Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 18 Nov 2015 14:48:56 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/18/t1447858233yadiqst3he6zi7r.htm/, Retrieved Tue, 14 May 2024 19:18:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283498, Retrieved Tue, 14 May 2024 19:18:46 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

137

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

-       [(Partial) Autocorrelation Function] [] [2015-11-18 14:48:56] [64c14b596f7fde091cf1a84a44b2a252] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283498&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283498&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283498&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	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.468584	3.5993	0.000327
2	0.024048	0.1847	0.427043
3	-0.071343	-0.548	0.29288
4	-0.040001	-0.3072	0.379868
5	-0.061826	-0.4749	0.318308
6	0.038503	0.2957	0.384231
7	0.024908	0.1913	0.424465
8	-0.122141	-0.9382	0.175988
9	-0.166728	-1.2807	0.102663
10	-0.08755	-0.6725	0.25195
11	0.004816	0.037	0.485307
12	0.060278	0.463	0.322532
13	-0.03669	-0.2818	0.389535
14	-0.060383	-0.4638	0.322244
15	-0.000743	-0.0057	0.497734
16	0.028951	0.2224	0.412395
17	-0.03383	-0.2599	0.39794

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.468584 & 3.5993 & 0.000327 \tabularnewline
2 & 0.024048 & 0.1847 & 0.427043 \tabularnewline
3 & -0.071343 & -0.548 & 0.29288 \tabularnewline
4 & -0.040001 & -0.3072 & 0.379868 \tabularnewline
5 & -0.061826 & -0.4749 & 0.318308 \tabularnewline
6 & 0.038503 & 0.2957 & 0.384231 \tabularnewline
7 & 0.024908 & 0.1913 & 0.424465 \tabularnewline
8 & -0.122141 & -0.9382 & 0.175988 \tabularnewline
9 & -0.166728 & -1.2807 & 0.102663 \tabularnewline
10 & -0.08755 & -0.6725 & 0.25195 \tabularnewline
11 & 0.004816 & 0.037 & 0.485307 \tabularnewline
12 & 0.060278 & 0.463 & 0.322532 \tabularnewline
13 & -0.03669 & -0.2818 & 0.389535 \tabularnewline
14 & -0.060383 & -0.4638 & 0.322244 \tabularnewline
15 & -0.000743 & -0.0057 & 0.497734 \tabularnewline
16 & 0.028951 & 0.2224 & 0.412395 \tabularnewline
17 & -0.03383 & -0.2599 & 0.39794 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283498&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]0.468584[/C][C]3.5993[/C][C]0.000327[/C][/ROW]
[ROW][C]2[/C][C]0.024048[/C][C]0.1847[/C][C]0.427043[/C][/ROW]
[ROW][C]3[/C][C]-0.071343[/C][C]-0.548[/C][C]0.29288[/C][/ROW]
[ROW][C]4[/C][C]-0.040001[/C][C]-0.3072[/C][C]0.379868[/C][/ROW]
[ROW][C]5[/C][C]-0.061826[/C][C]-0.4749[/C][C]0.318308[/C][/ROW]
[ROW][C]6[/C][C]0.038503[/C][C]0.2957[/C][C]0.384231[/C][/ROW]
[ROW][C]7[/C][C]0.024908[/C][C]0.1913[/C][C]0.424465[/C][/ROW]
[ROW][C]8[/C][C]-0.122141[/C][C]-0.9382[/C][C]0.175988[/C][/ROW]
[ROW][C]9[/C][C]-0.166728[/C][C]-1.2807[/C][C]0.102663[/C][/ROW]
[ROW][C]10[/C][C]-0.08755[/C][C]-0.6725[/C][C]0.25195[/C][/ROW]
[ROW][C]11[/C][C]0.004816[/C][C]0.037[/C][C]0.485307[/C][/ROW]
[ROW][C]12[/C][C]0.060278[/C][C]0.463[/C][C]0.322532[/C][/ROW]
[ROW][C]13[/C][C]-0.03669[/C][C]-0.2818[/C][C]0.389535[/C][/ROW]
[ROW][C]14[/C][C]-0.060383[/C][C]-0.4638[/C][C]0.322244[/C][/ROW]
[ROW][C]15[/C][C]-0.000743[/C][C]-0.0057[/C][C]0.497734[/C][/ROW]
[ROW][C]16[/C][C]0.028951[/C][C]0.2224[/C][C]0.412395[/C][/ROW]
[ROW][C]17[/C][C]-0.03383[/C][C]-0.2599[/C][C]0.39794[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283498&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283498&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	0.468584	3.5993	0.000327
2	0.024048	0.1847	0.427043
3	-0.071343	-0.548	0.29288
4	-0.040001	-0.3072	0.379868
5	-0.061826	-0.4749	0.318308
6	0.038503	0.2957	0.384231
7	0.024908	0.1913	0.424465
8	-0.122141	-0.9382	0.175988
9	-0.166728	-1.2807	0.102663
10	-0.08755	-0.6725	0.25195
11	0.004816	0.037	0.485307
12	0.060278	0.463	0.322532
13	-0.03669	-0.2818	0.389535
14	-0.060383	-0.4638	0.322244
15	-0.000743	-0.0057	0.497734
16	0.028951	0.2224	0.412395
17	-0.03383	-0.2599	0.39794

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.468584	3.5993	0.000327
2	-0.250533	-1.9244	0.029567
3	0.043695	0.3356	0.36917
4	-0.015407	-0.1183	0.453098
5	-0.071215	-0.547	0.293217
6	0.136859	1.0512	0.148719
7	-0.098861	-0.7594	0.225328
8	-0.131271	-1.0083	0.158712
9	-0.022232	-0.1708	0.432495
10	-0.022919	-0.176	0.430432
11	0.043186	0.3317	0.370639
12	0.027407	0.2105	0.416996
13	-0.154137	-1.1839	0.120591
14	0.06535	0.502	0.308781
15	0.029125	0.2237	0.411875
16	-0.025996	-0.1997	0.42121
17	-0.066426	-0.5102	0.305897

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.468584 & 3.5993 & 0.000327 \tabularnewline
2 & -0.250533 & -1.9244 & 0.029567 \tabularnewline
3 & 0.043695 & 0.3356 & 0.36917 \tabularnewline
4 & -0.015407 & -0.1183 & 0.453098 \tabularnewline
5 & -0.071215 & -0.547 & 0.293217 \tabularnewline
6 & 0.136859 & 1.0512 & 0.148719 \tabularnewline
7 & -0.098861 & -0.7594 & 0.225328 \tabularnewline
8 & -0.131271 & -1.0083 & 0.158712 \tabularnewline
9 & -0.022232 & -0.1708 & 0.432495 \tabularnewline
10 & -0.022919 & -0.176 & 0.430432 \tabularnewline
11 & 0.043186 & 0.3317 & 0.370639 \tabularnewline
12 & 0.027407 & 0.2105 & 0.416996 \tabularnewline
13 & -0.154137 & -1.1839 & 0.120591 \tabularnewline
14 & 0.06535 & 0.502 & 0.308781 \tabularnewline
15 & 0.029125 & 0.2237 & 0.411875 \tabularnewline
16 & -0.025996 & -0.1997 & 0.42121 \tabularnewline
17 & -0.066426 & -0.5102 & 0.305897 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283498&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]0.468584[/C][C]3.5993[/C][C]0.000327[/C][/ROW]
[ROW][C]2[/C][C]-0.250533[/C][C]-1.9244[/C][C]0.029567[/C][/ROW]
[ROW][C]3[/C][C]0.043695[/C][C]0.3356[/C][C]0.36917[/C][/ROW]
[ROW][C]4[/C][C]-0.015407[/C][C]-0.1183[/C][C]0.453098[/C][/ROW]
[ROW][C]5[/C][C]-0.071215[/C][C]-0.547[/C][C]0.293217[/C][/ROW]
[ROW][C]6[/C][C]0.136859[/C][C]1.0512[/C][C]0.148719[/C][/ROW]
[ROW][C]7[/C][C]-0.098861[/C][C]-0.7594[/C][C]0.225328[/C][/ROW]
[ROW][C]8[/C][C]-0.131271[/C][C]-1.0083[/C][C]0.158712[/C][/ROW]
[ROW][C]9[/C][C]-0.022232[/C][C]-0.1708[/C][C]0.432495[/C][/ROW]
[ROW][C]10[/C][C]-0.022919[/C][C]-0.176[/C][C]0.430432[/C][/ROW]
[ROW][C]11[/C][C]0.043186[/C][C]0.3317[/C][C]0.370639[/C][/ROW]
[ROW][C]12[/C][C]0.027407[/C][C]0.2105[/C][C]0.416996[/C][/ROW]
[ROW][C]13[/C][C]-0.154137[/C][C]-1.1839[/C][C]0.120591[/C][/ROW]
[ROW][C]14[/C][C]0.06535[/C][C]0.502[/C][C]0.308781[/C][/ROW]
[ROW][C]15[/C][C]0.029125[/C][C]0.2237[/C][C]0.411875[/C][/ROW]
[ROW][C]16[/C][C]-0.025996[/C][C]-0.1997[/C][C]0.42121[/C][/ROW]
[ROW][C]17[/C][C]-0.066426[/C][C]-0.5102[/C][C]0.305897[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283498&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283498&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	0.468584	3.5993	0.000327
2	-0.250533	-1.9244	0.029567
3	0.043695	0.3356	0.36917
4	-0.015407	-0.1183	0.453098
5	-0.071215	-0.547	0.293217
6	0.136859	1.0512	0.148719
7	-0.098861	-0.7594	0.225328
8	-0.131271	-1.0083	0.158712
9	-0.022232	-0.1708	0.432495
10	-0.022919	-0.176	0.430432
11	0.043186	0.3317	0.370639
12	0.027407	0.2105	0.416996
13	-0.154137	-1.1839	0.120591
14	0.06535	0.502	0.308781
15	0.029125	0.2237	0.411875
16	-0.025996	-0.1997	0.42121
17	-0.066426	-0.5102	0.305897

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 = 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)
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code