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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 18 Oct 2016 21:42:58 +0100

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/2016/Oct/18/t1476823390mmjxwm546l1i4of.htm/, Retrieved Sat, 27 Apr 2024 23:25:43 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 27 Apr 2024 23:25:43 +0200

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Estimated Impact

Dataseries X:

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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	'George Udny Yule' @ yule.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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.666209	-5.1172	2e-06
2	0.197671	1.5183	0.067135
3	0.159044	1.2216	0.113352
4	-0.431763	-3.3164	0.000782
5	0.418077	3.2113	0.00107
6	-0.283736	-2.1794	0.016652
7	0.220905	1.6968	0.047502
8	-0.189908	-1.4587	0.074974
9	0.022499	0.1728	0.431692
10	0.15539	1.1936	0.118711
11	-0.37351	-2.869	0.002853
12	0.590427	4.5352	1.4e-05
13	-0.465752	-3.5775	0.00035
14	0.197459	1.5167	0.06734
15	0.075624	0.5809	0.281766
16	-0.353537	-2.7156	0.004333
17	0.449381	3.4518	0.000518
18	-0.350707	-2.6938	0.004592
19	0.182493	1.4018	0.083114
20	-0.07347	-0.5643	0.287334
21	-0.054744	-0.4205	0.337825
22	0.133283	1.0238	0.155062
23	-0.180795	-1.3887	0.08507
24	0.314669	2.417	0.009379

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.666209 & -5.1172 & 2e-06 \tabularnewline
2 & 0.197671 & 1.5183 & 0.067135 \tabularnewline
3 & 0.159044 & 1.2216 & 0.113352 \tabularnewline
4 & -0.431763 & -3.3164 & 0.000782 \tabularnewline
5 & 0.418077 & 3.2113 & 0.00107 \tabularnewline
6 & -0.283736 & -2.1794 & 0.016652 \tabularnewline
7 & 0.220905 & 1.6968 & 0.047502 \tabularnewline
8 & -0.189908 & -1.4587 & 0.074974 \tabularnewline
9 & 0.022499 & 0.1728 & 0.431692 \tabularnewline
10 & 0.15539 & 1.1936 & 0.118711 \tabularnewline
11 & -0.37351 & -2.869 & 0.002853 \tabularnewline
12 & 0.590427 & 4.5352 & 1.4e-05 \tabularnewline
13 & -0.465752 & -3.5775 & 0.00035 \tabularnewline
14 & 0.197459 & 1.5167 & 0.06734 \tabularnewline
15 & 0.075624 & 0.5809 & 0.281766 \tabularnewline
16 & -0.353537 & -2.7156 & 0.004333 \tabularnewline
17 & 0.449381 & 3.4518 & 0.000518 \tabularnewline
18 & -0.350707 & -2.6938 & 0.004592 \tabularnewline
19 & 0.182493 & 1.4018 & 0.083114 \tabularnewline
20 & -0.07347 & -0.5643 & 0.287334 \tabularnewline
21 & -0.054744 & -0.4205 & 0.337825 \tabularnewline
22 & 0.133283 & 1.0238 & 0.155062 \tabularnewline
23 & -0.180795 & -1.3887 & 0.08507 \tabularnewline
24 & 0.314669 & 2.417 & 0.009379 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]-0.666209[/C][C]-5.1172[/C][C]2e-06[/C][/ROW]
[ROW][C]2[/C][C]0.197671[/C][C]1.5183[/C][C]0.067135[/C][/ROW]
[ROW][C]3[/C][C]0.159044[/C][C]1.2216[/C][C]0.113352[/C][/ROW]
[ROW][C]4[/C][C]-0.431763[/C][C]-3.3164[/C][C]0.000782[/C][/ROW]
[ROW][C]5[/C][C]0.418077[/C][C]3.2113[/C][C]0.00107[/C][/ROW]
[ROW][C]6[/C][C]-0.283736[/C][C]-2.1794[/C][C]0.016652[/C][/ROW]
[ROW][C]7[/C][C]0.220905[/C][C]1.6968[/C][C]0.047502[/C][/ROW]
[ROW][C]8[/C][C]-0.189908[/C][C]-1.4587[/C][C]0.074974[/C][/ROW]
[ROW][C]9[/C][C]0.022499[/C][C]0.1728[/C][C]0.431692[/C][/ROW]
[ROW][C]10[/C][C]0.15539[/C][C]1.1936[/C][C]0.118711[/C][/ROW]
[ROW][C]11[/C][C]-0.37351[/C][C]-2.869[/C][C]0.002853[/C][/ROW]
[ROW][C]12[/C][C]0.590427[/C][C]4.5352[/C][C]1.4e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.465752[/C][C]-3.5775[/C][C]0.00035[/C][/ROW]
[ROW][C]14[/C][C]0.197459[/C][C]1.5167[/C][C]0.06734[/C][/ROW]
[ROW][C]15[/C][C]0.075624[/C][C]0.5809[/C][C]0.281766[/C][/ROW]
[ROW][C]16[/C][C]-0.353537[/C][C]-2.7156[/C][C]0.004333[/C][/ROW]
[ROW][C]17[/C][C]0.449381[/C][C]3.4518[/C][C]0.000518[/C][/ROW]
[ROW][C]18[/C][C]-0.350707[/C][C]-2.6938[/C][C]0.004592[/C][/ROW]
[ROW][C]19[/C][C]0.182493[/C][C]1.4018[/C][C]0.083114[/C][/ROW]
[ROW][C]20[/C][C]-0.07347[/C][C]-0.5643[/C][C]0.287334[/C][/ROW]
[ROW][C]21[/C][C]-0.054744[/C][C]-0.4205[/C][C]0.337825[/C][/ROW]
[ROW][C]22[/C][C]0.133283[/C][C]1.0238[/C][C]0.155062[/C][/ROW]
[ROW][C]23[/C][C]-0.180795[/C][C]-1.3887[/C][C]0.08507[/C][/ROW]
[ROW][C]24[/C][C]0.314669[/C][C]2.417[/C][C]0.009379[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	-0.666209	-5.1172	2e-06
2	0.197671	1.5183	0.067135
3	0.159044	1.2216	0.113352
4	-0.431763	-3.3164	0.000782
5	0.418077	3.2113	0.00107
6	-0.283736	-2.1794	0.016652
7	0.220905	1.6968	0.047502
8	-0.189908	-1.4587	0.074974
9	0.022499	0.1728	0.431692
10	0.15539	1.1936	0.118711
11	-0.37351	-2.869	0.002853
12	0.590427	4.5352	1.4e-05
13	-0.465752	-3.5775	0.00035
14	0.197459	1.5167	0.06734
15	0.075624	0.5809	0.281766
16	-0.353537	-2.7156	0.004333
17	0.449381	3.4518	0.000518
18	-0.350707	-2.6938	0.004592
19	0.182493	1.4018	0.083114
20	-0.07347	-0.5643	0.287334
21	-0.054744	-0.4205	0.337825
22	0.133283	1.0238	0.155062
23	-0.180795	-1.3887	0.08507
24	0.314669	2.417	0.009379

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.666209	-5.1172	2e-06
2	-0.442609	-3.3997	0.000607
3	0.121085	0.9301	0.178061
4	-0.322878	-2.4801	0.008005
5	-0.175677	-1.3494	0.091181
6	-0.209134	-1.6064	0.056764
7	0.212962	1.6358	0.053604
8	-0.248812	-1.9112	0.030423
9	-0.327699	-2.5171	0.007285
10	-0.08508	-0.6535	0.257982
11	-0.395262	-3.0361	0.001782
12	0.083299	0.6398	0.262379
13	0.024316	0.1868	0.42624
14	0.111387	0.8556	0.197846
15	-0.010828	-0.0832	0.466999
16	-0.067522	-0.5186	0.302973
17	0.058742	0.4512	0.326748
18	0.025333	0.1946	0.423193
19	-0.090044	-0.6916	0.245938
20	-0.171501	-1.3173	0.096411
21	0.017535	0.1347	0.446657
22	-0.107418	-0.8251	0.206321
23	-0.032141	-0.2469	0.402929
24	0.013655	0.1049	0.458411

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.666209 & -5.1172 & 2e-06 \tabularnewline
2 & -0.442609 & -3.3997 & 0.000607 \tabularnewline
3 & 0.121085 & 0.9301 & 0.178061 \tabularnewline
4 & -0.322878 & -2.4801 & 0.008005 \tabularnewline
5 & -0.175677 & -1.3494 & 0.091181 \tabularnewline
6 & -0.209134 & -1.6064 & 0.056764 \tabularnewline
7 & 0.212962 & 1.6358 & 0.053604 \tabularnewline
8 & -0.248812 & -1.9112 & 0.030423 \tabularnewline
9 & -0.327699 & -2.5171 & 0.007285 \tabularnewline
10 & -0.08508 & -0.6535 & 0.257982 \tabularnewline
11 & -0.395262 & -3.0361 & 0.001782 \tabularnewline
12 & 0.083299 & 0.6398 & 0.262379 \tabularnewline
13 & 0.024316 & 0.1868 & 0.42624 \tabularnewline
14 & 0.111387 & 0.8556 & 0.197846 \tabularnewline
15 & -0.010828 & -0.0832 & 0.466999 \tabularnewline
16 & -0.067522 & -0.5186 & 0.302973 \tabularnewline
17 & 0.058742 & 0.4512 & 0.326748 \tabularnewline
18 & 0.025333 & 0.1946 & 0.423193 \tabularnewline
19 & -0.090044 & -0.6916 & 0.245938 \tabularnewline
20 & -0.171501 & -1.3173 & 0.096411 \tabularnewline
21 & 0.017535 & 0.1347 & 0.446657 \tabularnewline
22 & -0.107418 & -0.8251 & 0.206321 \tabularnewline
23 & -0.032141 & -0.2469 & 0.402929 \tabularnewline
24 & 0.013655 & 0.1049 & 0.458411 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]-0.666209[/C][C]-5.1172[/C][C]2e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.442609[/C][C]-3.3997[/C][C]0.000607[/C][/ROW]
[ROW][C]3[/C][C]0.121085[/C][C]0.9301[/C][C]0.178061[/C][/ROW]
[ROW][C]4[/C][C]-0.322878[/C][C]-2.4801[/C][C]0.008005[/C][/ROW]
[ROW][C]5[/C][C]-0.175677[/C][C]-1.3494[/C][C]0.091181[/C][/ROW]
[ROW][C]6[/C][C]-0.209134[/C][C]-1.6064[/C][C]0.056764[/C][/ROW]
[ROW][C]7[/C][C]0.212962[/C][C]1.6358[/C][C]0.053604[/C][/ROW]
[ROW][C]8[/C][C]-0.248812[/C][C]-1.9112[/C][C]0.030423[/C][/ROW]
[ROW][C]9[/C][C]-0.327699[/C][C]-2.5171[/C][C]0.007285[/C][/ROW]
[ROW][C]10[/C][C]-0.08508[/C][C]-0.6535[/C][C]0.257982[/C][/ROW]
[ROW][C]11[/C][C]-0.395262[/C][C]-3.0361[/C][C]0.001782[/C][/ROW]
[ROW][C]12[/C][C]0.083299[/C][C]0.6398[/C][C]0.262379[/C][/ROW]
[ROW][C]13[/C][C]0.024316[/C][C]0.1868[/C][C]0.42624[/C][/ROW]
[ROW][C]14[/C][C]0.111387[/C][C]0.8556[/C][C]0.197846[/C][/ROW]
[ROW][C]15[/C][C]-0.010828[/C][C]-0.0832[/C][C]0.466999[/C][/ROW]
[ROW][C]16[/C][C]-0.067522[/C][C]-0.5186[/C][C]0.302973[/C][/ROW]
[ROW][C]17[/C][C]0.058742[/C][C]0.4512[/C][C]0.326748[/C][/ROW]
[ROW][C]18[/C][C]0.025333[/C][C]0.1946[/C][C]0.423193[/C][/ROW]
[ROW][C]19[/C][C]-0.090044[/C][C]-0.6916[/C][C]0.245938[/C][/ROW]
[ROW][C]20[/C][C]-0.171501[/C][C]-1.3173[/C][C]0.096411[/C][/ROW]
[ROW][C]21[/C][C]0.017535[/C][C]0.1347[/C][C]0.446657[/C][/ROW]
[ROW][C]22[/C][C]-0.107418[/C][C]-0.8251[/C][C]0.206321[/C][/ROW]
[ROW][C]23[/C][C]-0.032141[/C][C]-0.2469[/C][C]0.402929[/C][/ROW]
[ROW][C]24[/C][C]0.013655[/C][C]0.1049[/C][C]0.458411[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	-0.666209	-5.1172	2e-06
2	-0.442609	-3.3997	0.000607
3	0.121085	0.9301	0.178061
4	-0.322878	-2.4801	0.008005
5	-0.175677	-1.3494	0.091181
6	-0.209134	-1.6064	0.056764
7	0.212962	1.6358	0.053604
8	-0.248812	-1.9112	0.030423
9	-0.327699	-2.5171	0.007285
10	-0.08508	-0.6535	0.257982
11	-0.395262	-3.0361	0.001782
12	0.083299	0.6398	0.262379
13	0.024316	0.1868	0.42624
14	0.111387	0.8556	0.197846
15	-0.010828	-0.0832	0.466999
16	-0.067522	-0.5186	0.302973
17	0.058742	0.4512	0.326748
18	0.025333	0.1946	0.423193
19	-0.090044	-0.6916	0.245938
20	-0.171501	-1.3173	0.096411
21	0.017535	0.1347	0.446657
22	-0.107418	-0.8251	0.206321
23	-0.032141	-0.2469	0.402929
24	0.013655	0.1049	0.458411

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

Parameters (R input):

par1 = 24 ; 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)
x <- na.omit(x)
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