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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 09 Apr 2011 16:26:01 +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/2011/Apr/09/t1302366656ek3ijy7hdxkouio.htm/, Retrieved Wed, 08 May 2024 03:44:15 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=120424, Retrieved Wed, 08 May 2024 03:44:15 +0000

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Estimated Impact

210

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

-       [(Partial) Autocorrelation Function] [] [2011-04-09 16:26:01] [d41d8cd98f00b204e9800998ecf8427e] [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	1 seconds
R Server	'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120424&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=120424&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120424&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	1 seconds
R Server	'Herman Ole Andreas Wold' @ www.yougetit.org

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.420779	3.1488	0.001314
2	0.056587	0.4235	0.336792
3	-0.059186	-0.4429	0.329771
4	-0.187877	-1.4059	0.082633
5	-0.287279	-2.1498	0.017953
6	-0.423752	-3.1711	0.001232
7	-0.342649	-2.5642	0.006526
8	-0.156347	-1.17	0.12348
9	-0.007662	-0.0573	0.477241
10	0.050666	0.3791	0.353006
11	0.373686	2.7964	0.003534
12	0.595827	4.4588	2e-05
13	0.302793	2.2659	0.013671
14	0.081859	0.6126	0.271318
15	-0.076835	-0.575	0.283804
16	-0.178806	-1.3381	0.093142
17	-0.157854	-1.1813	0.121244
18	-0.30249	-2.2636	0.013746
19	-0.258529	-1.9347	0.029045
20	-0.117306	-0.8778	0.191891
21	-0.034168	-0.2557	0.399564
22	0.012207	0.0913	0.46377
23	0.25207	1.8863	0.03222
24	0.384969	2.8808	0.002806

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.420779 & 3.1488 & 0.001314 \tabularnewline
2 & 0.056587 & 0.4235 & 0.336792 \tabularnewline
3 & -0.059186 & -0.4429 & 0.329771 \tabularnewline
4 & -0.187877 & -1.4059 & 0.082633 \tabularnewline
5 & -0.287279 & -2.1498 & 0.017953 \tabularnewline
6 & -0.423752 & -3.1711 & 0.001232 \tabularnewline
7 & -0.342649 & -2.5642 & 0.006526 \tabularnewline
8 & -0.156347 & -1.17 & 0.12348 \tabularnewline
9 & -0.007662 & -0.0573 & 0.477241 \tabularnewline
10 & 0.050666 & 0.3791 & 0.353006 \tabularnewline
11 & 0.373686 & 2.7964 & 0.003534 \tabularnewline
12 & 0.595827 & 4.4588 & 2e-05 \tabularnewline
13 & 0.302793 & 2.2659 & 0.013671 \tabularnewline
14 & 0.081859 & 0.6126 & 0.271318 \tabularnewline
15 & -0.076835 & -0.575 & 0.283804 \tabularnewline
16 & -0.178806 & -1.3381 & 0.093142 \tabularnewline
17 & -0.157854 & -1.1813 & 0.121244 \tabularnewline
18 & -0.30249 & -2.2636 & 0.013746 \tabularnewline
19 & -0.258529 & -1.9347 & 0.029045 \tabularnewline
20 & -0.117306 & -0.8778 & 0.191891 \tabularnewline
21 & -0.034168 & -0.2557 & 0.399564 \tabularnewline
22 & 0.012207 & 0.0913 & 0.46377 \tabularnewline
23 & 0.25207 & 1.8863 & 0.03222 \tabularnewline
24 & 0.384969 & 2.8808 & 0.002806 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120424&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]0.420779[/C][C]3.1488[/C][C]0.001314[/C][/ROW]
[ROW][C]2[/C][C]0.056587[/C][C]0.4235[/C][C]0.336792[/C][/ROW]
[ROW][C]3[/C][C]-0.059186[/C][C]-0.4429[/C][C]0.329771[/C][/ROW]
[ROW][C]4[/C][C]-0.187877[/C][C]-1.4059[/C][C]0.082633[/C][/ROW]
[ROW][C]5[/C][C]-0.287279[/C][C]-2.1498[/C][C]0.017953[/C][/ROW]
[ROW][C]6[/C][C]-0.423752[/C][C]-3.1711[/C][C]0.001232[/C][/ROW]
[ROW][C]7[/C][C]-0.342649[/C][C]-2.5642[/C][C]0.006526[/C][/ROW]
[ROW][C]8[/C][C]-0.156347[/C][C]-1.17[/C][C]0.12348[/C][/ROW]
[ROW][C]9[/C][C]-0.007662[/C][C]-0.0573[/C][C]0.477241[/C][/ROW]
[ROW][C]10[/C][C]0.050666[/C][C]0.3791[/C][C]0.353006[/C][/ROW]
[ROW][C]11[/C][C]0.373686[/C][C]2.7964[/C][C]0.003534[/C][/ROW]
[ROW][C]12[/C][C]0.595827[/C][C]4.4588[/C][C]2e-05[/C][/ROW]
[ROW][C]13[/C][C]0.302793[/C][C]2.2659[/C][C]0.013671[/C][/ROW]
[ROW][C]14[/C][C]0.081859[/C][C]0.6126[/C][C]0.271318[/C][/ROW]
[ROW][C]15[/C][C]-0.076835[/C][C]-0.575[/C][C]0.283804[/C][/ROW]
[ROW][C]16[/C][C]-0.178806[/C][C]-1.3381[/C][C]0.093142[/C][/ROW]
[ROW][C]17[/C][C]-0.157854[/C][C]-1.1813[/C][C]0.121244[/C][/ROW]
[ROW][C]18[/C][C]-0.30249[/C][C]-2.2636[/C][C]0.013746[/C][/ROW]
[ROW][C]19[/C][C]-0.258529[/C][C]-1.9347[/C][C]0.029045[/C][/ROW]
[ROW][C]20[/C][C]-0.117306[/C][C]-0.8778[/C][C]0.191891[/C][/ROW]
[ROW][C]21[/C][C]-0.034168[/C][C]-0.2557[/C][C]0.399564[/C][/ROW]
[ROW][C]22[/C][C]0.012207[/C][C]0.0913[/C][C]0.46377[/C][/ROW]
[ROW][C]23[/C][C]0.25207[/C][C]1.8863[/C][C]0.03222[/C][/ROW]
[ROW][C]24[/C][C]0.384969[/C][C]2.8808[/C][C]0.002806[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=120424&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120424&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	0.420779	3.1488	0.001314
2	0.056587	0.4235	0.336792
3	-0.059186	-0.4429	0.329771
4	-0.187877	-1.4059	0.082633
5	-0.287279	-2.1498	0.017953
6	-0.423752	-3.1711	0.001232
7	-0.342649	-2.5642	0.006526
8	-0.156347	-1.17	0.12348
9	-0.007662	-0.0573	0.477241
10	0.050666	0.3791	0.353006
11	0.373686	2.7964	0.003534
12	0.595827	4.4588	2e-05
13	0.302793	2.2659	0.013671
14	0.081859	0.6126	0.271318
15	-0.076835	-0.575	0.283804
16	-0.178806	-1.3381	0.093142
17	-0.157854	-1.1813	0.121244
18	-0.30249	-2.2636	0.013746
19	-0.258529	-1.9347	0.029045
20	-0.117306	-0.8778	0.191891
21	-0.034168	-0.2557	0.399564
22	0.012207	0.0913	0.46377
23	0.25207	1.8863	0.03222
24	0.384969	2.8808	0.002806

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.420779	3.1488	0.001314
2	-0.146386	-1.0955	0.139003
3	-0.030902	-0.2312	0.408983
4	-0.172959	-1.2943	0.100436
5	-0.17654	-1.3211	0.09592
6	-0.32168	-2.4072	0.009697
7	-0.138742	-1.0383	0.151808
8	-0.099468	-0.7444	0.229888
9	-0.068595	-0.5133	0.304875
10	-0.143396	-1.0731	0.143919
11	0.309619	2.317	0.012093
12	0.32158	2.4065	0.009715
13	-0.092452	-0.6918	0.245946
14	0.023408	0.1752	0.430789
15	-0.028434	-0.2128	0.416136
16	-0.046676	-0.3493	0.36409
17	0.179585	1.3439	0.092202
18	-0.003757	-0.0281	0.488835
19	0.05358	0.401	0.34499
20	-0.029915	-0.2239	0.411838
21	-0.024898	-0.1863	0.426433
22	-0.118998	-0.8905	0.188504
23	0.043384	0.3247	0.373325
24	0.048727	0.3646	0.358378

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.420779 & 3.1488 & 0.001314 \tabularnewline
2 & -0.146386 & -1.0955 & 0.139003 \tabularnewline
3 & -0.030902 & -0.2312 & 0.408983 \tabularnewline
4 & -0.172959 & -1.2943 & 0.100436 \tabularnewline
5 & -0.17654 & -1.3211 & 0.09592 \tabularnewline
6 & -0.32168 & -2.4072 & 0.009697 \tabularnewline
7 & -0.138742 & -1.0383 & 0.151808 \tabularnewline
8 & -0.099468 & -0.7444 & 0.229888 \tabularnewline
9 & -0.068595 & -0.5133 & 0.304875 \tabularnewline
10 & -0.143396 & -1.0731 & 0.143919 \tabularnewline
11 & 0.309619 & 2.317 & 0.012093 \tabularnewline
12 & 0.32158 & 2.4065 & 0.009715 \tabularnewline
13 & -0.092452 & -0.6918 & 0.245946 \tabularnewline
14 & 0.023408 & 0.1752 & 0.430789 \tabularnewline
15 & -0.028434 & -0.2128 & 0.416136 \tabularnewline
16 & -0.046676 & -0.3493 & 0.36409 \tabularnewline
17 & 0.179585 & 1.3439 & 0.092202 \tabularnewline
18 & -0.003757 & -0.0281 & 0.488835 \tabularnewline
19 & 0.05358 & 0.401 & 0.34499 \tabularnewline
20 & -0.029915 & -0.2239 & 0.411838 \tabularnewline
21 & -0.024898 & -0.1863 & 0.426433 \tabularnewline
22 & -0.118998 & -0.8905 & 0.188504 \tabularnewline
23 & 0.043384 & 0.3247 & 0.373325 \tabularnewline
24 & 0.048727 & 0.3646 & 0.358378 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120424&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]0.420779[/C][C]3.1488[/C][C]0.001314[/C][/ROW]
[ROW][C]2[/C][C]-0.146386[/C][C]-1.0955[/C][C]0.139003[/C][/ROW]
[ROW][C]3[/C][C]-0.030902[/C][C]-0.2312[/C][C]0.408983[/C][/ROW]
[ROW][C]4[/C][C]-0.172959[/C][C]-1.2943[/C][C]0.100436[/C][/ROW]
[ROW][C]5[/C][C]-0.17654[/C][C]-1.3211[/C][C]0.09592[/C][/ROW]
[ROW][C]6[/C][C]-0.32168[/C][C]-2.4072[/C][C]0.009697[/C][/ROW]
[ROW][C]7[/C][C]-0.138742[/C][C]-1.0383[/C][C]0.151808[/C][/ROW]
[ROW][C]8[/C][C]-0.099468[/C][C]-0.7444[/C][C]0.229888[/C][/ROW]
[ROW][C]9[/C][C]-0.068595[/C][C]-0.5133[/C][C]0.304875[/C][/ROW]
[ROW][C]10[/C][C]-0.143396[/C][C]-1.0731[/C][C]0.143919[/C][/ROW]
[ROW][C]11[/C][C]0.309619[/C][C]2.317[/C][C]0.012093[/C][/ROW]
[ROW][C]12[/C][C]0.32158[/C][C]2.4065[/C][C]0.009715[/C][/ROW]
[ROW][C]13[/C][C]-0.092452[/C][C]-0.6918[/C][C]0.245946[/C][/ROW]
[ROW][C]14[/C][C]0.023408[/C][C]0.1752[/C][C]0.430789[/C][/ROW]
[ROW][C]15[/C][C]-0.028434[/C][C]-0.2128[/C][C]0.416136[/C][/ROW]
[ROW][C]16[/C][C]-0.046676[/C][C]-0.3493[/C][C]0.36409[/C][/ROW]
[ROW][C]17[/C][C]0.179585[/C][C]1.3439[/C][C]0.092202[/C][/ROW]
[ROW][C]18[/C][C]-0.003757[/C][C]-0.0281[/C][C]0.488835[/C][/ROW]
[ROW][C]19[/C][C]0.05358[/C][C]0.401[/C][C]0.34499[/C][/ROW]
[ROW][C]20[/C][C]-0.029915[/C][C]-0.2239[/C][C]0.411838[/C][/ROW]
[ROW][C]21[/C][C]-0.024898[/C][C]-0.1863[/C][C]0.426433[/C][/ROW]
[ROW][C]22[/C][C]-0.118998[/C][C]-0.8905[/C][C]0.188504[/C][/ROW]
[ROW][C]23[/C][C]0.043384[/C][C]0.3247[/C][C]0.373325[/C][/ROW]
[ROW][C]24[/C][C]0.048727[/C][C]0.3646[/C][C]0.358378[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=120424&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120424&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	0.420779	3.1488	0.001314
2	-0.146386	-1.0955	0.139003
3	-0.030902	-0.2312	0.408983
4	-0.172959	-1.2943	0.100436
5	-0.17654	-1.3211	0.09592
6	-0.32168	-2.4072	0.009697
7	-0.138742	-1.0383	0.151808
8	-0.099468	-0.7444	0.229888
9	-0.068595	-0.5133	0.304875
10	-0.143396	-1.0731	0.143919
11	0.309619	2.317	0.012093
12	0.32158	2.4065	0.009715
13	-0.092452	-0.6918	0.245946
14	0.023408	0.1752	0.430789
15	-0.028434	-0.2128	0.416136
16	-0.046676	-0.3493	0.36409
17	0.179585	1.3439	0.092202
18	-0.003757	-0.0281	0.488835
19	0.05358	0.401	0.34499
20	-0.029915	-0.2239	0.411838
21	-0.024898	-0.1863	0.426433
22	-0.118998	-0.8905	0.188504
23	0.043384	0.3247	0.373325
24	0.048727	0.3646	0.358378

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 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 24 ; 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