewline
11 & 0.352375 & 3.2296 & 0.000885 \tabularnewline
12 & 0.438718 & 4.0209 & 6.3e-05 \tabularnewline
13 & 0.252239 & 2.3118 & 0.011618 \tabularnewline
14 & 0.001775 & 0.0163 & 0.493528 \tabularnewline
15 & -0.13256 & -1.2149 & 0.113897 \tabularnewline
16 & -0.149072 & -1.3663 & 0.087751 \tabularnewline
17 & -0.094382 & -0.865 & 0.194745 \tabularnewline
18 & -0.064086 & -0.5874 & 0.279269 \tabularnewline
19 & -0.118764 & -1.0885 & 0.139746 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258826&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]1[/C][C]0.809504[/C][C]7.4192[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.536089[/C][C]4.9133[/C][C]2e-06[/C][/ROW]
[ROW][C]3[/C][C]0.392854[/C][C]3.6006[/C][C]0.000268[/C][/ROW]
[ROW][C]4[/C][C]0.372431[/C][C]3.4134[/C][C]0.000495[/C][/ROW]
[ROW][C]5[/C][C]0.429697[/C][C]3.9382[/C][C]8.4e-05[/C][/ROW]
[ROW][C]6[/C][C]0.450124[/C][C]4.1255[/C][C]4.3e-05[/C][/ROW]
[ROW][C]7[/C][C]0.360501[/C][C]3.304[/C][C]0.000701[/C][/ROW]
[ROW][C]8[/C][C]0.22192[/C][C]2.0339[/C][C]0.022557[/C][/ROW]
[ROW][C]9[/C][C]0.143933[/C][C]1.3192[/C][C]0.095348[/C][/ROW]
[ROW][C]10[/C][C]0.186508[/C][C]1.7094[/C][C]0.045537[/C][/ROW]
[ROW][C]11[/C][C]0.352375[/C][C]3.2296[/C][C]0.000885[/C][/ROW]
[ROW][C]12[/C][C]0.438718[/C][C]4.0209[/C][C]6.3e-05[/C][/ROW]
[ROW][C]13[/C][C]0.252239[/C][C]2.3118[/C][C]0.011618[/C][/ROW]
[ROW][C]14[/C][C]0.001775[/C][C]0.0163[/C][C]0.493528[/C][/ROW]
[ROW][C]15[/C][C]-0.13256[/C][C]-1.2149[/C][C]0.113897[/C][/ROW]
[ROW][C]16[/C][C]-0.149072[/C][C]-1.3663[/C][C]0.087751[/C][/ROW]
[ROW][C]17[/C][C]-0.094382[/C][C]-0.865[/C][C]0.194745[/C][/ROW]
[ROW][C]18[/C][C]-0.064086[/C][C]-0.5874[/C][C]0.279269[/C][/ROW]
[ROW][C]19[/C][C]-0.118764[/C][C]-1.0885[/C][C]0.139746[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258826&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258826&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
1	0.809504	7.4192	0
2	0.536089	4.9133	2e-06
3	0.392854	3.6006	0.000268
4	0.372431	3.4134	0.000495
5	0.429697	3.9382	8.4e-05
6	0.450124	4.1255	4.3e-05
7	0.360501	3.304	0.000701
8	0.22192	2.0339	0.022557
9	0.143933	1.3192	0.095348
10	0.186508	1.7094	0.045537
11	0.352375	3.2296	0.000885
12	0.438718	4.0209	6.3e-05
13	0.252239	2.3118	0.011618
14	0.001775	0.0163	0.493528
15	-0.13256	-1.2149	0.113897
16	-0.149072	-1.3663	0.087751
17	-0.094382	-0.865	0.194745
18	-0.064086	-0.5874	0.279269
19	-0.118764	-1.0885	0.139746

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.809504	7.4192	0
2	-0.345828	-3.1696	0.001065
3	0.292474	2.6806	0.004422
4	0.087028	0.7976	0.213668
5	0.226518	2.0761	0.020472
6	-0.064735	-0.5933	0.277285
7	-0.114774	-1.0519	0.147927
8	-0.060564	-0.5551	0.290158
9	0.056923	0.5217	0.301625
10	0.161336	1.4787	0.071485
11	0.331733	3.0404	0.001575
12	-0.179067	-1.6412	0.05225
13	-0.547646	-5.0193	1e-06
14	0.004648	0.0426	0.483059
15	-0.031565	-0.2893	0.386534
16	-0.046144	-0.4229	0.336719
17	-0.083773	-0.7678	0.222381
18	0.004399	0.0403	0.483968
19	0.079336	0.7271	0.234585

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.809504 & 7.4192 & 0 \tabularnewline
2 & -0.345828 & -3.1696 & 0.001065 \tabularnewline
3 & 0.292474 & 2.6806 & 0.004422 \tabularnewline
4 & 0.087028 & 0.7976 & 0.213668 \tabularnewline
5 & 0.226518 & 2.0761 & 0.020472 \tabularnewline
6 & -0.064735 & -0.5933 & 0.277285 \tabularnewline
7 & -0.114774 & -1.0519 & 0.147927 \tabularnewline
8 & -0.060564 & -0.5551 & 0.290158 \tabularnewline
9 & 0.056923 & 0.5217 & 0.301625 \tabularnewline
10 & 0.161336 & 1.4787 & 0.071485 \tabularnewline
11 & 0.331733 & 3.0404 & 0.001575 \tabularnewline
12 & -0.179067 & -1.6412 & 0.05225 \tabularnewline
13 & -0.547646 & -5.0193 & 1e-06 \tabularnewline
14 & 0.004648 & 0.0426 & 0.483059 \tabularnewline
15 & -0.031565 & -0.2893 & 0.386534 \tabularnewline
16 & -0.046144 & -0.4229 & 0.336719 \tabularnewline
17 & -0.083773 & -0.7678 & 0.222381 \tabularnewline
18 & 0.004399 & 0.0403 & 0.483968 \tabularnewline
19 & 0.079336 & 0.7271 & 0.234585 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258826&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]1[/C][C]0.809504[/C][C]7.4192[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.345828[/C][C]-3.1696[/C][C]0.001065[/C][/ROW]
[ROW][C]3[/C][C]0.292474[/C][C]2.6806[/C][C]0.004422[/C][/ROW]
[ROW][C]4[/C][C]0.087028[/C][C]0.7976[/C][C]0.213668[/C][/ROW]
[ROW][C]5[/C][C]0.226518[/C][C]2.0761[/C][C]0.020472[/C][/ROW]
[ROW][C]6[/C][C]-0.064735[/C][C]-0.5933[/C][C]0.277285[/C][/ROW]
[ROW][C]7[/C][C]-0.114774[/C][C]-1.0519[/C][C]0.147927[/C][/ROW]
[ROW][C]8[/C][C]-0.060564[/C][C]-0.5551[/C][C]0.290158[/C][/ROW]
[ROW][C]9[/C][C]0.056923[/C][C]0.5217[/C][C]0.301625[/C][/ROW]
[ROW][C]10[/C][C]0.161336[/C][C]1.4787[/C][C]0.071485[/C][/ROW]
[ROW][C]11[/C][C]0.331733[/C][C]3.0404[/C][C]0.001575[/C][/ROW]
[ROW][C]12[/C][C]-0.179067[/C][C]-1.6412[/C][C]0.05225[/C][/ROW]
[ROW][C]13[/C][C]-0.547646[/C][C]-5.0193[/C][C]1e-06[/C][/ROW]
[ROW][C]14[/C][C]0.004648[/C][C]0.0426[/C][C]0.483059[/C][/ROW]
[ROW][C]15[/C][C]-0.031565[/C][C]-0.2893[/C][C]0.386534[/C][/ROW]
[ROW][C]16[/C][C]-0.046144[/C][C]-0.4229[/C][C]0.336719[/C][/ROW]
[ROW][C]17[/C][C]-0.083773[/C][C]-0.7678[/C][C]0.222381[/C][/ROW]
[ROW][C]18[/C][C]0.004399[/C][C]0.0403[/C][C]0.483968[/C][/ROW]
[ROW][C]19[/C][C]0.079336[/C][C]0.7271[/C][C]0.234585[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258826&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258826&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
1	0.809504	7.4192	0
2	-0.345828	-3.1696	0.001065
3	0.292474	2.6806	0.004422
4	0.087028	0.7976	0.213668
5	0.226518	2.0761	0.020472
6	-0.064735	-0.5933	0.277285
7	-0.114774	-1.0519	0.147927
8	-0.060564	-0.5551	0.290158
9	0.056923	0.5217	0.301625
10	0.161336	1.4787	0.071485
11	0.331733	3.0404	0.001575
12	-0.179067	-1.6412	0.05225
13	-0.547646	-5.0193	1e-06
14	0.004648	0.0426	0.483059
15	-0.031565	-0.2893	0.386534
16	-0.046144	-0.4229	0.336719
17	-0.083773	-0.7678	0.222381
18	0.004399	0.0403	0.483968
19	0.079336	0.7271	0.234585

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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 2:(par1+1)) {
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(abs(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,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(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code