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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 04 Dec 2015 11:53:27 +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/2015/Dec/04/t14492304352m0991sny74ikk9.htm/, Retrieved Thu, 16 May 2024 14:08:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285088, Retrieved Thu, 16 May 2024 14:08:33 +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] [Autocorrelatie lo...] [2015-12-04 11:53:27] [9e0721fac163b9902ccf1ac483b8097c] [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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285088&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285088&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285088&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.787794	2.9477	0.005297
2	0.580902	2.1735	0.023695
3	0.367657	1.3756	0.095271
4	0.167911	0.6283	0.269972
5	0.013293	0.0497	0.480517
6	-0.125977	-0.4714	0.322322
7	-0.238957	-0.8941	0.193192
8	-0.336489	-1.259	0.114304
9	-0.400647	-1.4991	0.07803
10	-0.432527	-1.6184	0.063942
11	-0.396062	-1.4819	0.080258

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.787794 & 2.9477 & 0.005297 \tabularnewline
2 & 0.580902 & 2.1735 & 0.023695 \tabularnewline
3 & 0.367657 & 1.3756 & 0.095271 \tabularnewline
4 & 0.167911 & 0.6283 & 0.269972 \tabularnewline
5 & 0.013293 & 0.0497 & 0.480517 \tabularnewline
6 & -0.125977 & -0.4714 & 0.322322 \tabularnewline
7 & -0.238957 & -0.8941 & 0.193192 \tabularnewline
8 & -0.336489 & -1.259 & 0.114304 \tabularnewline
9 & -0.400647 & -1.4991 & 0.07803 \tabularnewline
10 & -0.432527 & -1.6184 & 0.063942 \tabularnewline
11 & -0.396062 & -1.4819 & 0.080258 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285088&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]0.787794[/C][C]2.9477[/C][C]0.005297[/C][/ROW]
[ROW][C]2[/C][C]0.580902[/C][C]2.1735[/C][C]0.023695[/C][/ROW]
[ROW][C]3[/C][C]0.367657[/C][C]1.3756[/C][C]0.095271[/C][/ROW]
[ROW][C]4[/C][C]0.167911[/C][C]0.6283[/C][C]0.269972[/C][/ROW]
[ROW][C]5[/C][C]0.013293[/C][C]0.0497[/C][C]0.480517[/C][/ROW]
[ROW][C]6[/C][C]-0.125977[/C][C]-0.4714[/C][C]0.322322[/C][/ROW]
[ROW][C]7[/C][C]-0.238957[/C][C]-0.8941[/C][C]0.193192[/C][/ROW]
[ROW][C]8[/C][C]-0.336489[/C][C]-1.259[/C][C]0.114304[/C][/ROW]
[ROW][C]9[/C][C]-0.400647[/C][C]-1.4991[/C][C]0.07803[/C][/ROW]
[ROW][C]10[/C][C]-0.432527[/C][C]-1.6184[/C][C]0.063942[/C][/ROW]
[ROW][C]11[/C][C]-0.396062[/C][C]-1.4819[/C][C]0.080258[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285088&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285088&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	0.787794	2.9477	0.005297
2	0.580902	2.1735	0.023695
3	0.367657	1.3756	0.095271
4	0.167911	0.6283	0.269972
5	0.013293	0.0497	0.480517
6	-0.125977	-0.4714	0.322322
7	-0.238957	-0.8941	0.193192
8	-0.336489	-1.259	0.114304
9	-0.400647	-1.4991	0.07803
10	-0.432527	-1.6184	0.063942
11	-0.396062	-1.4819	0.080258

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.787794	2.9477	0.005297
2	-0.104691	-0.3917	0.350582
3	-0.14767	-0.5525	0.294649
4	-0.119523	-0.4472	0.33078
5	-0.045577	-0.1705	0.433515
6	-0.115522	-0.4322	0.336074
7	-0.10165	-0.3803	0.354701
8	-0.128233	-0.4798	0.319388
9	-0.085453	-0.3197	0.376945
10	-0.083407	-0.3121	0.379789
11	0.033654	0.1259	0.450792

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.787794 & 2.9477 & 0.005297 \tabularnewline
2 & -0.104691 & -0.3917 & 0.350582 \tabularnewline
3 & -0.14767 & -0.5525 & 0.294649 \tabularnewline
4 & -0.119523 & -0.4472 & 0.33078 \tabularnewline
5 & -0.045577 & -0.1705 & 0.433515 \tabularnewline
6 & -0.115522 & -0.4322 & 0.336074 \tabularnewline
7 & -0.10165 & -0.3803 & 0.354701 \tabularnewline
8 & -0.128233 & -0.4798 & 0.319388 \tabularnewline
9 & -0.085453 & -0.3197 & 0.376945 \tabularnewline
10 & -0.083407 & -0.3121 & 0.379789 \tabularnewline
11 & 0.033654 & 0.1259 & 0.450792 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285088&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]0.787794[/C][C]2.9477[/C][C]0.005297[/C][/ROW]
[ROW][C]2[/C][C]-0.104691[/C][C]-0.3917[/C][C]0.350582[/C][/ROW]
[ROW][C]3[/C][C]-0.14767[/C][C]-0.5525[/C][C]0.294649[/C][/ROW]
[ROW][C]4[/C][C]-0.119523[/C][C]-0.4472[/C][C]0.33078[/C][/ROW]
[ROW][C]5[/C][C]-0.045577[/C][C]-0.1705[/C][C]0.433515[/C][/ROW]
[ROW][C]6[/C][C]-0.115522[/C][C]-0.4322[/C][C]0.336074[/C][/ROW]
[ROW][C]7[/C][C]-0.10165[/C][C]-0.3803[/C][C]0.354701[/C][/ROW]
[ROW][C]8[/C][C]-0.128233[/C][C]-0.4798[/C][C]0.319388[/C][/ROW]
[ROW][C]9[/C][C]-0.085453[/C][C]-0.3197[/C][C]0.376945[/C][/ROW]
[ROW][C]10[/C][C]-0.083407[/C][C]-0.3121[/C][C]0.379789[/C][/ROW]
[ROW][C]11[/C][C]0.033654[/C][C]0.1259[/C][C]0.450792[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285088&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285088&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	0.787794	2.9477	0.005297
2	-0.104691	-0.3917	0.350582
3	-0.14767	-0.5525	0.294649
4	-0.119523	-0.4472	0.33078
5	-0.045577	-0.1705	0.433515
6	-0.115522	-0.4322	0.336074
7	-0.10165	-0.3803	0.354701
8	-0.128233	-0.4798	0.319388
9	-0.085453	-0.3197	0.376945
10	-0.083407	-0.3121	0.379789
11	0.033654	0.1259	0.450792

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 = 0 ; par2 = 0 ;

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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