Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 16 Dec 2010 20:13:36 +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/2010/Dec/16/t1292530281fv46lday2ywrsgg.htm/, Retrieved Fri, 03 May 2024 11:24:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111254, Retrieved Fri, 03 May 2024 11:24:55 +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

182

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

-       [(Partial) Autocorrelation Function] [] [2010-12-16 20:13:36] [e7b77eb06cdf8868fc9cf2043e42b3da] [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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111254&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111254&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111254&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.488322	-5.0512	1e-06
2	-0.109251	-1.1301	0.130481
3	0.258725	2.6763	0.004308
4	-0.161337	-1.6689	0.049032
5	0.009217	0.0953	0.462109
6	0.009324	0.0964	0.461673
7	0.035417	0.3664	0.357412
8	-0.153779	-1.5907	0.057314
9	0.179324	1.8549	0.033179
10	-0.069387	-0.7177	0.237238
11	-0.142049	-1.4694	0.072334
12	0.33925	3.5092	0.000329
13	-0.238785	-2.47	0.007546
14	0.022945	0.2373	0.406421
15	0.145358	1.5036	0.067816
16	-0.167816	-1.7359	0.04273
17	0.029427	0.3044	0.38071
18	0.089551	0.9263	0.178182
19	-0.075391	-0.7798	0.218601
20	-0.078	-0.8068	0.210774

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.488322 & -5.0512 & 1e-06 \tabularnewline
2 & -0.109251 & -1.1301 & 0.130481 \tabularnewline
3 & 0.258725 & 2.6763 & 0.004308 \tabularnewline
4 & -0.161337 & -1.6689 & 0.049032 \tabularnewline
5 & 0.009217 & 0.0953 & 0.462109 \tabularnewline
6 & 0.009324 & 0.0964 & 0.461673 \tabularnewline
7 & 0.035417 & 0.3664 & 0.357412 \tabularnewline
8 & -0.153779 & -1.5907 & 0.057314 \tabularnewline
9 & 0.179324 & 1.8549 & 0.033179 \tabularnewline
10 & -0.069387 & -0.7177 & 0.237238 \tabularnewline
11 & -0.142049 & -1.4694 & 0.072334 \tabularnewline
12 & 0.33925 & 3.5092 & 0.000329 \tabularnewline
13 & -0.238785 & -2.47 & 0.007546 \tabularnewline
14 & 0.022945 & 0.2373 & 0.406421 \tabularnewline
15 & 0.145358 & 1.5036 & 0.067816 \tabularnewline
16 & -0.167816 & -1.7359 & 0.04273 \tabularnewline
17 & 0.029427 & 0.3044 & 0.38071 \tabularnewline
18 & 0.089551 & 0.9263 & 0.178182 \tabularnewline
19 & -0.075391 & -0.7798 & 0.218601 \tabularnewline
20 & -0.078 & -0.8068 & 0.210774 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111254&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]-0.488322[/C][C]-5.0512[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.109251[/C][C]-1.1301[/C][C]0.130481[/C][/ROW]
[ROW][C]3[/C][C]0.258725[/C][C]2.6763[/C][C]0.004308[/C][/ROW]
[ROW][C]4[/C][C]-0.161337[/C][C]-1.6689[/C][C]0.049032[/C][/ROW]
[ROW][C]5[/C][C]0.009217[/C][C]0.0953[/C][C]0.462109[/C][/ROW]
[ROW][C]6[/C][C]0.009324[/C][C]0.0964[/C][C]0.461673[/C][/ROW]
[ROW][C]7[/C][C]0.035417[/C][C]0.3664[/C][C]0.357412[/C][/ROW]
[ROW][C]8[/C][C]-0.153779[/C][C]-1.5907[/C][C]0.057314[/C][/ROW]
[ROW][C]9[/C][C]0.179324[/C][C]1.8549[/C][C]0.033179[/C][/ROW]
[ROW][C]10[/C][C]-0.069387[/C][C]-0.7177[/C][C]0.237238[/C][/ROW]
[ROW][C]11[/C][C]-0.142049[/C][C]-1.4694[/C][C]0.072334[/C][/ROW]
[ROW][C]12[/C][C]0.33925[/C][C]3.5092[/C][C]0.000329[/C][/ROW]
[ROW][C]13[/C][C]-0.238785[/C][C]-2.47[/C][C]0.007546[/C][/ROW]
[ROW][C]14[/C][C]0.022945[/C][C]0.2373[/C][C]0.406421[/C][/ROW]
[ROW][C]15[/C][C]0.145358[/C][C]1.5036[/C][C]0.067816[/C][/ROW]
[ROW][C]16[/C][C]-0.167816[/C][C]-1.7359[/C][C]0.04273[/C][/ROW]
[ROW][C]17[/C][C]0.029427[/C][C]0.3044[/C][C]0.38071[/C][/ROW]
[ROW][C]18[/C][C]0.089551[/C][C]0.9263[/C][C]0.178182[/C][/ROW]
[ROW][C]19[/C][C]-0.075391[/C][C]-0.7798[/C][C]0.218601[/C][/ROW]
[ROW][C]20[/C][C]-0.078[/C][C]-0.8068[/C][C]0.210774[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111254&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111254&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	-0.488322	-5.0512	1e-06
2	-0.109251	-1.1301	0.130481
3	0.258725	2.6763	0.004308
4	-0.161337	-1.6689	0.049032
5	0.009217	0.0953	0.462109
6	0.009324	0.0964	0.461673
7	0.035417	0.3664	0.357412
8	-0.153779	-1.5907	0.057314
9	0.179324	1.8549	0.033179
10	-0.069387	-0.7177	0.237238
11	-0.142049	-1.4694	0.072334
12	0.33925	3.5092	0.000329
13	-0.238785	-2.47	0.007546
14	0.022945	0.2373	0.406421
15	0.145358	1.5036	0.067816
16	-0.167816	-1.7359	0.04273
17	0.029427	0.3044	0.38071
18	0.089551	0.9263	0.178182
19	-0.075391	-0.7798	0.218601
20	-0.078	-0.8068	0.210774

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.488322	-5.0512	1e-06
2	-0.456586	-4.723	4e-06
3	-0.069584	-0.7198	0.236613
4	-0.097288	-1.0064	0.158258
5	-0.052325	-0.5413	0.294729
6	-0.119399	-1.2351	0.109755
7	-0.007161	-0.0741	0.470546
8	-0.225822	-2.3359	0.01068
9	-0.011695	-0.121	0.451971
10	-0.069339	-0.7172	0.237391
11	-0.195608	-2.0234	0.022763
12	0.151635	1.5685	0.059856
13	0.024254	0.2509	0.401192
14	0.056642	0.5859	0.279585
15	0.105223	1.0884	0.139424
16	-0.004938	-0.0511	0.479678
17	-0.030164	-0.312	0.377815
18	0.06323	0.6541	0.257238
19	0.014389	0.1488	0.440978
20	-0.033279	-0.3442	0.365669

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.488322 & -5.0512 & 1e-06 \tabularnewline
2 & -0.456586 & -4.723 & 4e-06 \tabularnewline
3 & -0.069584 & -0.7198 & 0.236613 \tabularnewline
4 & -0.097288 & -1.0064 & 0.158258 \tabularnewline
5 & -0.052325 & -0.5413 & 0.294729 \tabularnewline
6 & -0.119399 & -1.2351 & 0.109755 \tabularnewline
7 & -0.007161 & -0.0741 & 0.470546 \tabularnewline
8 & -0.225822 & -2.3359 & 0.01068 \tabularnewline
9 & -0.011695 & -0.121 & 0.451971 \tabularnewline
10 & -0.069339 & -0.7172 & 0.237391 \tabularnewline
11 & -0.195608 & -2.0234 & 0.022763 \tabularnewline
12 & 0.151635 & 1.5685 & 0.059856 \tabularnewline
13 & 0.024254 & 0.2509 & 0.401192 \tabularnewline
14 & 0.056642 & 0.5859 & 0.279585 \tabularnewline
15 & 0.105223 & 1.0884 & 0.139424 \tabularnewline
16 & -0.004938 & -0.0511 & 0.479678 \tabularnewline
17 & -0.030164 & -0.312 & 0.377815 \tabularnewline
18 & 0.06323 & 0.6541 & 0.257238 \tabularnewline
19 & 0.014389 & 0.1488 & 0.440978 \tabularnewline
20 & -0.033279 & -0.3442 & 0.365669 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111254&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]-0.488322[/C][C]-5.0512[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.456586[/C][C]-4.723[/C][C]4e-06[/C][/ROW]
[ROW][C]3[/C][C]-0.069584[/C][C]-0.7198[/C][C]0.236613[/C][/ROW]
[ROW][C]4[/C][C]-0.097288[/C][C]-1.0064[/C][C]0.158258[/C][/ROW]
[ROW][C]5[/C][C]-0.052325[/C][C]-0.5413[/C][C]0.294729[/C][/ROW]
[ROW][C]6[/C][C]-0.119399[/C][C]-1.2351[/C][C]0.109755[/C][/ROW]
[ROW][C]7[/C][C]-0.007161[/C][C]-0.0741[/C][C]0.470546[/C][/ROW]
[ROW][C]8[/C][C]-0.225822[/C][C]-2.3359[/C][C]0.01068[/C][/ROW]
[ROW][C]9[/C][C]-0.011695[/C][C]-0.121[/C][C]0.451971[/C][/ROW]
[ROW][C]10[/C][C]-0.069339[/C][C]-0.7172[/C][C]0.237391[/C][/ROW]
[ROW][C]11[/C][C]-0.195608[/C][C]-2.0234[/C][C]0.022763[/C][/ROW]
[ROW][C]12[/C][C]0.151635[/C][C]1.5685[/C][C]0.059856[/C][/ROW]
[ROW][C]13[/C][C]0.024254[/C][C]0.2509[/C][C]0.401192[/C][/ROW]
[ROW][C]14[/C][C]0.056642[/C][C]0.5859[/C][C]0.279585[/C][/ROW]
[ROW][C]15[/C][C]0.105223[/C][C]1.0884[/C][C]0.139424[/C][/ROW]
[ROW][C]16[/C][C]-0.004938[/C][C]-0.0511[/C][C]0.479678[/C][/ROW]
[ROW][C]17[/C][C]-0.030164[/C][C]-0.312[/C][C]0.377815[/C][/ROW]
[ROW][C]18[/C][C]0.06323[/C][C]0.6541[/C][C]0.257238[/C][/ROW]
[ROW][C]19[/C][C]0.014389[/C][C]0.1488[/C][C]0.440978[/C][/ROW]
[ROW][C]20[/C][C]-0.033279[/C][C]-0.3442[/C][C]0.365669[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111254&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111254&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	-0.488322	-5.0512	1e-06
2	-0.456586	-4.723	4e-06
3	-0.069584	-0.7198	0.236613
4	-0.097288	-1.0064	0.158258
5	-0.052325	-0.5413	0.294729
6	-0.119399	-1.2351	0.109755
7	-0.007161	-0.0741	0.470546
8	-0.225822	-2.3359	0.01068
9	-0.011695	-0.121	0.451971
10	-0.069339	-0.7172	0.237391
11	-0.195608	-2.0234	0.022763
12	0.151635	1.5685	0.059856
13	0.024254	0.2509	0.401192
14	0.056642	0.5859	0.279585
15	0.105223	1.0884	0.139424
16	-0.004938	-0.0511	0.479678
17	-0.030164	-0.312	0.377815
18	0.06323	0.6541	0.257238
19	0.014389	0.1488	0.440978
20	-0.033279	-0.3442	0.365669

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