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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 14 Mar 2016 19:27:33 +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/14/t14579837220bplppmfamw37jg.htm/, Retrieved Mon, 29 Apr 2024 01:53:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294041, Retrieved Mon, 29 Apr 2024 01:53:20 +0000

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

-       [(Partial) Autocorrelation Function] [Moerman Nicola�] [2016-03-14 19:27:33] [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 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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294041&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 Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294041&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294041&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 Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.922456	7.1453	0
2	0.841734	6.52	0
3	0.76753	5.9453	0
4	0.698467	5.4103	1e-06
5	0.633523	4.9072	4e-06
6	0.568217	4.4014	2.2e-05
7	0.502081	3.8891	0.000127
8	0.43507	3.37	0.000659
9	0.368779	2.8565	0.002938
10	0.299898	2.323	0.011794
11	0.227528	1.7624	0.041545
12	0.155381	1.2036	0.116741
13	0.095479	0.7396	0.23122
14	0.044836	0.3473	0.364792
15	0.006507	0.0504	0.479984
16	-0.01627	-0.126	0.450067
17	-0.045483	-0.3523	0.36292

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.922456 & 7.1453 & 0 \tabularnewline
2 & 0.841734 & 6.52 & 0 \tabularnewline
3 & 0.76753 & 5.9453 & 0 \tabularnewline
4 & 0.698467 & 5.4103 & 1e-06 \tabularnewline
5 & 0.633523 & 4.9072 & 4e-06 \tabularnewline
6 & 0.568217 & 4.4014 & 2.2e-05 \tabularnewline
7 & 0.502081 & 3.8891 & 0.000127 \tabularnewline
8 & 0.43507 & 3.37 & 0.000659 \tabularnewline
9 & 0.368779 & 2.8565 & 0.002938 \tabularnewline
10 & 0.299898 & 2.323 & 0.011794 \tabularnewline
11 & 0.227528 & 1.7624 & 0.041545 \tabularnewline
12 & 0.155381 & 1.2036 & 0.116741 \tabularnewline
13 & 0.095479 & 0.7396 & 0.23122 \tabularnewline
14 & 0.044836 & 0.3473 & 0.364792 \tabularnewline
15 & 0.006507 & 0.0504 & 0.479984 \tabularnewline
16 & -0.01627 & -0.126 & 0.450067 \tabularnewline
17 & -0.045483 & -0.3523 & 0.36292 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294041&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]0.922456[/C][C]7.1453[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.841734[/C][C]6.52[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.76753[/C][C]5.9453[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.698467[/C][C]5.4103[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]0.633523[/C][C]4.9072[/C][C]4e-06[/C][/ROW]
[ROW][C]6[/C][C]0.568217[/C][C]4.4014[/C][C]2.2e-05[/C][/ROW]
[ROW][C]7[/C][C]0.502081[/C][C]3.8891[/C][C]0.000127[/C][/ROW]
[ROW][C]8[/C][C]0.43507[/C][C]3.37[/C][C]0.000659[/C][/ROW]
[ROW][C]9[/C][C]0.368779[/C][C]2.8565[/C][C]0.002938[/C][/ROW]
[ROW][C]10[/C][C]0.299898[/C][C]2.323[/C][C]0.011794[/C][/ROW]
[ROW][C]11[/C][C]0.227528[/C][C]1.7624[/C][C]0.041545[/C][/ROW]
[ROW][C]12[/C][C]0.155381[/C][C]1.2036[/C][C]0.116741[/C][/ROW]
[ROW][C]13[/C][C]0.095479[/C][C]0.7396[/C][C]0.23122[/C][/ROW]
[ROW][C]14[/C][C]0.044836[/C][C]0.3473[/C][C]0.364792[/C][/ROW]
[ROW][C]15[/C][C]0.006507[/C][C]0.0504[/C][C]0.479984[/C][/ROW]
[ROW][C]16[/C][C]-0.01627[/C][C]-0.126[/C][C]0.450067[/C][/ROW]
[ROW][C]17[/C][C]-0.045483[/C][C]-0.3523[/C][C]0.36292[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294041&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294041&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	0.922456	7.1453	0
2	0.841734	6.52	0
3	0.76753	5.9453	0
4	0.698467	5.4103	1e-06
5	0.633523	4.9072	4e-06
6	0.568217	4.4014	2.2e-05
7	0.502081	3.8891	0.000127
8	0.43507	3.37	0.000659
9	0.368779	2.8565	0.002938
10	0.299898	2.323	0.011794
11	0.227528	1.7624	0.041545
12	0.155381	1.2036	0.116741
13	0.095479	0.7396	0.23122
14	0.044836	0.3473	0.364792
15	0.006507	0.0504	0.479984
16	-0.01627	-0.126	0.450067
17	-0.045483	-0.3523	0.36292

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.922456	7.1453	0
2	-0.061657	-0.4776	0.317337
3	0.000467	0.0036	0.498564
4	-0.009223	-0.0714	0.471642
5	-0.012828	-0.0994	0.46059
6	-0.041156	-0.3188	0.375495
7	-0.044301	-0.3432	0.366341
8	-0.048357	-0.3746	0.354651
9	-0.041299	-0.3199	0.375078
10	-0.06698	-0.5188	0.302896
11	-0.076027	-0.5889	0.27907
12	-0.057513	-0.4455	0.328782
13	0.019366	0.15	0.440629
14	0.002105	0.0163	0.493522
15	0.035561	0.2755	0.391956
16	0.068642	0.5317	0.298449
17	-0.068365	-0.5296	0.299187

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.922456 & 7.1453 & 0 \tabularnewline
2 & -0.061657 & -0.4776 & 0.317337 \tabularnewline
3 & 0.000467 & 0.0036 & 0.498564 \tabularnewline
4 & -0.009223 & -0.0714 & 0.471642 \tabularnewline
5 & -0.012828 & -0.0994 & 0.46059 \tabularnewline
6 & -0.041156 & -0.3188 & 0.375495 \tabularnewline
7 & -0.044301 & -0.3432 & 0.366341 \tabularnewline
8 & -0.048357 & -0.3746 & 0.354651 \tabularnewline
9 & -0.041299 & -0.3199 & 0.375078 \tabularnewline
10 & -0.06698 & -0.5188 & 0.302896 \tabularnewline
11 & -0.076027 & -0.5889 & 0.27907 \tabularnewline
12 & -0.057513 & -0.4455 & 0.328782 \tabularnewline
13 & 0.019366 & 0.15 & 0.440629 \tabularnewline
14 & 0.002105 & 0.0163 & 0.493522 \tabularnewline
15 & 0.035561 & 0.2755 & 0.391956 \tabularnewline
16 & 0.068642 & 0.5317 & 0.298449 \tabularnewline
17 & -0.068365 & -0.5296 & 0.299187 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294041&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]0.922456[/C][C]7.1453[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.061657[/C][C]-0.4776[/C][C]0.317337[/C][/ROW]
[ROW][C]3[/C][C]0.000467[/C][C]0.0036[/C][C]0.498564[/C][/ROW]
[ROW][C]4[/C][C]-0.009223[/C][C]-0.0714[/C][C]0.471642[/C][/ROW]
[ROW][C]5[/C][C]-0.012828[/C][C]-0.0994[/C][C]0.46059[/C][/ROW]
[ROW][C]6[/C][C]-0.041156[/C][C]-0.3188[/C][C]0.375495[/C][/ROW]
[ROW][C]7[/C][C]-0.044301[/C][C]-0.3432[/C][C]0.366341[/C][/ROW]
[ROW][C]8[/C][C]-0.048357[/C][C]-0.3746[/C][C]0.354651[/C][/ROW]
[ROW][C]9[/C][C]-0.041299[/C][C]-0.3199[/C][C]0.375078[/C][/ROW]
[ROW][C]10[/C][C]-0.06698[/C][C]-0.5188[/C][C]0.302896[/C][/ROW]
[ROW][C]11[/C][C]-0.076027[/C][C]-0.5889[/C][C]0.27907[/C][/ROW]
[ROW][C]12[/C][C]-0.057513[/C][C]-0.4455[/C][C]0.328782[/C][/ROW]
[ROW][C]13[/C][C]0.019366[/C][C]0.15[/C][C]0.440629[/C][/ROW]
[ROW][C]14[/C][C]0.002105[/C][C]0.0163[/C][C]0.493522[/C][/ROW]
[ROW][C]15[/C][C]0.035561[/C][C]0.2755[/C][C]0.391956[/C][/ROW]
[ROW][C]16[/C][C]0.068642[/C][C]0.5317[/C][C]0.298449[/C][/ROW]
[ROW][C]17[/C][C]-0.068365[/C][C]-0.5296[/C][C]0.299187[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294041&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294041&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	0.922456	7.1453	0
2	-0.061657	-0.4776	0.317337
3	0.000467	0.0036	0.498564
4	-0.009223	-0.0714	0.471642
5	-0.012828	-0.0994	0.46059
6	-0.041156	-0.3188	0.375495
7	-0.044301	-0.3432	0.366341
8	-0.048357	-0.3746	0.354651
9	-0.041299	-0.3199	0.375078
10	-0.06698	-0.5188	0.302896
11	-0.076027	-0.5889	0.27907
12	-0.057513	-0.4455	0.328782
13	0.019366	0.15	0.440629
14	0.002105	0.0163	0.493522
15	0.035561	0.2755	0.391956
16	0.068642	0.5317	0.298449
17	-0.068365	-0.5296	0.299187

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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