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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 08 Mar 2016 10:40:29 +0000

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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/Mar/08/t1457433759co4qto3hofljuvd.htm/, Retrieved Mon, 29 Apr 2024 02:31:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293664, Retrieved Mon, 29 Apr 2024 02:31:05 +0000

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Estimated Impact

105

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-       [(Partial) Autocorrelation Function] [] [2016-03-08 10:40:29] [b94c13d84d922b33c8d74b1e5b1d38c1] [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	'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=293664&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=293664&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293664&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	0.954442	8.0987	0
2	0.907629	7.7015	0
3	0.842305	7.1472	0
4	0.766801	6.5065	0
5	0.688691	5.8437	0
6	0.609187	5.1691	1e-06
7	0.533934	4.5306	1.1e-05
8	0.455932	3.8687	0.000119
9	0.39531	3.3543	0.000636
10	0.338117	2.869	0.0027
11	0.276008	2.342	0.010975
12	0.210994	1.7903	0.038801
13	0.148643	1.2613	0.10564
14	0.084394	0.7161	0.238121
15	0.022244	0.1887	0.425412
16	-0.041401	-0.3513	0.363194
17	-0.095683	-0.8119	0.209763
18	-0.154457	-1.3106	0.097077

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.954442 & 8.0987 & 0 \tabularnewline
2 & 0.907629 & 7.7015 & 0 \tabularnewline
3 & 0.842305 & 7.1472 & 0 \tabularnewline
4 & 0.766801 & 6.5065 & 0 \tabularnewline
5 & 0.688691 & 5.8437 & 0 \tabularnewline
6 & 0.609187 & 5.1691 & 1e-06 \tabularnewline
7 & 0.533934 & 4.5306 & 1.1e-05 \tabularnewline
8 & 0.455932 & 3.8687 & 0.000119 \tabularnewline
9 & 0.39531 & 3.3543 & 0.000636 \tabularnewline
10 & 0.338117 & 2.869 & 0.0027 \tabularnewline
11 & 0.276008 & 2.342 & 0.010975 \tabularnewline
12 & 0.210994 & 1.7903 & 0.038801 \tabularnewline
13 & 0.148643 & 1.2613 & 0.10564 \tabularnewline
14 & 0.084394 & 0.7161 & 0.238121 \tabularnewline
15 & 0.022244 & 0.1887 & 0.425412 \tabularnewline
16 & -0.041401 & -0.3513 & 0.363194 \tabularnewline
17 & -0.095683 & -0.8119 & 0.209763 \tabularnewline
18 & -0.154457 & -1.3106 & 0.097077 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293664&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]0.954442[/C][C]8.0987[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.907629[/C][C]7.7015[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.842305[/C][C]7.1472[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.766801[/C][C]6.5065[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.688691[/C][C]5.8437[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.609187[/C][C]5.1691[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.533934[/C][C]4.5306[/C][C]1.1e-05[/C][/ROW]
[ROW][C]8[/C][C]0.455932[/C][C]3.8687[/C][C]0.000119[/C][/ROW]
[ROW][C]9[/C][C]0.39531[/C][C]3.3543[/C][C]0.000636[/C][/ROW]
[ROW][C]10[/C][C]0.338117[/C][C]2.869[/C][C]0.0027[/C][/ROW]
[ROW][C]11[/C][C]0.276008[/C][C]2.342[/C][C]0.010975[/C][/ROW]
[ROW][C]12[/C][C]0.210994[/C][C]1.7903[/C][C]0.038801[/C][/ROW]
[ROW][C]13[/C][C]0.148643[/C][C]1.2613[/C][C]0.10564[/C][/ROW]
[ROW][C]14[/C][C]0.084394[/C][C]0.7161[/C][C]0.238121[/C][/ROW]
[ROW][C]15[/C][C]0.022244[/C][C]0.1887[/C][C]0.425412[/C][/ROW]
[ROW][C]16[/C][C]-0.041401[/C][C]-0.3513[/C][C]0.363194[/C][/ROW]
[ROW][C]17[/C][C]-0.095683[/C][C]-0.8119[/C][C]0.209763[/C][/ROW]
[ROW][C]18[/C][C]-0.154457[/C][C]-1.3106[/C][C]0.097077[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293664&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293664&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	0.954442	8.0987	0
2	0.907629	7.7015	0
3	0.842305	7.1472	0
4	0.766801	6.5065	0
5	0.688691	5.8437	0
6	0.609187	5.1691	1e-06
7	0.533934	4.5306	1.1e-05
8	0.455932	3.8687	0.000119
9	0.39531	3.3543	0.000636
10	0.338117	2.869	0.0027
11	0.276008	2.342	0.010975
12	0.210994	1.7903	0.038801
13	0.148643	1.2613	0.10564
14	0.084394	0.7161	0.238121
15	0.022244	0.1887	0.425412
16	-0.041401	-0.3513	0.363194
17	-0.095683	-0.8119	0.209763
18	-0.154457	-1.3106	0.097077

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.954442	8.0987	0
2	-0.037408	-0.3174	0.375922
3	-0.232528	-1.9731	0.026164
4	-0.154082	-1.3074	0.097613
5	-0.036542	-0.3101	0.378702
6	-0.018823	-0.1597	0.436775
7	0.018224	0.1546	0.43877
8	-0.080511	-0.6832	0.248348
9	0.132411	1.1235	0.13247
10	0.005991	0.0508	0.479797
11	-0.173596	-1.473	0.072554
12	-0.155829	-1.3223	0.095134
13	-0.001515	-0.0129	0.494888
14	-0.030202	-0.2563	0.399237
15	-0.016435	-0.1395	0.444739
16	-0.096457	-0.8185	0.207895
17	0.074305	0.6305	0.265183
18	-0.087337	-0.7411	0.230527

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.954442 & 8.0987 & 0 \tabularnewline
2 & -0.037408 & -0.3174 & 0.375922 \tabularnewline
3 & -0.232528 & -1.9731 & 0.026164 \tabularnewline
4 & -0.154082 & -1.3074 & 0.097613 \tabularnewline
5 & -0.036542 & -0.3101 & 0.378702 \tabularnewline
6 & -0.018823 & -0.1597 & 0.436775 \tabularnewline
7 & 0.018224 & 0.1546 & 0.43877 \tabularnewline
8 & -0.080511 & -0.6832 & 0.248348 \tabularnewline
9 & 0.132411 & 1.1235 & 0.13247 \tabularnewline
10 & 0.005991 & 0.0508 & 0.479797 \tabularnewline
11 & -0.173596 & -1.473 & 0.072554 \tabularnewline
12 & -0.155829 & -1.3223 & 0.095134 \tabularnewline
13 & -0.001515 & -0.0129 & 0.494888 \tabularnewline
14 & -0.030202 & -0.2563 & 0.399237 \tabularnewline
15 & -0.016435 & -0.1395 & 0.444739 \tabularnewline
16 & -0.096457 & -0.8185 & 0.207895 \tabularnewline
17 & 0.074305 & 0.6305 & 0.265183 \tabularnewline
18 & -0.087337 & -0.7411 & 0.230527 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293664&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]0.954442[/C][C]8.0987[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.037408[/C][C]-0.3174[/C][C]0.375922[/C][/ROW]
[ROW][C]3[/C][C]-0.232528[/C][C]-1.9731[/C][C]0.026164[/C][/ROW]
[ROW][C]4[/C][C]-0.154082[/C][C]-1.3074[/C][C]0.097613[/C][/ROW]
[ROW][C]5[/C][C]-0.036542[/C][C]-0.3101[/C][C]0.378702[/C][/ROW]
[ROW][C]6[/C][C]-0.018823[/C][C]-0.1597[/C][C]0.436775[/C][/ROW]
[ROW][C]7[/C][C]0.018224[/C][C]0.1546[/C][C]0.43877[/C][/ROW]
[ROW][C]8[/C][C]-0.080511[/C][C]-0.6832[/C][C]0.248348[/C][/ROW]
[ROW][C]9[/C][C]0.132411[/C][C]1.1235[/C][C]0.13247[/C][/ROW]
[ROW][C]10[/C][C]0.005991[/C][C]0.0508[/C][C]0.479797[/C][/ROW]
[ROW][C]11[/C][C]-0.173596[/C][C]-1.473[/C][C]0.072554[/C][/ROW]
[ROW][C]12[/C][C]-0.155829[/C][C]-1.3223[/C][C]0.095134[/C][/ROW]
[ROW][C]13[/C][C]-0.001515[/C][C]-0.0129[/C][C]0.494888[/C][/ROW]
[ROW][C]14[/C][C]-0.030202[/C][C]-0.2563[/C][C]0.399237[/C][/ROW]
[ROW][C]15[/C][C]-0.016435[/C][C]-0.1395[/C][C]0.444739[/C][/ROW]
[ROW][C]16[/C][C]-0.096457[/C][C]-0.8185[/C][C]0.207895[/C][/ROW]
[ROW][C]17[/C][C]0.074305[/C][C]0.6305[/C][C]0.265183[/C][/ROW]
[ROW][C]18[/C][C]-0.087337[/C][C]-0.7411[/C][C]0.230527[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293664&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293664&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	0.954442	8.0987	0
2	-0.037408	-0.3174	0.375922
3	-0.232528	-1.9731	0.026164
4	-0.154082	-1.3074	0.097613
5	-0.036542	-0.3101	0.378702
6	-0.018823	-0.1597	0.436775
7	0.018224	0.1546	0.43877
8	-0.080511	-0.6832	0.248348
9	0.132411	1.1235	0.13247
10	0.005991	0.0508	0.479797
11	-0.173596	-1.473	0.072554
12	-0.155829	-1.3223	0.095134
13	-0.001515	-0.0129	0.494888
14	-0.030202	-0.2563	0.399237
15	-0.016435	-0.1395	0.444739
16	-0.096457	-0.8185	0.207895
17	0.074305	0.6305	0.265183
18	-0.087337	-0.7411	0.230527

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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Dataset

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Input Parameters & R Code