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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 29 May 2016 22:34:06 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/May/29/t1464557743thg6fceqfsq4kra.htm/, Retrieved Sun, 28 Apr 2024 13:57:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295695, Retrieved Sun, 28 Apr 2024 13:57:05 +0000

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student

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-       [(Partial) Autocorrelation Function] [] [2016-05-29 21:34:06] [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	'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295695&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295695&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295695&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.910112	7.56	0
2	0.84065	6.983	0
3	0.778747	6.4688	0
4	0.722155	5.9987	0
5	0.670876	5.5727	0
6	0.617351	5.1281	1e-06
7	0.550956	4.5766	1e-05
8	0.495898	4.1192	5.2e-05
9	0.424192	3.5236	0.00038
10	0.35024	2.9093	0.002435
11	0.267197	2.2195	0.014871
12	0.187933	1.5611	0.061539
13	0.136653	1.1351	0.130125
14	0.081595	0.6778	0.250089
15	0.034094	0.2832	0.388932
16	-0.028521	-0.2369	0.406712
17	-0.094916	-0.7884	0.216573
18	-0.146195	-1.2144	0.11437

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.910112 & 7.56 & 0 \tabularnewline
2 & 0.84065 & 6.983 & 0 \tabularnewline
3 & 0.778747 & 6.4688 & 0 \tabularnewline
4 & 0.722155 & 5.9987 & 0 \tabularnewline
5 & 0.670876 & 5.5727 & 0 \tabularnewline
6 & 0.617351 & 5.1281 & 1e-06 \tabularnewline
7 & 0.550956 & 4.5766 & 1e-05 \tabularnewline
8 & 0.495898 & 4.1192 & 5.2e-05 \tabularnewline
9 & 0.424192 & 3.5236 & 0.00038 \tabularnewline
10 & 0.35024 & 2.9093 & 0.002435 \tabularnewline
11 & 0.267197 & 2.2195 & 0.014871 \tabularnewline
12 & 0.187933 & 1.5611 & 0.061539 \tabularnewline
13 & 0.136653 & 1.1351 & 0.130125 \tabularnewline
14 & 0.081595 & 0.6778 & 0.250089 \tabularnewline
15 & 0.034094 & 0.2832 & 0.388932 \tabularnewline
16 & -0.028521 & -0.2369 & 0.406712 \tabularnewline
17 & -0.094916 & -0.7884 & 0.216573 \tabularnewline
18 & -0.146195 & -1.2144 & 0.11437 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295695&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]0.910112[/C][C]7.56[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.84065[/C][C]6.983[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.778747[/C][C]6.4688[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.722155[/C][C]5.9987[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.670876[/C][C]5.5727[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.617351[/C][C]5.1281[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.550956[/C][C]4.5766[/C][C]1e-05[/C][/ROW]
[ROW][C]8[/C][C]0.495898[/C][C]4.1192[/C][C]5.2e-05[/C][/ROW]
[ROW][C]9[/C][C]0.424192[/C][C]3.5236[/C][C]0.00038[/C][/ROW]
[ROW][C]10[/C][C]0.35024[/C][C]2.9093[/C][C]0.002435[/C][/ROW]
[ROW][C]11[/C][C]0.267197[/C][C]2.2195[/C][C]0.014871[/C][/ROW]
[ROW][C]12[/C][C]0.187933[/C][C]1.5611[/C][C]0.061539[/C][/ROW]
[ROW][C]13[/C][C]0.136653[/C][C]1.1351[/C][C]0.130125[/C][/ROW]
[ROW][C]14[/C][C]0.081595[/C][C]0.6778[/C][C]0.250089[/C][/ROW]
[ROW][C]15[/C][C]0.034094[/C][C]0.2832[/C][C]0.388932[/C][/ROW]
[ROW][C]16[/C][C]-0.028521[/C][C]-0.2369[/C][C]0.406712[/C][/ROW]
[ROW][C]17[/C][C]-0.094916[/C][C]-0.7884[/C][C]0.216573[/C][/ROW]
[ROW][C]18[/C][C]-0.146195[/C][C]-1.2144[/C][C]0.11437[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295695&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295695&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	0.910112	7.56	0
2	0.84065	6.983	0
3	0.778747	6.4688	0
4	0.722155	5.9987	0
5	0.670876	5.5727	0
6	0.617351	5.1281	1e-06
7	0.550956	4.5766	1e-05
8	0.495898	4.1192	5.2e-05
9	0.424192	3.5236	0.00038
10	0.35024	2.9093	0.002435
11	0.267197	2.2195	0.014871
12	0.187933	1.5611	0.061539
13	0.136653	1.1351	0.130125
14	0.081595	0.6778	0.250089
15	0.034094	0.2832	0.388932
16	-0.028521	-0.2369	0.406712
17	-0.094916	-0.7884	0.216573
18	-0.146195	-1.2144	0.11437

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.910112	7.56	0
2	0.071913	0.5974	0.276113
3	0.01892	0.1572	0.437788
4	0.007015	0.0583	0.476851
5	0.008251	0.0685	0.472777
6	-0.032983	-0.274	0.39246
7	-0.105662	-0.8777	0.191579
8	0.010273	0.0853	0.466122
9	-0.129733	-1.0776	0.142473
10	-0.084004	-0.6978	0.243827
11	-0.126071	-1.0472	0.149325
12	-0.062955	-0.5229	0.301344
13	0.094708	0.7867	0.217075
14	-0.046515	-0.3864	0.350202
15	0.023998	0.1993	0.42129
16	-0.122046	-1.0138	0.157113
17	-0.074016	-0.6148	0.270348
18	0.009594	0.0797	0.468355

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.910112 & 7.56 & 0 \tabularnewline
2 & 0.071913 & 0.5974 & 0.276113 \tabularnewline
3 & 0.01892 & 0.1572 & 0.437788 \tabularnewline
4 & 0.007015 & 0.0583 & 0.476851 \tabularnewline
5 & 0.008251 & 0.0685 & 0.472777 \tabularnewline
6 & -0.032983 & -0.274 & 0.39246 \tabularnewline
7 & -0.105662 & -0.8777 & 0.191579 \tabularnewline
8 & 0.010273 & 0.0853 & 0.466122 \tabularnewline
9 & -0.129733 & -1.0776 & 0.142473 \tabularnewline
10 & -0.084004 & -0.6978 & 0.243827 \tabularnewline
11 & -0.126071 & -1.0472 & 0.149325 \tabularnewline
12 & -0.062955 & -0.5229 & 0.301344 \tabularnewline
13 & 0.094708 & 0.7867 & 0.217075 \tabularnewline
14 & -0.046515 & -0.3864 & 0.350202 \tabularnewline
15 & 0.023998 & 0.1993 & 0.42129 \tabularnewline
16 & -0.122046 & -1.0138 & 0.157113 \tabularnewline
17 & -0.074016 & -0.6148 & 0.270348 \tabularnewline
18 & 0.009594 & 0.0797 & 0.468355 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295695&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]0.910112[/C][C]7.56[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.071913[/C][C]0.5974[/C][C]0.276113[/C][/ROW]
[ROW][C]3[/C][C]0.01892[/C][C]0.1572[/C][C]0.437788[/C][/ROW]
[ROW][C]4[/C][C]0.007015[/C][C]0.0583[/C][C]0.476851[/C][/ROW]
[ROW][C]5[/C][C]0.008251[/C][C]0.0685[/C][C]0.472777[/C][/ROW]
[ROW][C]6[/C][C]-0.032983[/C][C]-0.274[/C][C]0.39246[/C][/ROW]
[ROW][C]7[/C][C]-0.105662[/C][C]-0.8777[/C][C]0.191579[/C][/ROW]
[ROW][C]8[/C][C]0.010273[/C][C]0.0853[/C][C]0.466122[/C][/ROW]
[ROW][C]9[/C][C]-0.129733[/C][C]-1.0776[/C][C]0.142473[/C][/ROW]
[ROW][C]10[/C][C]-0.084004[/C][C]-0.6978[/C][C]0.243827[/C][/ROW]
[ROW][C]11[/C][C]-0.126071[/C][C]-1.0472[/C][C]0.149325[/C][/ROW]
[ROW][C]12[/C][C]-0.062955[/C][C]-0.5229[/C][C]0.301344[/C][/ROW]
[ROW][C]13[/C][C]0.094708[/C][C]0.7867[/C][C]0.217075[/C][/ROW]
[ROW][C]14[/C][C]-0.046515[/C][C]-0.3864[/C][C]0.350202[/C][/ROW]
[ROW][C]15[/C][C]0.023998[/C][C]0.1993[/C][C]0.42129[/C][/ROW]
[ROW][C]16[/C][C]-0.122046[/C][C]-1.0138[/C][C]0.157113[/C][/ROW]
[ROW][C]17[/C][C]-0.074016[/C][C]-0.6148[/C][C]0.270348[/C][/ROW]
[ROW][C]18[/C][C]0.009594[/C][C]0.0797[/C][C]0.468355[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295695&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295695&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	0.910112	7.56	0
2	0.071913	0.5974	0.276113
3	0.01892	0.1572	0.437788
4	0.007015	0.0583	0.476851
5	0.008251	0.0685	0.472777
6	-0.032983	-0.274	0.39246
7	-0.105662	-0.8777	0.191579
8	0.010273	0.0853	0.466122
9	-0.129733	-1.0776	0.142473
10	-0.084004	-0.6978	0.243827
11	-0.126071	-1.0472	0.149325
12	-0.062955	-0.5229	0.301344
13	0.094708	0.7867	0.217075
14	-0.046515	-0.3864	0.350202
15	0.023998	0.1993	0.42129
16	-0.122046	-1.0138	0.157113
17	-0.074016	-0.6148	0.270348
18	0.009594	0.0797	0.468355

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

Parameters (R input):

par1 = Default ; 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)
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')

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