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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 19 Oct 2016 12:25:26 +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/19/t1476876358w4e167vhcmq1sit.htm/, Retrieved Tue, 30 Apr 2024 06:29:06 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 30 Apr 2024 06:29:06 +0200

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Estimated Impact

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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	'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.963763	8.1778	0
2	0.923478	7.836	0
3	0.881602	7.4806	0
4	0.839294	7.1216	0
5	0.799222	6.7816	0
6	0.758642	6.4373	0
7	0.716685	6.0813	0
8	0.673524	5.715	0
9	0.630211	5.3475	1e-06
10	0.589297	5.0004	2e-06
11	0.553585	4.6973	6e-06
12	0.51842	4.3989	1.8e-05
13	0.480352	4.0759	5.8e-05
14	0.440187	3.7351	0.000186
15	0.398922	3.385	0.000578
16	0.357006	3.0293	0.001701
17	0.315067	2.6734	0.004641
18	0.273047	2.3169	0.011679

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.963763 & 8.1778 & 0 \tabularnewline
2 & 0.923478 & 7.836 & 0 \tabularnewline
3 & 0.881602 & 7.4806 & 0 \tabularnewline
4 & 0.839294 & 7.1216 & 0 \tabularnewline
5 & 0.799222 & 6.7816 & 0 \tabularnewline
6 & 0.758642 & 6.4373 & 0 \tabularnewline
7 & 0.716685 & 6.0813 & 0 \tabularnewline
8 & 0.673524 & 5.715 & 0 \tabularnewline
9 & 0.630211 & 5.3475 & 1e-06 \tabularnewline
10 & 0.589297 & 5.0004 & 2e-06 \tabularnewline
11 & 0.553585 & 4.6973 & 6e-06 \tabularnewline
12 & 0.51842 & 4.3989 & 1.8e-05 \tabularnewline
13 & 0.480352 & 4.0759 & 5.8e-05 \tabularnewline
14 & 0.440187 & 3.7351 & 0.000186 \tabularnewline
15 & 0.398922 & 3.385 & 0.000578 \tabularnewline
16 & 0.357006 & 3.0293 & 0.001701 \tabularnewline
17 & 0.315067 & 2.6734 & 0.004641 \tabularnewline
18 & 0.273047 & 2.3169 & 0.011679 \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]0.963763[/C][C]8.1778[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.923478[/C][C]7.836[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.881602[/C][C]7.4806[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.839294[/C][C]7.1216[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.799222[/C][C]6.7816[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.758642[/C][C]6.4373[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.716685[/C][C]6.0813[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.673524[/C][C]5.715[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.630211[/C][C]5.3475[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.589297[/C][C]5.0004[/C][C]2e-06[/C][/ROW]
[ROW][C]11[/C][C]0.553585[/C][C]4.6973[/C][C]6e-06[/C][/ROW]
[ROW][C]12[/C][C]0.51842[/C][C]4.3989[/C][C]1.8e-05[/C][/ROW]
[ROW][C]13[/C][C]0.480352[/C][C]4.0759[/C][C]5.8e-05[/C][/ROW]
[ROW][C]14[/C][C]0.440187[/C][C]3.7351[/C][C]0.000186[/C][/ROW]
[ROW][C]15[/C][C]0.398922[/C][C]3.385[/C][C]0.000578[/C][/ROW]
[ROW][C]16[/C][C]0.357006[/C][C]3.0293[/C][C]0.001701[/C][/ROW]
[ROW][C]17[/C][C]0.315067[/C][C]2.6734[/C][C]0.004641[/C][/ROW]
[ROW][C]18[/C][C]0.273047[/C][C]2.3169[/C][C]0.011679[/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	0.963763	8.1778	0
2	0.923478	7.836	0
3	0.881602	7.4806	0
4	0.839294	7.1216	0
5	0.799222	6.7816	0
6	0.758642	6.4373	0
7	0.716685	6.0813	0
8	0.673524	5.715	0
9	0.630211	5.3475	1e-06
10	0.589297	5.0004	2e-06
11	0.553585	4.6973	6e-06
12	0.51842	4.3989	1.8e-05
13	0.480352	4.0759	5.8e-05
14	0.440187	3.7351	0.000186
15	0.398922	3.385	0.000578
16	0.357006	3.0293	0.001701
17	0.315067	2.6734	0.004641
18	0.273047	2.3169	0.011679

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.963763	8.1778	0
2	-0.075349	-0.6394	0.26231
3	-0.040342	-0.3423	0.366555
4	-0.026183	-0.2222	0.412406
5	0.009574	0.0812	0.467738
6	-0.032614	-0.2767	0.391387
7	-0.04295	-0.3644	0.358296
8	-0.039526	-0.3354	0.369152
9	-0.024415	-0.2072	0.41823
10	0.007971	0.0676	0.473131
11	0.043844	0.372	0.355484
12	-0.024873	-0.2111	0.416722
13	-0.068145	-0.5782	0.282457
14	-0.050146	-0.4255	0.335868
15	-0.034892	-0.2961	0.384016
16	-0.037584	-0.3189	0.375359
17	-0.035558	-0.3017	0.381869
18	-0.036036	-0.3058	0.380328

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.963763 & 8.1778 & 0 \tabularnewline
2 & -0.075349 & -0.6394 & 0.26231 \tabularnewline
3 & -0.040342 & -0.3423 & 0.366555 \tabularnewline
4 & -0.026183 & -0.2222 & 0.412406 \tabularnewline
5 & 0.009574 & 0.0812 & 0.467738 \tabularnewline
6 & -0.032614 & -0.2767 & 0.391387 \tabularnewline
7 & -0.04295 & -0.3644 & 0.358296 \tabularnewline
8 & -0.039526 & -0.3354 & 0.369152 \tabularnewline
9 & -0.024415 & -0.2072 & 0.41823 \tabularnewline
10 & 0.007971 & 0.0676 & 0.473131 \tabularnewline
11 & 0.043844 & 0.372 & 0.355484 \tabularnewline
12 & -0.024873 & -0.2111 & 0.416722 \tabularnewline
13 & -0.068145 & -0.5782 & 0.282457 \tabularnewline
14 & -0.050146 & -0.4255 & 0.335868 \tabularnewline
15 & -0.034892 & -0.2961 & 0.384016 \tabularnewline
16 & -0.037584 & -0.3189 & 0.375359 \tabularnewline
17 & -0.035558 & -0.3017 & 0.381869 \tabularnewline
18 & -0.036036 & -0.3058 & 0.380328 \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]0.963763[/C][C]8.1778[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.075349[/C][C]-0.6394[/C][C]0.26231[/C][/ROW]
[ROW][C]3[/C][C]-0.040342[/C][C]-0.3423[/C][C]0.366555[/C][/ROW]
[ROW][C]4[/C][C]-0.026183[/C][C]-0.2222[/C][C]0.412406[/C][/ROW]
[ROW][C]5[/C][C]0.009574[/C][C]0.0812[/C][C]0.467738[/C][/ROW]
[ROW][C]6[/C][C]-0.032614[/C][C]-0.2767[/C][C]0.391387[/C][/ROW]
[ROW][C]7[/C][C]-0.04295[/C][C]-0.3644[/C][C]0.358296[/C][/ROW]
[ROW][C]8[/C][C]-0.039526[/C][C]-0.3354[/C][C]0.369152[/C][/ROW]
[ROW][C]9[/C][C]-0.024415[/C][C]-0.2072[/C][C]0.41823[/C][/ROW]
[ROW][C]10[/C][C]0.007971[/C][C]0.0676[/C][C]0.473131[/C][/ROW]
[ROW][C]11[/C][C]0.043844[/C][C]0.372[/C][C]0.355484[/C][/ROW]
[ROW][C]12[/C][C]-0.024873[/C][C]-0.2111[/C][C]0.416722[/C][/ROW]
[ROW][C]13[/C][C]-0.068145[/C][C]-0.5782[/C][C]0.282457[/C][/ROW]
[ROW][C]14[/C][C]-0.050146[/C][C]-0.4255[/C][C]0.335868[/C][/ROW]
[ROW][C]15[/C][C]-0.034892[/C][C]-0.2961[/C][C]0.384016[/C][/ROW]
[ROW][C]16[/C][C]-0.037584[/C][C]-0.3189[/C][C]0.375359[/C][/ROW]
[ROW][C]17[/C][C]-0.035558[/C][C]-0.3017[/C][C]0.381869[/C][/ROW]
[ROW][C]18[/C][C]-0.036036[/C][C]-0.3058[/C][C]0.380328[/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	0.963763	8.1778	0
2	-0.075349	-0.6394	0.26231
3	-0.040342	-0.3423	0.366555
4	-0.026183	-0.2222	0.412406
5	0.009574	0.0812	0.467738
6	-0.032614	-0.2767	0.391387
7	-0.04295	-0.3644	0.358296
8	-0.039526	-0.3354	0.369152
9	-0.024415	-0.2072	0.41823
10	0.007971	0.0676	0.473131
11	0.043844	0.372	0.355484
12	-0.024873	-0.2111	0.416722
13	-0.068145	-0.5782	0.282457
14	-0.050146	-0.4255	0.335868
15	-0.034892	-0.2961	0.384016
16	-0.037584	-0.3189	0.375359
17	-0.035558	-0.3017	0.381869
18	-0.036036	-0.3058	0.380328

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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code