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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 15 Apr 2013 14:24:59 -0400

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/2013/Apr/15/t13660503138az46djj6hih56h.htm/, Retrieved Mon, 29 Apr 2024 10:42:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=208068, Retrieved Mon, 29 Apr 2024 10:42:51 +0000

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Estimated Impact

169

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

-       [(Partial) Autocorrelation Function] [] [2013-04-15 18:24:59] [bda1405f45fc71f9cfac8f9f3e5dea22] [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	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208068&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208068&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208068&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	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.009527	-0.0868	0.46552
2	-0.013526	-0.1232	0.451113
3	-0.00139	-0.0127	0.494962
4	-0.005301	-0.0483	0.480799
5	-0.014014	-0.1277	0.449357
6	-0.021405	-0.195	0.422932
7	0.007588	0.0691	0.472527
8	0.027214	0.2479	0.402402
9	-0.013132	-0.1196	0.45253
10	-0.011743	-0.107	0.457532
11	-0.019512	-0.1778	0.429673
12	-0.02035	-0.1854	0.426684
13	-0.019145	-0.1744	0.430981
14	-0.017188	-0.1566	0.437974
15	-0.007032	-0.0641	0.474536
16	-0.018288	-0.1666	0.434041
17	-0.020038	-0.1826	0.427797
18	-0.022634	-0.2062	0.418566
19	-0.012716	-0.1158	0.454026
20	-0.015762	-0.1436	0.443084
21	-0.003561	-0.0324	0.487099
22	-0.002633	-0.024	0.49046
23	-0.021747	-0.1981	0.421717
24	-0.019412	-0.1769	0.430028

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.009527 & -0.0868 & 0.46552 \tabularnewline
2 & -0.013526 & -0.1232 & 0.451113 \tabularnewline
3 & -0.00139 & -0.0127 & 0.494962 \tabularnewline
4 & -0.005301 & -0.0483 & 0.480799 \tabularnewline
5 & -0.014014 & -0.1277 & 0.449357 \tabularnewline
6 & -0.021405 & -0.195 & 0.422932 \tabularnewline
7 & 0.007588 & 0.0691 & 0.472527 \tabularnewline
8 & 0.027214 & 0.2479 & 0.402402 \tabularnewline
9 & -0.013132 & -0.1196 & 0.45253 \tabularnewline
10 & -0.011743 & -0.107 & 0.457532 \tabularnewline
11 & -0.019512 & -0.1778 & 0.429673 \tabularnewline
12 & -0.02035 & -0.1854 & 0.426684 \tabularnewline
13 & -0.019145 & -0.1744 & 0.430981 \tabularnewline
14 & -0.017188 & -0.1566 & 0.437974 \tabularnewline
15 & -0.007032 & -0.0641 & 0.474536 \tabularnewline
16 & -0.018288 & -0.1666 & 0.434041 \tabularnewline
17 & -0.020038 & -0.1826 & 0.427797 \tabularnewline
18 & -0.022634 & -0.2062 & 0.418566 \tabularnewline
19 & -0.012716 & -0.1158 & 0.454026 \tabularnewline
20 & -0.015762 & -0.1436 & 0.443084 \tabularnewline
21 & -0.003561 & -0.0324 & 0.487099 \tabularnewline
22 & -0.002633 & -0.024 & 0.49046 \tabularnewline
23 & -0.021747 & -0.1981 & 0.421717 \tabularnewline
24 & -0.019412 & -0.1769 & 0.430028 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208068&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]-0.009527[/C][C]-0.0868[/C][C]0.46552[/C][/ROW]
[ROW][C]2[/C][C]-0.013526[/C][C]-0.1232[/C][C]0.451113[/C][/ROW]
[ROW][C]3[/C][C]-0.00139[/C][C]-0.0127[/C][C]0.494962[/C][/ROW]
[ROW][C]4[/C][C]-0.005301[/C][C]-0.0483[/C][C]0.480799[/C][/ROW]
[ROW][C]5[/C][C]-0.014014[/C][C]-0.1277[/C][C]0.449357[/C][/ROW]
[ROW][C]6[/C][C]-0.021405[/C][C]-0.195[/C][C]0.422932[/C][/ROW]
[ROW][C]7[/C][C]0.007588[/C][C]0.0691[/C][C]0.472527[/C][/ROW]
[ROW][C]8[/C][C]0.027214[/C][C]0.2479[/C][C]0.402402[/C][/ROW]
[ROW][C]9[/C][C]-0.013132[/C][C]-0.1196[/C][C]0.45253[/C][/ROW]
[ROW][C]10[/C][C]-0.011743[/C][C]-0.107[/C][C]0.457532[/C][/ROW]
[ROW][C]11[/C][C]-0.019512[/C][C]-0.1778[/C][C]0.429673[/C][/ROW]
[ROW][C]12[/C][C]-0.02035[/C][C]-0.1854[/C][C]0.426684[/C][/ROW]
[ROW][C]13[/C][C]-0.019145[/C][C]-0.1744[/C][C]0.430981[/C][/ROW]
[ROW][C]14[/C][C]-0.017188[/C][C]-0.1566[/C][C]0.437974[/C][/ROW]
[ROW][C]15[/C][C]-0.007032[/C][C]-0.0641[/C][C]0.474536[/C][/ROW]
[ROW][C]16[/C][C]-0.018288[/C][C]-0.1666[/C][C]0.434041[/C][/ROW]
[ROW][C]17[/C][C]-0.020038[/C][C]-0.1826[/C][C]0.427797[/C][/ROW]
[ROW][C]18[/C][C]-0.022634[/C][C]-0.2062[/C][C]0.418566[/C][/ROW]
[ROW][C]19[/C][C]-0.012716[/C][C]-0.1158[/C][C]0.454026[/C][/ROW]
[ROW][C]20[/C][C]-0.015762[/C][C]-0.1436[/C][C]0.443084[/C][/ROW]
[ROW][C]21[/C][C]-0.003561[/C][C]-0.0324[/C][C]0.487099[/C][/ROW]
[ROW][C]22[/C][C]-0.002633[/C][C]-0.024[/C][C]0.49046[/C][/ROW]
[ROW][C]23[/C][C]-0.021747[/C][C]-0.1981[/C][C]0.421717[/C][/ROW]
[ROW][C]24[/C][C]-0.019412[/C][C]-0.1769[/C][C]0.430028[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208068&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208068&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	-0.009527	-0.0868	0.46552
2	-0.013526	-0.1232	0.451113
3	-0.00139	-0.0127	0.494962
4	-0.005301	-0.0483	0.480799
5	-0.014014	-0.1277	0.449357
6	-0.021405	-0.195	0.422932
7	0.007588	0.0691	0.472527
8	0.027214	0.2479	0.402402
9	-0.013132	-0.1196	0.45253
10	-0.011743	-0.107	0.457532
11	-0.019512	-0.1778	0.429673
12	-0.02035	-0.1854	0.426684
13	-0.019145	-0.1744	0.430981
14	-0.017188	-0.1566	0.437974
15	-0.007032	-0.0641	0.474536
16	-0.018288	-0.1666	0.434041
17	-0.020038	-0.1826	0.427797
18	-0.022634	-0.2062	0.418566
19	-0.012716	-0.1158	0.454026
20	-0.015762	-0.1436	0.443084
21	-0.003561	-0.0324	0.487099
22	-0.002633	-0.024	0.49046
23	-0.021747	-0.1981	0.421717
24	-0.019412	-0.1769	0.430028

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.009527	-0.0868	0.46552
2	-0.013618	-0.1241	0.450782
3	-0.001651	-0.015	0.494017
4	-0.005516	-0.0503	0.48002
5	-0.014165	-0.129	0.448817
6	-0.02184	-0.199	0.421386
7	0.006763	0.0616	0.475507
8	0.026714	0.2434	0.404158
9	-0.012648	-0.1152	0.454271
10	-0.011716	-0.1067	0.457626
11	-0.020566	-0.1874	0.425914
12	-0.021098	-0.1922	0.424023
13	-0.019257	-0.1754	0.430579
14	-0.01766	-0.1609	0.436286
15	-0.009536	-0.0869	0.465489
16	-0.020948	-0.1908	0.424555
17	-0.021698	-0.1977	0.421891
18	-0.024753	-0.2255	0.41107
19	-0.014468	-0.1318	0.447727
20	-0.017579	-0.1602	0.436574
21	-0.005594	-0.051	0.47974
22	-0.005621	-0.0512	0.479642
23	-0.025221	-0.2298	0.409416
24	-0.022698	-0.2068	0.418339

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.009527 & -0.0868 & 0.46552 \tabularnewline
2 & -0.013618 & -0.1241 & 0.450782 \tabularnewline
3 & -0.001651 & -0.015 & 0.494017 \tabularnewline
4 & -0.005516 & -0.0503 & 0.48002 \tabularnewline
5 & -0.014165 & -0.129 & 0.448817 \tabularnewline
6 & -0.02184 & -0.199 & 0.421386 \tabularnewline
7 & 0.006763 & 0.0616 & 0.475507 \tabularnewline
8 & 0.026714 & 0.2434 & 0.404158 \tabularnewline
9 & -0.012648 & -0.1152 & 0.454271 \tabularnewline
10 & -0.011716 & -0.1067 & 0.457626 \tabularnewline
11 & -0.020566 & -0.1874 & 0.425914 \tabularnewline
12 & -0.021098 & -0.1922 & 0.424023 \tabularnewline
13 & -0.019257 & -0.1754 & 0.430579 \tabularnewline
14 & -0.01766 & -0.1609 & 0.436286 \tabularnewline
15 & -0.009536 & -0.0869 & 0.465489 \tabularnewline
16 & -0.020948 & -0.1908 & 0.424555 \tabularnewline
17 & -0.021698 & -0.1977 & 0.421891 \tabularnewline
18 & -0.024753 & -0.2255 & 0.41107 \tabularnewline
19 & -0.014468 & -0.1318 & 0.447727 \tabularnewline
20 & -0.017579 & -0.1602 & 0.436574 \tabularnewline
21 & -0.005594 & -0.051 & 0.47974 \tabularnewline
22 & -0.005621 & -0.0512 & 0.479642 \tabularnewline
23 & -0.025221 & -0.2298 & 0.409416 \tabularnewline
24 & -0.022698 & -0.2068 & 0.418339 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208068&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]-0.009527[/C][C]-0.0868[/C][C]0.46552[/C][/ROW]
[ROW][C]2[/C][C]-0.013618[/C][C]-0.1241[/C][C]0.450782[/C][/ROW]
[ROW][C]3[/C][C]-0.001651[/C][C]-0.015[/C][C]0.494017[/C][/ROW]
[ROW][C]4[/C][C]-0.005516[/C][C]-0.0503[/C][C]0.48002[/C][/ROW]
[ROW][C]5[/C][C]-0.014165[/C][C]-0.129[/C][C]0.448817[/C][/ROW]
[ROW][C]6[/C][C]-0.02184[/C][C]-0.199[/C][C]0.421386[/C][/ROW]
[ROW][C]7[/C][C]0.006763[/C][C]0.0616[/C][C]0.475507[/C][/ROW]
[ROW][C]8[/C][C]0.026714[/C][C]0.2434[/C][C]0.404158[/C][/ROW]
[ROW][C]9[/C][C]-0.012648[/C][C]-0.1152[/C][C]0.454271[/C][/ROW]
[ROW][C]10[/C][C]-0.011716[/C][C]-0.1067[/C][C]0.457626[/C][/ROW]
[ROW][C]11[/C][C]-0.020566[/C][C]-0.1874[/C][C]0.425914[/C][/ROW]
[ROW][C]12[/C][C]-0.021098[/C][C]-0.1922[/C][C]0.424023[/C][/ROW]
[ROW][C]13[/C][C]-0.019257[/C][C]-0.1754[/C][C]0.430579[/C][/ROW]
[ROW][C]14[/C][C]-0.01766[/C][C]-0.1609[/C][C]0.436286[/C][/ROW]
[ROW][C]15[/C][C]-0.009536[/C][C]-0.0869[/C][C]0.465489[/C][/ROW]
[ROW][C]16[/C][C]-0.020948[/C][C]-0.1908[/C][C]0.424555[/C][/ROW]
[ROW][C]17[/C][C]-0.021698[/C][C]-0.1977[/C][C]0.421891[/C][/ROW]
[ROW][C]18[/C][C]-0.024753[/C][C]-0.2255[/C][C]0.41107[/C][/ROW]
[ROW][C]19[/C][C]-0.014468[/C][C]-0.1318[/C][C]0.447727[/C][/ROW]
[ROW][C]20[/C][C]-0.017579[/C][C]-0.1602[/C][C]0.436574[/C][/ROW]
[ROW][C]21[/C][C]-0.005594[/C][C]-0.051[/C][C]0.47974[/C][/ROW]
[ROW][C]22[/C][C]-0.005621[/C][C]-0.0512[/C][C]0.479642[/C][/ROW]
[ROW][C]23[/C][C]-0.025221[/C][C]-0.2298[/C][C]0.409416[/C][/ROW]
[ROW][C]24[/C][C]-0.022698[/C][C]-0.2068[/C][C]0.418339[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208068&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208068&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	-0.009527	-0.0868	0.46552
2	-0.013618	-0.1241	0.450782
3	-0.001651	-0.015	0.494017
4	-0.005516	-0.0503	0.48002
5	-0.014165	-0.129	0.448817
6	-0.02184	-0.199	0.421386
7	0.006763	0.0616	0.475507
8	0.026714	0.2434	0.404158
9	-0.012648	-0.1152	0.454271
10	-0.011716	-0.1067	0.457626
11	-0.020566	-0.1874	0.425914
12	-0.021098	-0.1922	0.424023
13	-0.019257	-0.1754	0.430579
14	-0.01766	-0.1609	0.436286
15	-0.009536	-0.0869	0.465489
16	-0.020948	-0.1908	0.424555
17	-0.021698	-0.1977	0.421891
18	-0.024753	-0.2255	0.41107
19	-0.014468	-0.1318	0.447727
20	-0.017579	-0.1602	0.436574
21	-0.005594	-0.051	0.47974
22	-0.005621	-0.0512	0.479642
23	-0.025221	-0.2298	0.409416
24	-0.022698	-0.2068	0.418339

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)
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