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

Fri, 22 May 2015 12:08:27 +0100

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/May/22/t1432292965xvzwxgu8ezfp747.htm/, Retrieved Fri, 03 May 2024 14:50:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279217, Retrieved Fri, 03 May 2024 14:50:36 +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

124

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

-       [(Partial) Autocorrelation Function] [consumentenprijze...] [2015-05-22 11:08:27] [0793dda36b6d92f80d1980fc1d00d6bd] [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	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=279217&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=279217&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279217&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	0.3367	3.2817	0.000722
2	-0.206972	-2.0173	0.023242
3	-0.565756	-5.5143	0
4	-0.304714	-2.97	0.001885
5	0.207306	2.0206	0.02307
6	0.393307	3.8335	0.000114
7	0.139196	1.3567	0.089043
8	-0.358717	-3.4963	0.000359
9	-0.534773	-5.2123	1e-06
10	-0.160656	-1.5659	0.06035
11	0.320277	3.1217	0.001191
12	0.723921	7.0559	0
13	0.242565	2.3642	0.010051
14	-0.230057	-2.2423	0.013633
15	-0.477529	-4.6544	5e-06
16	-0.230906	-2.2506	0.013359
17	0.178471	1.7395	0.042591
18	0.346816	3.3803	0.000526
19	0.043085	0.4199	0.337737

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.3367 & 3.2817 & 0.000722 \tabularnewline
2 & -0.206972 & -2.0173 & 0.023242 \tabularnewline
3 & -0.565756 & -5.5143 & 0 \tabularnewline
4 & -0.304714 & -2.97 & 0.001885 \tabularnewline
5 & 0.207306 & 2.0206 & 0.02307 \tabularnewline
6 & 0.393307 & 3.8335 & 0.000114 \tabularnewline
7 & 0.139196 & 1.3567 & 0.089043 \tabularnewline
8 & -0.358717 & -3.4963 & 0.000359 \tabularnewline
9 & -0.534773 & -5.2123 & 1e-06 \tabularnewline
10 & -0.160656 & -1.5659 & 0.06035 \tabularnewline
11 & 0.320277 & 3.1217 & 0.001191 \tabularnewline
12 & 0.723921 & 7.0559 & 0 \tabularnewline
13 & 0.242565 & 2.3642 & 0.010051 \tabularnewline
14 & -0.230057 & -2.2423 & 0.013633 \tabularnewline
15 & -0.477529 & -4.6544 & 5e-06 \tabularnewline
16 & -0.230906 & -2.2506 & 0.013359 \tabularnewline
17 & 0.178471 & 1.7395 & 0.042591 \tabularnewline
18 & 0.346816 & 3.3803 & 0.000526 \tabularnewline
19 & 0.043085 & 0.4199 & 0.337737 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279217&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]0.3367[/C][C]3.2817[/C][C]0.000722[/C][/ROW]
[ROW][C]2[/C][C]-0.206972[/C][C]-2.0173[/C][C]0.023242[/C][/ROW]
[ROW][C]3[/C][C]-0.565756[/C][C]-5.5143[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.304714[/C][C]-2.97[/C][C]0.001885[/C][/ROW]
[ROW][C]5[/C][C]0.207306[/C][C]2.0206[/C][C]0.02307[/C][/ROW]
[ROW][C]6[/C][C]0.393307[/C][C]3.8335[/C][C]0.000114[/C][/ROW]
[ROW][C]7[/C][C]0.139196[/C][C]1.3567[/C][C]0.089043[/C][/ROW]
[ROW][C]8[/C][C]-0.358717[/C][C]-3.4963[/C][C]0.000359[/C][/ROW]
[ROW][C]9[/C][C]-0.534773[/C][C]-5.2123[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]-0.160656[/C][C]-1.5659[/C][C]0.06035[/C][/ROW]
[ROW][C]11[/C][C]0.320277[/C][C]3.1217[/C][C]0.001191[/C][/ROW]
[ROW][C]12[/C][C]0.723921[/C][C]7.0559[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.242565[/C][C]2.3642[/C][C]0.010051[/C][/ROW]
[ROW][C]14[/C][C]-0.230057[/C][C]-2.2423[/C][C]0.013633[/C][/ROW]
[ROW][C]15[/C][C]-0.477529[/C][C]-4.6544[/C][C]5e-06[/C][/ROW]
[ROW][C]16[/C][C]-0.230906[/C][C]-2.2506[/C][C]0.013359[/C][/ROW]
[ROW][C]17[/C][C]0.178471[/C][C]1.7395[/C][C]0.042591[/C][/ROW]
[ROW][C]18[/C][C]0.346816[/C][C]3.3803[/C][C]0.000526[/C][/ROW]
[ROW][C]19[/C][C]0.043085[/C][C]0.4199[/C][C]0.337737[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279217&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279217&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	0.3367	3.2817	0.000722
2	-0.206972	-2.0173	0.023242
3	-0.565756	-5.5143	0
4	-0.304714	-2.97	0.001885
5	0.207306	2.0206	0.02307
6	0.393307	3.8335	0.000114
7	0.139196	1.3567	0.089043
8	-0.358717	-3.4963	0.000359
9	-0.534773	-5.2123	1e-06
10	-0.160656	-1.5659	0.06035
11	0.320277	3.1217	0.001191
12	0.723921	7.0559	0
13	0.242565	2.3642	0.010051
14	-0.230057	-2.2423	0.013633
15	-0.477529	-4.6544	5e-06
16	-0.230906	-2.2506	0.013359
17	0.178471	1.7395	0.042591
18	0.346816	3.3803	0.000526
19	0.043085	0.4199	0.337737

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.3367	3.2817	0.000722
2	-0.361298	-3.5215	0.000331
3	-0.453034	-4.4156	1.3e-05
4	-0.028185	-0.2747	0.392065
5	0.198091	1.9308	0.028248
6	-0.009479	-0.0924	0.463291
7	-0.153526	-1.4964	0.068934
8	-0.300976	-2.9335	0.0021
9	-0.26462	-2.5792	0.005719
10	0.005914	0.0576	0.477078
11	0.029237	0.285	0.388145
12	0.462118	4.5042	9e-06
13	-0.090704	-0.8841	0.189444
14	0.009618	0.0937	0.462755
15	0.05625	0.5483	0.2924
16	-0.071963	-0.7014	0.242382
17	-0.170135	-1.6583	0.05028
18	0.001381	0.0135	0.494646
19	-0.166231	-1.6202	0.05425

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.3367 & 3.2817 & 0.000722 \tabularnewline
2 & -0.361298 & -3.5215 & 0.000331 \tabularnewline
3 & -0.453034 & -4.4156 & 1.3e-05 \tabularnewline
4 & -0.028185 & -0.2747 & 0.392065 \tabularnewline
5 & 0.198091 & 1.9308 & 0.028248 \tabularnewline
6 & -0.009479 & -0.0924 & 0.463291 \tabularnewline
7 & -0.153526 & -1.4964 & 0.068934 \tabularnewline
8 & -0.300976 & -2.9335 & 0.0021 \tabularnewline
9 & -0.26462 & -2.5792 & 0.005719 \tabularnewline
10 & 0.005914 & 0.0576 & 0.477078 \tabularnewline
11 & 0.029237 & 0.285 & 0.388145 \tabularnewline
12 & 0.462118 & 4.5042 & 9e-06 \tabularnewline
13 & -0.090704 & -0.8841 & 0.189444 \tabularnewline
14 & 0.009618 & 0.0937 & 0.462755 \tabularnewline
15 & 0.05625 & 0.5483 & 0.2924 \tabularnewline
16 & -0.071963 & -0.7014 & 0.242382 \tabularnewline
17 & -0.170135 & -1.6583 & 0.05028 \tabularnewline
18 & 0.001381 & 0.0135 & 0.494646 \tabularnewline
19 & -0.166231 & -1.6202 & 0.05425 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279217&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]0.3367[/C][C]3.2817[/C][C]0.000722[/C][/ROW]
[ROW][C]2[/C][C]-0.361298[/C][C]-3.5215[/C][C]0.000331[/C][/ROW]
[ROW][C]3[/C][C]-0.453034[/C][C]-4.4156[/C][C]1.3e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.028185[/C][C]-0.2747[/C][C]0.392065[/C][/ROW]
[ROW][C]5[/C][C]0.198091[/C][C]1.9308[/C][C]0.028248[/C][/ROW]
[ROW][C]6[/C][C]-0.009479[/C][C]-0.0924[/C][C]0.463291[/C][/ROW]
[ROW][C]7[/C][C]-0.153526[/C][C]-1.4964[/C][C]0.068934[/C][/ROW]
[ROW][C]8[/C][C]-0.300976[/C][C]-2.9335[/C][C]0.0021[/C][/ROW]
[ROW][C]9[/C][C]-0.26462[/C][C]-2.5792[/C][C]0.005719[/C][/ROW]
[ROW][C]10[/C][C]0.005914[/C][C]0.0576[/C][C]0.477078[/C][/ROW]
[ROW][C]11[/C][C]0.029237[/C][C]0.285[/C][C]0.388145[/C][/ROW]
[ROW][C]12[/C][C]0.462118[/C][C]4.5042[/C][C]9e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.090704[/C][C]-0.8841[/C][C]0.189444[/C][/ROW]
[ROW][C]14[/C][C]0.009618[/C][C]0.0937[/C][C]0.462755[/C][/ROW]
[ROW][C]15[/C][C]0.05625[/C][C]0.5483[/C][C]0.2924[/C][/ROW]
[ROW][C]16[/C][C]-0.071963[/C][C]-0.7014[/C][C]0.242382[/C][/ROW]
[ROW][C]17[/C][C]-0.170135[/C][C]-1.6583[/C][C]0.05028[/C][/ROW]
[ROW][C]18[/C][C]0.001381[/C][C]0.0135[/C][C]0.494646[/C][/ROW]
[ROW][C]19[/C][C]-0.166231[/C][C]-1.6202[/C][C]0.05425[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279217&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279217&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	0.3367	3.2817	0.000722
2	-0.361298	-3.5215	0.000331
3	-0.453034	-4.4156	1.3e-05
4	-0.028185	-0.2747	0.392065
5	0.198091	1.9308	0.028248
6	-0.009479	-0.0924	0.463291
7	-0.153526	-1.4964	0.068934
8	-0.300976	-2.9335	0.0021
9	-0.26462	-2.5792	0.005719
10	0.005914	0.0576	0.477078
11	0.029237	0.285	0.388145
12	0.462118	4.5042	9e-06
13	-0.090704	-0.8841	0.189444
14	0.009618	0.0937	0.462755
15	0.05625	0.5483	0.2924
16	-0.071963	-0.7014	0.242382
17	-0.170135	-1.6583	0.05028
18	0.001381	0.0135	0.494646
19	-0.166231	-1.6202	0.05425

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