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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 14 Jan 2015 15:58:45 +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/2015/Jan/14/t1421251236yfqppjv7upwmg6z.htm/, Retrieved Fri, 31 May 2024 11:24:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=272372, Retrieved Fri, 31 May 2024 11:24:10 +0000

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User-defined keywords

Estimated Impact

108

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

-     [Univariate Data Series] [] [2008-12-14 11:54:22] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [Variance Reduction Matrix] [] [2011-12-06 20:14:08] [b98453cac15ba1066b407e146608df68]
- RMP       [(Partial) Autocorrelation Function] [] [2015-01-14 15:58:45] [c1a39181a3b44a9ce4729a0a50ab187e] [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=272372&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=272372&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=272372&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	0.000789	0.0061	0.497572
2	0.022785	0.1765	0.430251
3	-0.09981	-0.7731	0.221242
4	-0.06262	-0.4851	0.314702
5	-0.107815	-0.8351	0.203478
6	-0.038152	-0.2955	0.384308
7	0.03004	0.2327	0.408398
8	0.042367	0.3282	0.371962
9	-0.02141	-0.1658	0.43442
10	0.073888	0.5723	0.284616
11	0.167872	1.3003	0.099231
12	-0.379446	-2.9392	0.002333
13	-0.107581	-0.8333	0.203986
14	-0.011117	-0.0861	0.465831
15	0.013853	0.1073	0.457453
16	-0.010529	-0.0816	0.467635
17	-0.035094	-0.2718	0.393342
18	0.036891	0.2858	0.388026

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.000789 & 0.0061 & 0.497572 \tabularnewline
2 & 0.022785 & 0.1765 & 0.430251 \tabularnewline
3 & -0.09981 & -0.7731 & 0.221242 \tabularnewline
4 & -0.06262 & -0.4851 & 0.314702 \tabularnewline
5 & -0.107815 & -0.8351 & 0.203478 \tabularnewline
6 & -0.038152 & -0.2955 & 0.384308 \tabularnewline
7 & 0.03004 & 0.2327 & 0.408398 \tabularnewline
8 & 0.042367 & 0.3282 & 0.371962 \tabularnewline
9 & -0.02141 & -0.1658 & 0.43442 \tabularnewline
10 & 0.073888 & 0.5723 & 0.284616 \tabularnewline
11 & 0.167872 & 1.3003 & 0.099231 \tabularnewline
12 & -0.379446 & -2.9392 & 0.002333 \tabularnewline
13 & -0.107581 & -0.8333 & 0.203986 \tabularnewline
14 & -0.011117 & -0.0861 & 0.465831 \tabularnewline
15 & 0.013853 & 0.1073 & 0.457453 \tabularnewline
16 & -0.010529 & -0.0816 & 0.467635 \tabularnewline
17 & -0.035094 & -0.2718 & 0.393342 \tabularnewline
18 & 0.036891 & 0.2858 & 0.388026 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=272372&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]0.000789[/C][C]0.0061[/C][C]0.497572[/C][/ROW]
[ROW][C]2[/C][C]0.022785[/C][C]0.1765[/C][C]0.430251[/C][/ROW]
[ROW][C]3[/C][C]-0.09981[/C][C]-0.7731[/C][C]0.221242[/C][/ROW]
[ROW][C]4[/C][C]-0.06262[/C][C]-0.4851[/C][C]0.314702[/C][/ROW]
[ROW][C]5[/C][C]-0.107815[/C][C]-0.8351[/C][C]0.203478[/C][/ROW]
[ROW][C]6[/C][C]-0.038152[/C][C]-0.2955[/C][C]0.384308[/C][/ROW]
[ROW][C]7[/C][C]0.03004[/C][C]0.2327[/C][C]0.408398[/C][/ROW]
[ROW][C]8[/C][C]0.042367[/C][C]0.3282[/C][C]0.371962[/C][/ROW]
[ROW][C]9[/C][C]-0.02141[/C][C]-0.1658[/C][C]0.43442[/C][/ROW]
[ROW][C]10[/C][C]0.073888[/C][C]0.5723[/C][C]0.284616[/C][/ROW]
[ROW][C]11[/C][C]0.167872[/C][C]1.3003[/C][C]0.099231[/C][/ROW]
[ROW][C]12[/C][C]-0.379446[/C][C]-2.9392[/C][C]0.002333[/C][/ROW]
[ROW][C]13[/C][C]-0.107581[/C][C]-0.8333[/C][C]0.203986[/C][/ROW]
[ROW][C]14[/C][C]-0.011117[/C][C]-0.0861[/C][C]0.465831[/C][/ROW]
[ROW][C]15[/C][C]0.013853[/C][C]0.1073[/C][C]0.457453[/C][/ROW]
[ROW][C]16[/C][C]-0.010529[/C][C]-0.0816[/C][C]0.467635[/C][/ROW]
[ROW][C]17[/C][C]-0.035094[/C][C]-0.2718[/C][C]0.393342[/C][/ROW]
[ROW][C]18[/C][C]0.036891[/C][C]0.2858[/C][C]0.388026[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=272372&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=272372&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	0.000789	0.0061	0.497572
2	0.022785	0.1765	0.430251
3	-0.09981	-0.7731	0.221242
4	-0.06262	-0.4851	0.314702
5	-0.107815	-0.8351	0.203478
6	-0.038152	-0.2955	0.384308
7	0.03004	0.2327	0.408398
8	0.042367	0.3282	0.371962
9	-0.02141	-0.1658	0.43442
10	0.073888	0.5723	0.284616
11	0.167872	1.3003	0.099231
12	-0.379446	-2.9392	0.002333
13	-0.107581	-0.8333	0.203986
14	-0.011117	-0.0861	0.465831
15	0.013853	0.1073	0.457453
16	-0.010529	-0.0816	0.467635
17	-0.035094	-0.2718	0.393342
18	0.036891	0.2858	0.388026

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.000789	0.0061	0.497572
2	0.022784	0.1765	0.430253
3	-0.099897	-0.7738	0.221043
4	-0.063424	-0.4913	0.312511
5	-0.10479	-0.8117	0.210087
6	-0.047724	-0.3697	0.356467
7	0.020977	0.1625	0.435735
8	0.019718	0.1527	0.43956
9	-0.044416	-0.344	0.366006
10	0.0625	0.4841	0.31503
11	0.176663	1.3684	0.088141
12	-0.400705	-3.1038	0.001457
13	-0.108209	-0.8382	0.202628
14	0.075422	0.5842	0.280633
15	-0.041636	-0.3225	0.374093
16	-0.060471	-0.4684	0.320596
17	-0.120973	-0.9371	0.176244
18	-0.020985	-0.1625	0.43571

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.000789 & 0.0061 & 0.497572 \tabularnewline
2 & 0.022784 & 0.1765 & 0.430253 \tabularnewline
3 & -0.099897 & -0.7738 & 0.221043 \tabularnewline
4 & -0.063424 & -0.4913 & 0.312511 \tabularnewline
5 & -0.10479 & -0.8117 & 0.210087 \tabularnewline
6 & -0.047724 & -0.3697 & 0.356467 \tabularnewline
7 & 0.020977 & 0.1625 & 0.435735 \tabularnewline
8 & 0.019718 & 0.1527 & 0.43956 \tabularnewline
9 & -0.044416 & -0.344 & 0.366006 \tabularnewline
10 & 0.0625 & 0.4841 & 0.31503 \tabularnewline
11 & 0.176663 & 1.3684 & 0.088141 \tabularnewline
12 & -0.400705 & -3.1038 & 0.001457 \tabularnewline
13 & -0.108209 & -0.8382 & 0.202628 \tabularnewline
14 & 0.075422 & 0.5842 & 0.280633 \tabularnewline
15 & -0.041636 & -0.3225 & 0.374093 \tabularnewline
16 & -0.060471 & -0.4684 & 0.320596 \tabularnewline
17 & -0.120973 & -0.9371 & 0.176244 \tabularnewline
18 & -0.020985 & -0.1625 & 0.43571 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=272372&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]0.000789[/C][C]0.0061[/C][C]0.497572[/C][/ROW]
[ROW][C]2[/C][C]0.022784[/C][C]0.1765[/C][C]0.430253[/C][/ROW]
[ROW][C]3[/C][C]-0.099897[/C][C]-0.7738[/C][C]0.221043[/C][/ROW]
[ROW][C]4[/C][C]-0.063424[/C][C]-0.4913[/C][C]0.312511[/C][/ROW]
[ROW][C]5[/C][C]-0.10479[/C][C]-0.8117[/C][C]0.210087[/C][/ROW]
[ROW][C]6[/C][C]-0.047724[/C][C]-0.3697[/C][C]0.356467[/C][/ROW]
[ROW][C]7[/C][C]0.020977[/C][C]0.1625[/C][C]0.435735[/C][/ROW]
[ROW][C]8[/C][C]0.019718[/C][C]0.1527[/C][C]0.43956[/C][/ROW]
[ROW][C]9[/C][C]-0.044416[/C][C]-0.344[/C][C]0.366006[/C][/ROW]
[ROW][C]10[/C][C]0.0625[/C][C]0.4841[/C][C]0.31503[/C][/ROW]
[ROW][C]11[/C][C]0.176663[/C][C]1.3684[/C][C]0.088141[/C][/ROW]
[ROW][C]12[/C][C]-0.400705[/C][C]-3.1038[/C][C]0.001457[/C][/ROW]
[ROW][C]13[/C][C]-0.108209[/C][C]-0.8382[/C][C]0.202628[/C][/ROW]
[ROW][C]14[/C][C]0.075422[/C][C]0.5842[/C][C]0.280633[/C][/ROW]
[ROW][C]15[/C][C]-0.041636[/C][C]-0.3225[/C][C]0.374093[/C][/ROW]
[ROW][C]16[/C][C]-0.060471[/C][C]-0.4684[/C][C]0.320596[/C][/ROW]
[ROW][C]17[/C][C]-0.120973[/C][C]-0.9371[/C][C]0.176244[/C][/ROW]
[ROW][C]18[/C][C]-0.020985[/C][C]-0.1625[/C][C]0.43571[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=272372&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=272372&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	0.000789	0.0061	0.497572
2	0.022784	0.1765	0.430253
3	-0.099897	-0.7738	0.221043
4	-0.063424	-0.4913	0.312511
5	-0.10479	-0.8117	0.210087
6	-0.047724	-0.3697	0.356467
7	0.020977	0.1625	0.435735
8	0.019718	0.1527	0.43956
9	-0.044416	-0.344	0.366006
10	0.0625	0.4841	0.31503
11	0.176663	1.3684	0.088141
12	-0.400705	-3.1038	0.001457
13	-0.108209	-0.8382	0.202628
14	0.075422	0.5842	0.280633
15	-0.041636	-0.3225	0.374093
16	-0.060471	-0.4684	0.320596
17	-0.120973	-0.9371	0.176244
18	-0.020985	-0.1625	0.43571

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 = 1.4 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1.4 ; par3 = 0 ; par4 = 1 ; 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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code