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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 01 Dec 2016 11:16:35 +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/01/t14805875759kbkfwv9zzxnn46.htm/, Retrieved Thu, 02 May 2024 10:43:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297510, Retrieved Thu, 02 May 2024 10:43:00 +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] [(Partial) Autocor...] [2016-12-01 10:16:35] [2322cf848a5cbdeb3105c2829b69db5d] [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=297510&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=297510&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297510&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	0.303351	1.7688	0.042947
2	0.228291	1.3312	0.095998
3	0.158973	0.927	0.18024
4	0.069504	0.4053	0.343907
5	-0.068775	-0.401	0.345456
6	-0.42969	-2.5055	0.00859
7	-0.210908	-1.2298	0.113608
8	-0.031131	-0.1815	0.428517
9	-0.079372	-0.4628	0.323222
10	-0.057513	-0.3354	0.369708
11	0.050346	0.2936	0.385438
12	0.135866	0.7922	0.216861
13	0.134222	0.7826	0.219627
14	-0.02595	-0.1513	0.440311
15	-0.009187	-0.0536	0.478795

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.303351 & 1.7688 & 0.042947 \tabularnewline
2 & 0.228291 & 1.3312 & 0.095998 \tabularnewline
3 & 0.158973 & 0.927 & 0.18024 \tabularnewline
4 & 0.069504 & 0.4053 & 0.343907 \tabularnewline
5 & -0.068775 & -0.401 & 0.345456 \tabularnewline
6 & -0.42969 & -2.5055 & 0.00859 \tabularnewline
7 & -0.210908 & -1.2298 & 0.113608 \tabularnewline
8 & -0.031131 & -0.1815 & 0.428517 \tabularnewline
9 & -0.079372 & -0.4628 & 0.323222 \tabularnewline
10 & -0.057513 & -0.3354 & 0.369708 \tabularnewline
11 & 0.050346 & 0.2936 & 0.385438 \tabularnewline
12 & 0.135866 & 0.7922 & 0.216861 \tabularnewline
13 & 0.134222 & 0.7826 & 0.219627 \tabularnewline
14 & -0.02595 & -0.1513 & 0.440311 \tabularnewline
15 & -0.009187 & -0.0536 & 0.478795 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297510&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]0.303351[/C][C]1.7688[/C][C]0.042947[/C][/ROW]
[ROW][C]2[/C][C]0.228291[/C][C]1.3312[/C][C]0.095998[/C][/ROW]
[ROW][C]3[/C][C]0.158973[/C][C]0.927[/C][C]0.18024[/C][/ROW]
[ROW][C]4[/C][C]0.069504[/C][C]0.4053[/C][C]0.343907[/C][/ROW]
[ROW][C]5[/C][C]-0.068775[/C][C]-0.401[/C][C]0.345456[/C][/ROW]
[ROW][C]6[/C][C]-0.42969[/C][C]-2.5055[/C][C]0.00859[/C][/ROW]
[ROW][C]7[/C][C]-0.210908[/C][C]-1.2298[/C][C]0.113608[/C][/ROW]
[ROW][C]8[/C][C]-0.031131[/C][C]-0.1815[/C][C]0.428517[/C][/ROW]
[ROW][C]9[/C][C]-0.079372[/C][C]-0.4628[/C][C]0.323222[/C][/ROW]
[ROW][C]10[/C][C]-0.057513[/C][C]-0.3354[/C][C]0.369708[/C][/ROW]
[ROW][C]11[/C][C]0.050346[/C][C]0.2936[/C][C]0.385438[/C][/ROW]
[ROW][C]12[/C][C]0.135866[/C][C]0.7922[/C][C]0.216861[/C][/ROW]
[ROW][C]13[/C][C]0.134222[/C][C]0.7826[/C][C]0.219627[/C][/ROW]
[ROW][C]14[/C][C]-0.02595[/C][C]-0.1513[/C][C]0.440311[/C][/ROW]
[ROW][C]15[/C][C]-0.009187[/C][C]-0.0536[/C][C]0.478795[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297510&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297510&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	0.303351	1.7688	0.042947
2	0.228291	1.3312	0.095998
3	0.158973	0.927	0.18024
4	0.069504	0.4053	0.343907
5	-0.068775	-0.401	0.345456
6	-0.42969	-2.5055	0.00859
7	-0.210908	-1.2298	0.113608
8	-0.031131	-0.1815	0.428517
9	-0.079372	-0.4628	0.323222
10	-0.057513	-0.3354	0.369708
11	0.050346	0.2936	0.385438
12	0.135866	0.7922	0.216861
13	0.134222	0.7826	0.219627
14	-0.02595	-0.1513	0.440311
15	-0.009187	-0.0536	0.478795

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.303351	1.7688	0.042947
2	0.15008	0.8751	0.193828
3	0.061504	0.3586	0.361045
4	-0.021845	-0.1274	0.449696
5	-0.131943	-0.7694	0.223498
6	-0.459347	-2.6784	0.005656
7	0.003066	0.0179	0.49292
8	0.268011	1.5628	0.063685
9	0.08855	0.5163	0.304483
10	-0.02239	-0.1306	0.448447
11	-0.019681	-0.1148	0.454656
12	-0.162858	-0.9496	0.174504
13	0.013104	0.0764	0.46977
14	0.041292	0.2408	0.40559
15	0.006169	0.036	0.485757

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.303351 & 1.7688 & 0.042947 \tabularnewline
2 & 0.15008 & 0.8751 & 0.193828 \tabularnewline
3 & 0.061504 & 0.3586 & 0.361045 \tabularnewline
4 & -0.021845 & -0.1274 & 0.449696 \tabularnewline
5 & -0.131943 & -0.7694 & 0.223498 \tabularnewline
6 & -0.459347 & -2.6784 & 0.005656 \tabularnewline
7 & 0.003066 & 0.0179 & 0.49292 \tabularnewline
8 & 0.268011 & 1.5628 & 0.063685 \tabularnewline
9 & 0.08855 & 0.5163 & 0.304483 \tabularnewline
10 & -0.02239 & -0.1306 & 0.448447 \tabularnewline
11 & -0.019681 & -0.1148 & 0.454656 \tabularnewline
12 & -0.162858 & -0.9496 & 0.174504 \tabularnewline
13 & 0.013104 & 0.0764 & 0.46977 \tabularnewline
14 & 0.041292 & 0.2408 & 0.40559 \tabularnewline
15 & 0.006169 & 0.036 & 0.485757 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297510&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]0.303351[/C][C]1.7688[/C][C]0.042947[/C][/ROW]
[ROW][C]2[/C][C]0.15008[/C][C]0.8751[/C][C]0.193828[/C][/ROW]
[ROW][C]3[/C][C]0.061504[/C][C]0.3586[/C][C]0.361045[/C][/ROW]
[ROW][C]4[/C][C]-0.021845[/C][C]-0.1274[/C][C]0.449696[/C][/ROW]
[ROW][C]5[/C][C]-0.131943[/C][C]-0.7694[/C][C]0.223498[/C][/ROW]
[ROW][C]6[/C][C]-0.459347[/C][C]-2.6784[/C][C]0.005656[/C][/ROW]
[ROW][C]7[/C][C]0.003066[/C][C]0.0179[/C][C]0.49292[/C][/ROW]
[ROW][C]8[/C][C]0.268011[/C][C]1.5628[/C][C]0.063685[/C][/ROW]
[ROW][C]9[/C][C]0.08855[/C][C]0.5163[/C][C]0.304483[/C][/ROW]
[ROW][C]10[/C][C]-0.02239[/C][C]-0.1306[/C][C]0.448447[/C][/ROW]
[ROW][C]11[/C][C]-0.019681[/C][C]-0.1148[/C][C]0.454656[/C][/ROW]
[ROW][C]12[/C][C]-0.162858[/C][C]-0.9496[/C][C]0.174504[/C][/ROW]
[ROW][C]13[/C][C]0.013104[/C][C]0.0764[/C][C]0.46977[/C][/ROW]
[ROW][C]14[/C][C]0.041292[/C][C]0.2408[/C][C]0.40559[/C][/ROW]
[ROW][C]15[/C][C]0.006169[/C][C]0.036[/C][C]0.485757[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297510&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297510&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	0.303351	1.7688	0.042947
2	0.15008	0.8751	0.193828
3	0.061504	0.3586	0.361045
4	-0.021845	-0.1274	0.449696
5	-0.131943	-0.7694	0.223498
6	-0.459347	-2.6784	0.005656
7	0.003066	0.0179	0.49292
8	0.268011	1.5628	0.063685
9	0.08855	0.5163	0.304483
10	-0.02239	-0.1306	0.448447
11	-0.019681	-0.1148	0.454656
12	-0.162858	-0.9496	0.174504
13	0.013104	0.0764	0.46977
14	0.041292	0.2408	0.40559
15	0.006169	0.036	0.485757

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 = 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