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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 27 Dec 2010 18:50:47 +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/2010/Dec/27/t1293475975yk7ne9oa7xi3y70.htm/, Retrieved Mon, 06 May 2024 16:05:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116085, Retrieved Mon, 06 May 2024 16:05:41 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

115

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

-     [Classical Decomposition] [] [2010-12-20 14:39:41] [1c63f3c303537b65dfa698074d619a3e]
- RMPD    [(Partial) Autocorrelation Function] [] [2010-12-27 18:50:47] [6d519594e32ce09ffe6000a98c6f6a83] [Current]

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Dataseries X:

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Histogram

Boxplots

9.4
9.4
9.5
9.5
9.4
9.4
9.3
9.4
9.4
9.2
9.1
9.1
9.1
9.0
9.0
8.9
8.8
8.7
8.5
8.3
8.1
7.9
7.8
7.6
7.4
7.2
7.0
7.0
6.8
6.8
6.7
6.8
6.7
6.7
6.7
6.5
6.3
6.3
6.3
6.5
6.6
6.5
6.3
6.3
6.5
7.0
7.1
7.3
7.3
7.4
7.4
7.3
7.4
7.5
7.7
7.7
7.7
7.7
7.7
7.8
8.0
8.1
8.1
8.2
8.2
8.2
8.1
8.1
8.2
8.3
8.3
8.4
8.5
8.5
8.4
8.0
7.9
8.1
8.5
8.8
8.8
8.6
8.3
8.3
8.3
8.4
8.4
8.5
8.6
8.6
8.6
8.6
8.6
8.5
8.4
8.4
8.4
8.5
8.5
8.6
8.6
8.4
8.2
8.0
8.0
8.0
8.0
7.9
7.9
7.8
7.8
8.0
7.8
7.4
7.2
7.0
7.0
7.2
7.2
7.2
7.0
6.9
6.8
6.8
6.8
6.9
7.2
7.2
7.2
7.1
7.2
7.3
7.5
7.6
7.7
7.7
7.7
7.8
8.0
8.1
8.1
8.0
8.1
8.2
8.3
8.4
8.4
8.4
8.5
8.5
8.6
8.6
8.5
8.5

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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116085&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116085&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116085&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.49013	6.0626	0
2	0.144271	1.7845	0.03816
3	-0.140977	-1.7438	0.041603
4	-0.087507	-1.0824	0.140387
5	0.140668	1.74	0.041938
6	0.290404	3.5921	0.000221
7	0.322271	3.9863	5.2e-05
8	0.247385	3.06	0.001307
9	0.197666	2.445	0.00781
10	0.101387	1.2541	0.105862
11	0.090468	1.119	0.13244
12	0.061723	0.7635	0.22318
13	0.008648	0.107	0.457475
14	0.047856	0.5919	0.277381
15	0.051409	0.6359	0.262898
16	0.029794	0.3685	0.356492
17	-0.016569	-0.2049	0.418944
18	0.019493	0.2411	0.404896
19	0.030596	0.3785	0.352809
20	0.045055	0.5573	0.289067
21	-0.086668	-1.072	0.142697

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.49013 & 6.0626 & 0 \tabularnewline
2 & 0.144271 & 1.7845 & 0.03816 \tabularnewline
3 & -0.140977 & -1.7438 & 0.041603 \tabularnewline
4 & -0.087507 & -1.0824 & 0.140387 \tabularnewline
5 & 0.140668 & 1.74 & 0.041938 \tabularnewline
6 & 0.290404 & 3.5921 & 0.000221 \tabularnewline
7 & 0.322271 & 3.9863 & 5.2e-05 \tabularnewline
8 & 0.247385 & 3.06 & 0.001307 \tabularnewline
9 & 0.197666 & 2.445 & 0.00781 \tabularnewline
10 & 0.101387 & 1.2541 & 0.105862 \tabularnewline
11 & 0.090468 & 1.119 & 0.13244 \tabularnewline
12 & 0.061723 & 0.7635 & 0.22318 \tabularnewline
13 & 0.008648 & 0.107 & 0.457475 \tabularnewline
14 & 0.047856 & 0.5919 & 0.277381 \tabularnewline
15 & 0.051409 & 0.6359 & 0.262898 \tabularnewline
16 & 0.029794 & 0.3685 & 0.356492 \tabularnewline
17 & -0.016569 & -0.2049 & 0.418944 \tabularnewline
18 & 0.019493 & 0.2411 & 0.404896 \tabularnewline
19 & 0.030596 & 0.3785 & 0.352809 \tabularnewline
20 & 0.045055 & 0.5573 & 0.289067 \tabularnewline
21 & -0.086668 & -1.072 & 0.142697 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116085&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]0.49013[/C][C]6.0626[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.144271[/C][C]1.7845[/C][C]0.03816[/C][/ROW]
[ROW][C]3[/C][C]-0.140977[/C][C]-1.7438[/C][C]0.041603[/C][/ROW]
[ROW][C]4[/C][C]-0.087507[/C][C]-1.0824[/C][C]0.140387[/C][/ROW]
[ROW][C]5[/C][C]0.140668[/C][C]1.74[/C][C]0.041938[/C][/ROW]
[ROW][C]6[/C][C]0.290404[/C][C]3.5921[/C][C]0.000221[/C][/ROW]
[ROW][C]7[/C][C]0.322271[/C][C]3.9863[/C][C]5.2e-05[/C][/ROW]
[ROW][C]8[/C][C]0.247385[/C][C]3.06[/C][C]0.001307[/C][/ROW]
[ROW][C]9[/C][C]0.197666[/C][C]2.445[/C][C]0.00781[/C][/ROW]
[ROW][C]10[/C][C]0.101387[/C][C]1.2541[/C][C]0.105862[/C][/ROW]
[ROW][C]11[/C][C]0.090468[/C][C]1.119[/C][C]0.13244[/C][/ROW]
[ROW][C]12[/C][C]0.061723[/C][C]0.7635[/C][C]0.22318[/C][/ROW]
[ROW][C]13[/C][C]0.008648[/C][C]0.107[/C][C]0.457475[/C][/ROW]
[ROW][C]14[/C][C]0.047856[/C][C]0.5919[/C][C]0.277381[/C][/ROW]
[ROW][C]15[/C][C]0.051409[/C][C]0.6359[/C][C]0.262898[/C][/ROW]
[ROW][C]16[/C][C]0.029794[/C][C]0.3685[/C][C]0.356492[/C][/ROW]
[ROW][C]17[/C][C]-0.016569[/C][C]-0.2049[/C][C]0.418944[/C][/ROW]
[ROW][C]18[/C][C]0.019493[/C][C]0.2411[/C][C]0.404896[/C][/ROW]
[ROW][C]19[/C][C]0.030596[/C][C]0.3785[/C][C]0.352809[/C][/ROW]
[ROW][C]20[/C][C]0.045055[/C][C]0.5573[/C][C]0.289067[/C][/ROW]
[ROW][C]21[/C][C]-0.086668[/C][C]-1.072[/C][C]0.142697[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116085&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116085&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	0.49013	6.0626	0
2	0.144271	1.7845	0.03816
3	-0.140977	-1.7438	0.041603
4	-0.087507	-1.0824	0.140387
5	0.140668	1.74	0.041938
6	0.290404	3.5921	0.000221
7	0.322271	3.9863	5.2e-05
8	0.247385	3.06	0.001307
9	0.197666	2.445	0.00781
10	0.101387	1.2541	0.105862
11	0.090468	1.119	0.13244
12	0.061723	0.7635	0.22318
13	0.008648	0.107	0.457475
14	0.047856	0.5919	0.277381
15	0.051409	0.6359	0.262898
16	0.029794	0.3685	0.356492
17	-0.016569	-0.2049	0.418944
18	0.019493	0.2411	0.404896
19	0.030596	0.3785	0.352809
20	0.045055	0.5573	0.289067
21	-0.086668	-1.072	0.142697

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.49013	6.0626	0
2	-0.126297	-1.5622	0.060152
3	-0.212286	-2.6258	0.004761
4	0.128717	1.5921	0.056709
5	0.235274	2.9102	0.002076
6	0.102043	1.2622	0.104398
7	0.107077	1.3245	0.09366
8	0.125035	1.5466	0.062013
9	0.160575	1.9862	0.024398
10	-0.002163	-0.0268	0.489343
11	0.047889	0.5924	0.277244
12	-0.009972	-0.1233	0.450997
13	-0.125214	-1.5488	0.061746
14	-0.002192	-0.0271	0.489204
15	-0.063928	-0.7907	0.215158
16	-0.144709	-1.7899	0.03772
17	-0.111474	-1.3789	0.084976
18	0.050003	0.6185	0.268584
19	-0.020354	-0.2518	0.40078
20	-0.025894	-0.3203	0.374592
21	-0.149572	-1.8501	0.033113

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.49013 & 6.0626 & 0 \tabularnewline
2 & -0.126297 & -1.5622 & 0.060152 \tabularnewline
3 & -0.212286 & -2.6258 & 0.004761 \tabularnewline
4 & 0.128717 & 1.5921 & 0.056709 \tabularnewline
5 & 0.235274 & 2.9102 & 0.002076 \tabularnewline
6 & 0.102043 & 1.2622 & 0.104398 \tabularnewline
7 & 0.107077 & 1.3245 & 0.09366 \tabularnewline
8 & 0.125035 & 1.5466 & 0.062013 \tabularnewline
9 & 0.160575 & 1.9862 & 0.024398 \tabularnewline
10 & -0.002163 & -0.0268 & 0.489343 \tabularnewline
11 & 0.047889 & 0.5924 & 0.277244 \tabularnewline
12 & -0.009972 & -0.1233 & 0.450997 \tabularnewline
13 & -0.125214 & -1.5488 & 0.061746 \tabularnewline
14 & -0.002192 & -0.0271 & 0.489204 \tabularnewline
15 & -0.063928 & -0.7907 & 0.215158 \tabularnewline
16 & -0.144709 & -1.7899 & 0.03772 \tabularnewline
17 & -0.111474 & -1.3789 & 0.084976 \tabularnewline
18 & 0.050003 & 0.6185 & 0.268584 \tabularnewline
19 & -0.020354 & -0.2518 & 0.40078 \tabularnewline
20 & -0.025894 & -0.3203 & 0.374592 \tabularnewline
21 & -0.149572 & -1.8501 & 0.033113 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116085&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]0.49013[/C][C]6.0626[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.126297[/C][C]-1.5622[/C][C]0.060152[/C][/ROW]
[ROW][C]3[/C][C]-0.212286[/C][C]-2.6258[/C][C]0.004761[/C][/ROW]
[ROW][C]4[/C][C]0.128717[/C][C]1.5921[/C][C]0.056709[/C][/ROW]
[ROW][C]5[/C][C]0.235274[/C][C]2.9102[/C][C]0.002076[/C][/ROW]
[ROW][C]6[/C][C]0.102043[/C][C]1.2622[/C][C]0.104398[/C][/ROW]
[ROW][C]7[/C][C]0.107077[/C][C]1.3245[/C][C]0.09366[/C][/ROW]
[ROW][C]8[/C][C]0.125035[/C][C]1.5466[/C][C]0.062013[/C][/ROW]
[ROW][C]9[/C][C]0.160575[/C][C]1.9862[/C][C]0.024398[/C][/ROW]
[ROW][C]10[/C][C]-0.002163[/C][C]-0.0268[/C][C]0.489343[/C][/ROW]
[ROW][C]11[/C][C]0.047889[/C][C]0.5924[/C][C]0.277244[/C][/ROW]
[ROW][C]12[/C][C]-0.009972[/C][C]-0.1233[/C][C]0.450997[/C][/ROW]
[ROW][C]13[/C][C]-0.125214[/C][C]-1.5488[/C][C]0.061746[/C][/ROW]
[ROW][C]14[/C][C]-0.002192[/C][C]-0.0271[/C][C]0.489204[/C][/ROW]
[ROW][C]15[/C][C]-0.063928[/C][C]-0.7907[/C][C]0.215158[/C][/ROW]
[ROW][C]16[/C][C]-0.144709[/C][C]-1.7899[/C][C]0.03772[/C][/ROW]
[ROW][C]17[/C][C]-0.111474[/C][C]-1.3789[/C][C]0.084976[/C][/ROW]
[ROW][C]18[/C][C]0.050003[/C][C]0.6185[/C][C]0.268584[/C][/ROW]
[ROW][C]19[/C][C]-0.020354[/C][C]-0.2518[/C][C]0.40078[/C][/ROW]
[ROW][C]20[/C][C]-0.025894[/C][C]-0.3203[/C][C]0.374592[/C][/ROW]
[ROW][C]21[/C][C]-0.149572[/C][C]-1.8501[/C][C]0.033113[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116085&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116085&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	0.49013	6.0626	0
2	-0.126297	-1.5622	0.060152
3	-0.212286	-2.6258	0.004761
4	0.128717	1.5921	0.056709
5	0.235274	2.9102	0.002076
6	0.102043	1.2622	0.104398
7	0.107077	1.3245	0.09366
8	0.125035	1.5466	0.062013
9	0.160575	1.9862	0.024398
10	-0.002163	-0.0268	0.489343
11	0.047889	0.5924	0.277244
12	-0.009972	-0.1233	0.450997
13	-0.125214	-1.5488	0.061746
14	-0.002192	-0.0271	0.489204
15	-0.063928	-0.7907	0.215158
16	-0.144709	-1.7899	0.03772
17	-0.111474	-1.3789	0.084976
18	0.050003	0.6185	0.268584
19	-0.020354	-0.2518	0.40078
20	-0.025894	-0.3203	0.374592
21	-0.149572	-1.8501	0.033113

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

Parameters (R input):

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