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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 19 Dec 2016 22:00:23 +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/19/t1482181282ogn27a76x5830k3.htm/, Retrieved Sat, 18 May 2024 20:42:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301505, Retrieved Sat, 18 May 2024 20:42:54 +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] [ACF] [2016-12-19 21:00:23] [2e11ca31a00cf8de75c33c1af2d59434] [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=301505&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=301505&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301505&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	0.336638	2.2075	0.016333
2	0.197176	1.293	0.101462
3	-0.039065	-0.2562	0.399522
4	-0.13706	-0.8988	0.186892
5	-0.053352	-0.3499	0.364078
6	-0.194944	-1.2783	0.103994
7	-0.104403	-0.6846	0.24863
8	-0.079151	-0.519	0.303202
9	0.029006	0.1902	0.425021
10	0.155067	1.0168	0.157458
11	-0.006541	-0.0429	0.482993
12	-0.148673	-0.9749	0.167529
13	-0.135427	-0.8881	0.189725
14	-0.105903	-0.6945	0.245567
15	-0.01435	-0.0941	0.462734
16	0.130433	0.8553	0.198562

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.336638 & 2.2075 & 0.016333 \tabularnewline
2 & 0.197176 & 1.293 & 0.101462 \tabularnewline
3 & -0.039065 & -0.2562 & 0.399522 \tabularnewline
4 & -0.13706 & -0.8988 & 0.186892 \tabularnewline
5 & -0.053352 & -0.3499 & 0.364078 \tabularnewline
6 & -0.194944 & -1.2783 & 0.103994 \tabularnewline
7 & -0.104403 & -0.6846 & 0.24863 \tabularnewline
8 & -0.079151 & -0.519 & 0.303202 \tabularnewline
9 & 0.029006 & 0.1902 & 0.425021 \tabularnewline
10 & 0.155067 & 1.0168 & 0.157458 \tabularnewline
11 & -0.006541 & -0.0429 & 0.482993 \tabularnewline
12 & -0.148673 & -0.9749 & 0.167529 \tabularnewline
13 & -0.135427 & -0.8881 & 0.189725 \tabularnewline
14 & -0.105903 & -0.6945 & 0.245567 \tabularnewline
15 & -0.01435 & -0.0941 & 0.462734 \tabularnewline
16 & 0.130433 & 0.8553 & 0.198562 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301505&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]0.336638[/C][C]2.2075[/C][C]0.016333[/C][/ROW]
[ROW][C]2[/C][C]0.197176[/C][C]1.293[/C][C]0.101462[/C][/ROW]
[ROW][C]3[/C][C]-0.039065[/C][C]-0.2562[/C][C]0.399522[/C][/ROW]
[ROW][C]4[/C][C]-0.13706[/C][C]-0.8988[/C][C]0.186892[/C][/ROW]
[ROW][C]5[/C][C]-0.053352[/C][C]-0.3499[/C][C]0.364078[/C][/ROW]
[ROW][C]6[/C][C]-0.194944[/C][C]-1.2783[/C][C]0.103994[/C][/ROW]
[ROW][C]7[/C][C]-0.104403[/C][C]-0.6846[/C][C]0.24863[/C][/ROW]
[ROW][C]8[/C][C]-0.079151[/C][C]-0.519[/C][C]0.303202[/C][/ROW]
[ROW][C]9[/C][C]0.029006[/C][C]0.1902[/C][C]0.425021[/C][/ROW]
[ROW][C]10[/C][C]0.155067[/C][C]1.0168[/C][C]0.157458[/C][/ROW]
[ROW][C]11[/C][C]-0.006541[/C][C]-0.0429[/C][C]0.482993[/C][/ROW]
[ROW][C]12[/C][C]-0.148673[/C][C]-0.9749[/C][C]0.167529[/C][/ROW]
[ROW][C]13[/C][C]-0.135427[/C][C]-0.8881[/C][C]0.189725[/C][/ROW]
[ROW][C]14[/C][C]-0.105903[/C][C]-0.6945[/C][C]0.245567[/C][/ROW]
[ROW][C]15[/C][C]-0.01435[/C][C]-0.0941[/C][C]0.462734[/C][/ROW]
[ROW][C]16[/C][C]0.130433[/C][C]0.8553[/C][C]0.198562[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301505&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301505&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	0.336638	2.2075	0.016333
2	0.197176	1.293	0.101462
3	-0.039065	-0.2562	0.399522
4	-0.13706	-0.8988	0.186892
5	-0.053352	-0.3499	0.364078
6	-0.194944	-1.2783	0.103994
7	-0.104403	-0.6846	0.24863
8	-0.079151	-0.519	0.303202
9	0.029006	0.1902	0.425021
10	0.155067	1.0168	0.157458
11	-0.006541	-0.0429	0.482993
12	-0.148673	-0.9749	0.167529
13	-0.135427	-0.8881	0.189725
14	-0.105903	-0.6945	0.245567
15	-0.01435	-0.0941	0.462734
16	0.130433	0.8553	0.198562

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.336638	2.2075	0.016333
2	0.094568	0.6201	0.269223
3	-0.149076	-0.9776	0.16688
4	-0.11874	-0.7786	0.22023
5	0.066048	0.4331	0.333552
6	-0.184524	-1.21	0.116443
7	-0.025182	-0.1651	0.434809
8	0.008004	0.0525	0.479193
9	0.058486	0.3835	0.351613
10	0.104596	0.6859	0.248235
11	-0.135945	-0.8915	0.188824
12	-0.228809	-1.5004	0.070409
13	0.018205	0.1194	0.452765
14	0.015042	0.0986	0.460943
15	-0.00994	-0.0652	0.474165
16	0.192116	1.2598	0.10727

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.336638 & 2.2075 & 0.016333 \tabularnewline
2 & 0.094568 & 0.6201 & 0.269223 \tabularnewline
3 & -0.149076 & -0.9776 & 0.16688 \tabularnewline
4 & -0.11874 & -0.7786 & 0.22023 \tabularnewline
5 & 0.066048 & 0.4331 & 0.333552 \tabularnewline
6 & -0.184524 & -1.21 & 0.116443 \tabularnewline
7 & -0.025182 & -0.1651 & 0.434809 \tabularnewline
8 & 0.008004 & 0.0525 & 0.479193 \tabularnewline
9 & 0.058486 & 0.3835 & 0.351613 \tabularnewline
10 & 0.104596 & 0.6859 & 0.248235 \tabularnewline
11 & -0.135945 & -0.8915 & 0.188824 \tabularnewline
12 & -0.228809 & -1.5004 & 0.070409 \tabularnewline
13 & 0.018205 & 0.1194 & 0.452765 \tabularnewline
14 & 0.015042 & 0.0986 & 0.460943 \tabularnewline
15 & -0.00994 & -0.0652 & 0.474165 \tabularnewline
16 & 0.192116 & 1.2598 & 0.10727 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301505&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]0.336638[/C][C]2.2075[/C][C]0.016333[/C][/ROW]
[ROW][C]2[/C][C]0.094568[/C][C]0.6201[/C][C]0.269223[/C][/ROW]
[ROW][C]3[/C][C]-0.149076[/C][C]-0.9776[/C][C]0.16688[/C][/ROW]
[ROW][C]4[/C][C]-0.11874[/C][C]-0.7786[/C][C]0.22023[/C][/ROW]
[ROW][C]5[/C][C]0.066048[/C][C]0.4331[/C][C]0.333552[/C][/ROW]
[ROW][C]6[/C][C]-0.184524[/C][C]-1.21[/C][C]0.116443[/C][/ROW]
[ROW][C]7[/C][C]-0.025182[/C][C]-0.1651[/C][C]0.434809[/C][/ROW]
[ROW][C]8[/C][C]0.008004[/C][C]0.0525[/C][C]0.479193[/C][/ROW]
[ROW][C]9[/C][C]0.058486[/C][C]0.3835[/C][C]0.351613[/C][/ROW]
[ROW][C]10[/C][C]0.104596[/C][C]0.6859[/C][C]0.248235[/C][/ROW]
[ROW][C]11[/C][C]-0.135945[/C][C]-0.8915[/C][C]0.188824[/C][/ROW]
[ROW][C]12[/C][C]-0.228809[/C][C]-1.5004[/C][C]0.070409[/C][/ROW]
[ROW][C]13[/C][C]0.018205[/C][C]0.1194[/C][C]0.452765[/C][/ROW]
[ROW][C]14[/C][C]0.015042[/C][C]0.0986[/C][C]0.460943[/C][/ROW]
[ROW][C]15[/C][C]-0.00994[/C][C]-0.0652[/C][C]0.474165[/C][/ROW]
[ROW][C]16[/C][C]0.192116[/C][C]1.2598[/C][C]0.10727[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301505&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301505&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	0.336638	2.2075	0.016333
2	0.094568	0.6201	0.269223
3	-0.149076	-0.9776	0.16688
4	-0.11874	-0.7786	0.22023
5	0.066048	0.4331	0.333552
6	-0.184524	-1.21	0.116443
7	-0.025182	-0.1651	0.434809
8	0.008004	0.0525	0.479193
9	0.058486	0.3835	0.351613
10	0.104596	0.6859	0.248235
11	-0.135945	-0.8915	0.188824
12	-0.228809	-1.5004	0.070409
13	0.018205	0.1194	0.452765
14	0.015042	0.0986	0.460943
15	-0.00994	-0.0652	0.474165
16	0.192116	1.2598	0.10727

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
par2 <- '1'
par1 <- 'Default'
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