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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 16 May 2013 17:56:34 -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/May/16/t1368741414xj2lg394j52yisu.htm/, Retrieved Mon, 29 Apr 2024 04:57:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=209004, Retrieved Mon, 29 Apr 2024 04:57:00 +0000

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Estimated Impact

145

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-       [(Partial) Autocorrelation Function] [] [2013-05-16 21:56:34] [16412acc5f1d1890f88c1afdf63f71fe] [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=209004&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=209004&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209004&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	-0.355143	-2.9925	0.001902
2	0.109622	0.9237	0.179388
3	0.031316	0.2639	0.396321
4	-0.208281	-1.755	0.041786
5	0.139571	1.176	0.121752
6	-0.141349	-1.191	0.118805
7	-0.013559	-0.1142	0.454681
8	-0.035105	-0.2958	0.384123
9	-0.047769	-0.4025	0.344258
10	0.086286	0.7271	0.23479
11	-0.080946	-0.6821	0.248709
12	0.139352	1.1742	0.12212
13	0.033597	0.2831	0.388965
14	-0.086298	-0.7272	0.23476
15	-0.015828	-0.1334	0.447138
16	-0.123148	-1.0377	0.151474
17	0.023304	0.1964	0.422443
18	0.08257	0.6957	0.24443

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.355143 & -2.9925 & 0.001902 \tabularnewline
2 & 0.109622 & 0.9237 & 0.179388 \tabularnewline
3 & 0.031316 & 0.2639 & 0.396321 \tabularnewline
4 & -0.208281 & -1.755 & 0.041786 \tabularnewline
5 & 0.139571 & 1.176 & 0.121752 \tabularnewline
6 & -0.141349 & -1.191 & 0.118805 \tabularnewline
7 & -0.013559 & -0.1142 & 0.454681 \tabularnewline
8 & -0.035105 & -0.2958 & 0.384123 \tabularnewline
9 & -0.047769 & -0.4025 & 0.344258 \tabularnewline
10 & 0.086286 & 0.7271 & 0.23479 \tabularnewline
11 & -0.080946 & -0.6821 & 0.248709 \tabularnewline
12 & 0.139352 & 1.1742 & 0.12212 \tabularnewline
13 & 0.033597 & 0.2831 & 0.388965 \tabularnewline
14 & -0.086298 & -0.7272 & 0.23476 \tabularnewline
15 & -0.015828 & -0.1334 & 0.447138 \tabularnewline
16 & -0.123148 & -1.0377 & 0.151474 \tabularnewline
17 & 0.023304 & 0.1964 & 0.422443 \tabularnewline
18 & 0.08257 & 0.6957 & 0.24443 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209004&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]-0.355143[/C][C]-2.9925[/C][C]0.001902[/C][/ROW]
[ROW][C]2[/C][C]0.109622[/C][C]0.9237[/C][C]0.179388[/C][/ROW]
[ROW][C]3[/C][C]0.031316[/C][C]0.2639[/C][C]0.396321[/C][/ROW]
[ROW][C]4[/C][C]-0.208281[/C][C]-1.755[/C][C]0.041786[/C][/ROW]
[ROW][C]5[/C][C]0.139571[/C][C]1.176[/C][C]0.121752[/C][/ROW]
[ROW][C]6[/C][C]-0.141349[/C][C]-1.191[/C][C]0.118805[/C][/ROW]
[ROW][C]7[/C][C]-0.013559[/C][C]-0.1142[/C][C]0.454681[/C][/ROW]
[ROW][C]8[/C][C]-0.035105[/C][C]-0.2958[/C][C]0.384123[/C][/ROW]
[ROW][C]9[/C][C]-0.047769[/C][C]-0.4025[/C][C]0.344258[/C][/ROW]
[ROW][C]10[/C][C]0.086286[/C][C]0.7271[/C][C]0.23479[/C][/ROW]
[ROW][C]11[/C][C]-0.080946[/C][C]-0.6821[/C][C]0.248709[/C][/ROW]
[ROW][C]12[/C][C]0.139352[/C][C]1.1742[/C][C]0.12212[/C][/ROW]
[ROW][C]13[/C][C]0.033597[/C][C]0.2831[/C][C]0.388965[/C][/ROW]
[ROW][C]14[/C][C]-0.086298[/C][C]-0.7272[/C][C]0.23476[/C][/ROW]
[ROW][C]15[/C][C]-0.015828[/C][C]-0.1334[/C][C]0.447138[/C][/ROW]
[ROW][C]16[/C][C]-0.123148[/C][C]-1.0377[/C][C]0.151474[/C][/ROW]
[ROW][C]17[/C][C]0.023304[/C][C]0.1964[/C][C]0.422443[/C][/ROW]
[ROW][C]18[/C][C]0.08257[/C][C]0.6957[/C][C]0.24443[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209004&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209004&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	-0.355143	-2.9925	0.001902
2	0.109622	0.9237	0.179388
3	0.031316	0.2639	0.396321
4	-0.208281	-1.755	0.041786
5	0.139571	1.176	0.121752
6	-0.141349	-1.191	0.118805
7	-0.013559	-0.1142	0.454681
8	-0.035105	-0.2958	0.384123
9	-0.047769	-0.4025	0.344258
10	0.086286	0.7271	0.23479
11	-0.080946	-0.6821	0.248709
12	0.139352	1.1742	0.12212
13	0.033597	0.2831	0.388965
14	-0.086298	-0.7272	0.23476
15	-0.015828	-0.1334	0.447138
16	-0.123148	-1.0377	0.151474
17	0.023304	0.1964	0.422443
18	0.08257	0.6957	0.24443

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.355143	-2.9925	0.001902
2	-0.018886	-0.1591	0.437006
3	0.073579	0.62	0.268627
4	-0.197633	-1.6653	0.050131
5	-0.003847	-0.0324	0.487115
6	-0.084635	-0.7131	0.239046
7	-0.097995	-0.8257	0.205864
8	-0.123101	-1.0373	0.151566
9	-0.080246	-0.6762	0.250566
10	0.011994	0.1011	0.459893
11	-0.071786	-0.6049	0.273593
12	0.066176	0.5576	0.289432
13	0.102695	0.8653	0.194889
14	-0.059709	-0.5031	0.308219
15	-0.147349	-1.2416	0.109239
16	-0.159576	-1.3446	0.091515
17	-0.073885	-0.6226	0.267781
18	0.076845	0.6475	0.259696

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.355143 & -2.9925 & 0.001902 \tabularnewline
2 & -0.018886 & -0.1591 & 0.437006 \tabularnewline
3 & 0.073579 & 0.62 & 0.268627 \tabularnewline
4 & -0.197633 & -1.6653 & 0.050131 \tabularnewline
5 & -0.003847 & -0.0324 & 0.487115 \tabularnewline
6 & -0.084635 & -0.7131 & 0.239046 \tabularnewline
7 & -0.097995 & -0.8257 & 0.205864 \tabularnewline
8 & -0.123101 & -1.0373 & 0.151566 \tabularnewline
9 & -0.080246 & -0.6762 & 0.250566 \tabularnewline
10 & 0.011994 & 0.1011 & 0.459893 \tabularnewline
11 & -0.071786 & -0.6049 & 0.273593 \tabularnewline
12 & 0.066176 & 0.5576 & 0.289432 \tabularnewline
13 & 0.102695 & 0.8653 & 0.194889 \tabularnewline
14 & -0.059709 & -0.5031 & 0.308219 \tabularnewline
15 & -0.147349 & -1.2416 & 0.109239 \tabularnewline
16 & -0.159576 & -1.3446 & 0.091515 \tabularnewline
17 & -0.073885 & -0.6226 & 0.267781 \tabularnewline
18 & 0.076845 & 0.6475 & 0.259696 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209004&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]-0.355143[/C][C]-2.9925[/C][C]0.001902[/C][/ROW]
[ROW][C]2[/C][C]-0.018886[/C][C]-0.1591[/C][C]0.437006[/C][/ROW]
[ROW][C]3[/C][C]0.073579[/C][C]0.62[/C][C]0.268627[/C][/ROW]
[ROW][C]4[/C][C]-0.197633[/C][C]-1.6653[/C][C]0.050131[/C][/ROW]
[ROW][C]5[/C][C]-0.003847[/C][C]-0.0324[/C][C]0.487115[/C][/ROW]
[ROW][C]6[/C][C]-0.084635[/C][C]-0.7131[/C][C]0.239046[/C][/ROW]
[ROW][C]7[/C][C]-0.097995[/C][C]-0.8257[/C][C]0.205864[/C][/ROW]
[ROW][C]8[/C][C]-0.123101[/C][C]-1.0373[/C][C]0.151566[/C][/ROW]
[ROW][C]9[/C][C]-0.080246[/C][C]-0.6762[/C][C]0.250566[/C][/ROW]
[ROW][C]10[/C][C]0.011994[/C][C]0.1011[/C][C]0.459893[/C][/ROW]
[ROW][C]11[/C][C]-0.071786[/C][C]-0.6049[/C][C]0.273593[/C][/ROW]
[ROW][C]12[/C][C]0.066176[/C][C]0.5576[/C][C]0.289432[/C][/ROW]
[ROW][C]13[/C][C]0.102695[/C][C]0.8653[/C][C]0.194889[/C][/ROW]
[ROW][C]14[/C][C]-0.059709[/C][C]-0.5031[/C][C]0.308219[/C][/ROW]
[ROW][C]15[/C][C]-0.147349[/C][C]-1.2416[/C][C]0.109239[/C][/ROW]
[ROW][C]16[/C][C]-0.159576[/C][C]-1.3446[/C][C]0.091515[/C][/ROW]
[ROW][C]17[/C][C]-0.073885[/C][C]-0.6226[/C][C]0.267781[/C][/ROW]
[ROW][C]18[/C][C]0.076845[/C][C]0.6475[/C][C]0.259696[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209004&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209004&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	-0.355143	-2.9925	0.001902
2	-0.018886	-0.1591	0.437006
3	0.073579	0.62	0.268627
4	-0.197633	-1.6653	0.050131
5	-0.003847	-0.0324	0.487115
6	-0.084635	-0.7131	0.239046
7	-0.097995	-0.8257	0.205864
8	-0.123101	-1.0373	0.151566
9	-0.080246	-0.6762	0.250566
10	0.011994	0.1011	0.459893
11	-0.071786	-0.6049	0.273593
12	0.066176	0.5576	0.289432
13	0.102695	0.8653	0.194889
14	-0.059709	-0.5031	0.308219
15	-0.147349	-1.2416	0.109239
16	-0.159576	-1.3446	0.091515
17	-0.073885	-0.6226	0.267781
18	0.076845	0.6475	0.259696

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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code