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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 09:17:01 +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/Dec/16/t14818762355ewukxxrugzmeh9.htm/, Retrieved Thu, 02 May 2024 17:34:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300097, Retrieved Thu, 02 May 2024 17:34:27 +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] [] [2016-12-16 08:17:01] [94ac3c9a028ddd47e8862e80eac9f626] [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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300097&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300097&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300097&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.428111	2.8398	0.003405
2	0.16483	1.0934	0.140093
3	0.077471	0.5139	0.304951
4	0.041287	0.2739	0.392735
5	-0.047461	-0.3148	0.377194
6	0.037897	0.2514	0.401345
7	0.030139	0.1999	0.421233
8	-0.148071	-0.9822	0.165688
9	0.017224	0.1143	0.454779
10	0.003362	0.0223	0.491155
11	-0.03242	-0.215	0.415361
12	-0.202811	-1.3453	0.092712
13	-0.070124	-0.4651	0.32206
14	-0.133589	-0.8861	0.190183
15	-0.095473	-0.6333	0.264909
16	0.006586	0.0437	0.482676

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.428111 & 2.8398 & 0.003405 \tabularnewline
2 & 0.16483 & 1.0934 & 0.140093 \tabularnewline
3 & 0.077471 & 0.5139 & 0.304951 \tabularnewline
4 & 0.041287 & 0.2739 & 0.392735 \tabularnewline
5 & -0.047461 & -0.3148 & 0.377194 \tabularnewline
6 & 0.037897 & 0.2514 & 0.401345 \tabularnewline
7 & 0.030139 & 0.1999 & 0.421233 \tabularnewline
8 & -0.148071 & -0.9822 & 0.165688 \tabularnewline
9 & 0.017224 & 0.1143 & 0.454779 \tabularnewline
10 & 0.003362 & 0.0223 & 0.491155 \tabularnewline
11 & -0.03242 & -0.215 & 0.415361 \tabularnewline
12 & -0.202811 & -1.3453 & 0.092712 \tabularnewline
13 & -0.070124 & -0.4651 & 0.32206 \tabularnewline
14 & -0.133589 & -0.8861 & 0.190183 \tabularnewline
15 & -0.095473 & -0.6333 & 0.264909 \tabularnewline
16 & 0.006586 & 0.0437 & 0.482676 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300097&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]0.428111[/C][C]2.8398[/C][C]0.003405[/C][/ROW]
[ROW][C]2[/C][C]0.16483[/C][C]1.0934[/C][C]0.140093[/C][/ROW]
[ROW][C]3[/C][C]0.077471[/C][C]0.5139[/C][C]0.304951[/C][/ROW]
[ROW][C]4[/C][C]0.041287[/C][C]0.2739[/C][C]0.392735[/C][/ROW]
[ROW][C]5[/C][C]-0.047461[/C][C]-0.3148[/C][C]0.377194[/C][/ROW]
[ROW][C]6[/C][C]0.037897[/C][C]0.2514[/C][C]0.401345[/C][/ROW]
[ROW][C]7[/C][C]0.030139[/C][C]0.1999[/C][C]0.421233[/C][/ROW]
[ROW][C]8[/C][C]-0.148071[/C][C]-0.9822[/C][C]0.165688[/C][/ROW]
[ROW][C]9[/C][C]0.017224[/C][C]0.1143[/C][C]0.454779[/C][/ROW]
[ROW][C]10[/C][C]0.003362[/C][C]0.0223[/C][C]0.491155[/C][/ROW]
[ROW][C]11[/C][C]-0.03242[/C][C]-0.215[/C][C]0.415361[/C][/ROW]
[ROW][C]12[/C][C]-0.202811[/C][C]-1.3453[/C][C]0.092712[/C][/ROW]
[ROW][C]13[/C][C]-0.070124[/C][C]-0.4651[/C][C]0.32206[/C][/ROW]
[ROW][C]14[/C][C]-0.133589[/C][C]-0.8861[/C][C]0.190183[/C][/ROW]
[ROW][C]15[/C][C]-0.095473[/C][C]-0.6333[/C][C]0.264909[/C][/ROW]
[ROW][C]16[/C][C]0.006586[/C][C]0.0437[/C][C]0.482676[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300097&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300097&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	0.428111	2.8398	0.003405
2	0.16483	1.0934	0.140093
3	0.077471	0.5139	0.304951
4	0.041287	0.2739	0.392735
5	-0.047461	-0.3148	0.377194
6	0.037897	0.2514	0.401345
7	0.030139	0.1999	0.421233
8	-0.148071	-0.9822	0.165688
9	0.017224	0.1143	0.454779
10	0.003362	0.0223	0.491155
11	-0.03242	-0.215	0.415361
12	-0.202811	-1.3453	0.092712
13	-0.070124	-0.4651	0.32206
14	-0.133589	-0.8861	0.190183
15	-0.095473	-0.6333	0.264909
16	0.006586	0.0437	0.482676

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.428111	2.8398	0.003405
2	-0.02259	-0.1498	0.440786
3	0.018354	0.1217	0.451826
4	0.00555	0.0368	0.485399
5	-0.083565	-0.5543	0.291087
6	0.108235	0.718	0.238291
7	-0.021434	-0.1422	0.443795
8	-0.201832	-1.3388	0.093756
9	0.20636	1.3688	0.088999
10	-0.09231	-0.6123	0.271741
11	-0.014569	-0.0966	0.461727
12	-0.213326	-1.415	0.082047
13	0.090649	0.6013	0.275363
14	-0.098845	-0.6557	0.257726
15	0.01119	0.0742	0.470583
16	0.027403	0.1818	0.428299

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.428111 & 2.8398 & 0.003405 \tabularnewline
2 & -0.02259 & -0.1498 & 0.440786 \tabularnewline
3 & 0.018354 & 0.1217 & 0.451826 \tabularnewline
4 & 0.00555 & 0.0368 & 0.485399 \tabularnewline
5 & -0.083565 & -0.5543 & 0.291087 \tabularnewline
6 & 0.108235 & 0.718 & 0.238291 \tabularnewline
7 & -0.021434 & -0.1422 & 0.443795 \tabularnewline
8 & -0.201832 & -1.3388 & 0.093756 \tabularnewline
9 & 0.20636 & 1.3688 & 0.088999 \tabularnewline
10 & -0.09231 & -0.6123 & 0.271741 \tabularnewline
11 & -0.014569 & -0.0966 & 0.461727 \tabularnewline
12 & -0.213326 & -1.415 & 0.082047 \tabularnewline
13 & 0.090649 & 0.6013 & 0.275363 \tabularnewline
14 & -0.098845 & -0.6557 & 0.257726 \tabularnewline
15 & 0.01119 & 0.0742 & 0.470583 \tabularnewline
16 & 0.027403 & 0.1818 & 0.428299 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300097&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]0.428111[/C][C]2.8398[/C][C]0.003405[/C][/ROW]
[ROW][C]2[/C][C]-0.02259[/C][C]-0.1498[/C][C]0.440786[/C][/ROW]
[ROW][C]3[/C][C]0.018354[/C][C]0.1217[/C][C]0.451826[/C][/ROW]
[ROW][C]4[/C][C]0.00555[/C][C]0.0368[/C][C]0.485399[/C][/ROW]
[ROW][C]5[/C][C]-0.083565[/C][C]-0.5543[/C][C]0.291087[/C][/ROW]
[ROW][C]6[/C][C]0.108235[/C][C]0.718[/C][C]0.238291[/C][/ROW]
[ROW][C]7[/C][C]-0.021434[/C][C]-0.1422[/C][C]0.443795[/C][/ROW]
[ROW][C]8[/C][C]-0.201832[/C][C]-1.3388[/C][C]0.093756[/C][/ROW]
[ROW][C]9[/C][C]0.20636[/C][C]1.3688[/C][C]0.088999[/C][/ROW]
[ROW][C]10[/C][C]-0.09231[/C][C]-0.6123[/C][C]0.271741[/C][/ROW]
[ROW][C]11[/C][C]-0.014569[/C][C]-0.0966[/C][C]0.461727[/C][/ROW]
[ROW][C]12[/C][C]-0.213326[/C][C]-1.415[/C][C]0.082047[/C][/ROW]
[ROW][C]13[/C][C]0.090649[/C][C]0.6013[/C][C]0.275363[/C][/ROW]
[ROW][C]14[/C][C]-0.098845[/C][C]-0.6557[/C][C]0.257726[/C][/ROW]
[ROW][C]15[/C][C]0.01119[/C][C]0.0742[/C][C]0.470583[/C][/ROW]
[ROW][C]16[/C][C]0.027403[/C][C]0.1818[/C][C]0.428299[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300097&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300097&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	0.428111	2.8398	0.003405
2	-0.02259	-0.1498	0.440786
3	0.018354	0.1217	0.451826
4	0.00555	0.0368	0.485399
5	-0.083565	-0.5543	0.291087
6	0.108235	0.718	0.238291
7	-0.021434	-0.1422	0.443795
8	-0.201832	-1.3388	0.093756
9	0.20636	1.3688	0.088999
10	-0.09231	-0.6123	0.271741
11	-0.014569	-0.0966	0.461727
12	-0.213326	-1.415	0.082047
13	0.090649	0.6013	0.275363
14	-0.098845	-0.6557	0.257726
15	0.01119	0.0742	0.470583
16	0.027403	0.1818	0.428299

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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,'ACF(k)',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,'PACF(k)',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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Input Parameters & R Code