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

Thu, 21 Nov 2013 17:27:25 -0500

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/2013/Nov/21/t1385072861vea3d0verm6d5bd.htm/, Retrieved Fri, 03 May 2024 10:20:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=227432, Retrieved Fri, 03 May 2024 10:20:58 +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

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

-       [(Partial) Autocorrelation Function] [] [2013-11-21 22:27:25] [818da16b08b21220aa14002c9e16e6e1] [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	3 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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=227432&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]3 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=227432&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=227432&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.958333	8.1317	0
2	0.916699	7.7784	0
3	0.875129	7.4257	0
4	0.833655	7.0738	0
5	0.79231	6.723	0
6	0.751125	6.3735	0
7	0.710134	6.0257	0
8	0.669368	5.6798	0
9	0.628859	5.336	1e-06
10	0.588639	4.9948	2e-06
11	0.548741	4.6562	7e-06
12	0.509197	4.3207	2.5e-05
13	0.470038	3.9884	7.9e-05
14	0.431298	3.6597	0.000239
15	0.393008	3.3348	0.000676
16	0.3552	3.014	0.001779
17	0.317906	2.6975	0.004348
18	0.28116	2.3857	0.009839

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.958333 & 8.1317 & 0 \tabularnewline
2 & 0.916699 & 7.7784 & 0 \tabularnewline
3 & 0.875129 & 7.4257 & 0 \tabularnewline
4 & 0.833655 & 7.0738 & 0 \tabularnewline
5 & 0.79231 & 6.723 & 0 \tabularnewline
6 & 0.751125 & 6.3735 & 0 \tabularnewline
7 & 0.710134 & 6.0257 & 0 \tabularnewline
8 & 0.669368 & 5.6798 & 0 \tabularnewline
9 & 0.628859 & 5.336 & 1e-06 \tabularnewline
10 & 0.588639 & 4.9948 & 2e-06 \tabularnewline
11 & 0.548741 & 4.6562 & 7e-06 \tabularnewline
12 & 0.509197 & 4.3207 & 2.5e-05 \tabularnewline
13 & 0.470038 & 3.9884 & 7.9e-05 \tabularnewline
14 & 0.431298 & 3.6597 & 0.000239 \tabularnewline
15 & 0.393008 & 3.3348 & 0.000676 \tabularnewline
16 & 0.3552 & 3.014 & 0.001779 \tabularnewline
17 & 0.317906 & 2.6975 & 0.004348 \tabularnewline
18 & 0.28116 & 2.3857 & 0.009839 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=227432&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]0.958333[/C][C]8.1317[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.916699[/C][C]7.7784[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.875129[/C][C]7.4257[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.833655[/C][C]7.0738[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.79231[/C][C]6.723[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.751125[/C][C]6.3735[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.710134[/C][C]6.0257[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.669368[/C][C]5.6798[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.628859[/C][C]5.336[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.588639[/C][C]4.9948[/C][C]2e-06[/C][/ROW]
[ROW][C]11[/C][C]0.548741[/C][C]4.6562[/C][C]7e-06[/C][/ROW]
[ROW][C]12[/C][C]0.509197[/C][C]4.3207[/C][C]2.5e-05[/C][/ROW]
[ROW][C]13[/C][C]0.470038[/C][C]3.9884[/C][C]7.9e-05[/C][/ROW]
[ROW][C]14[/C][C]0.431298[/C][C]3.6597[/C][C]0.000239[/C][/ROW]
[ROW][C]15[/C][C]0.393008[/C][C]3.3348[/C][C]0.000676[/C][/ROW]
[ROW][C]16[/C][C]0.3552[/C][C]3.014[/C][C]0.001779[/C][/ROW]
[ROW][C]17[/C][C]0.317906[/C][C]2.6975[/C][C]0.004348[/C][/ROW]
[ROW][C]18[/C][C]0.28116[/C][C]2.3857[/C][C]0.009839[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=227432&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=227432&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	0.958333	8.1317	0
2	0.916699	7.7784	0
3	0.875129	7.4257	0
4	0.833655	7.0738	0
5	0.79231	6.723	0
6	0.751125	6.3735	0
7	0.710134	6.0257	0
8	0.669368	5.6798	0
9	0.628859	5.336	1e-06
10	0.588639	4.9948	2e-06
11	0.548741	4.6562	7e-06
12	0.509197	4.3207	2.5e-05
13	0.470038	3.9884	7.9e-05
14	0.431298	3.6597	0.000239
15	0.393008	3.3348	0.000676
16	0.3552	3.014	0.001779
17	0.317906	2.6975	0.004348
18	0.28116	2.3857	0.009839

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.958333	8.1317	0
2	-0.020883	-0.1772	0.429927
3	-0.020933	-0.1776	0.429758
4	-0.020985	-0.1781	0.429585
5	-0.021038	-0.1785	0.429409
6	-0.021092	-0.179	0.429232
7	-0.021145	-0.1794	0.429055
8	-0.021198	-0.1799	0.42888
9	-0.02125	-0.1803	0.428707
10	-0.0213	-0.1807	0.42854
11	-0.021349	-0.1811	0.42838
12	-0.021394	-0.1815	0.428228
13	-0.021437	-0.1819	0.428087
14	-0.021475	-0.1822	0.42796
15	-0.021509	-0.1825	0.427848
16	-0.021537	-0.1827	0.427754
17	-0.021559	-0.1829	0.427681
18	-0.021574	-0.1831	0.427632

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.958333 & 8.1317 & 0 \tabularnewline
2 & -0.020883 & -0.1772 & 0.429927 \tabularnewline
3 & -0.020933 & -0.1776 & 0.429758 \tabularnewline
4 & -0.020985 & -0.1781 & 0.429585 \tabularnewline
5 & -0.021038 & -0.1785 & 0.429409 \tabularnewline
6 & -0.021092 & -0.179 & 0.429232 \tabularnewline
7 & -0.021145 & -0.1794 & 0.429055 \tabularnewline
8 & -0.021198 & -0.1799 & 0.42888 \tabularnewline
9 & -0.02125 & -0.1803 & 0.428707 \tabularnewline
10 & -0.0213 & -0.1807 & 0.42854 \tabularnewline
11 & -0.021349 & -0.1811 & 0.42838 \tabularnewline
12 & -0.021394 & -0.1815 & 0.428228 \tabularnewline
13 & -0.021437 & -0.1819 & 0.428087 \tabularnewline
14 & -0.021475 & -0.1822 & 0.42796 \tabularnewline
15 & -0.021509 & -0.1825 & 0.427848 \tabularnewline
16 & -0.021537 & -0.1827 & 0.427754 \tabularnewline
17 & -0.021559 & -0.1829 & 0.427681 \tabularnewline
18 & -0.021574 & -0.1831 & 0.427632 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=227432&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]0.958333[/C][C]8.1317[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.020883[/C][C]-0.1772[/C][C]0.429927[/C][/ROW]
[ROW][C]3[/C][C]-0.020933[/C][C]-0.1776[/C][C]0.429758[/C][/ROW]
[ROW][C]4[/C][C]-0.020985[/C][C]-0.1781[/C][C]0.429585[/C][/ROW]
[ROW][C]5[/C][C]-0.021038[/C][C]-0.1785[/C][C]0.429409[/C][/ROW]
[ROW][C]6[/C][C]-0.021092[/C][C]-0.179[/C][C]0.429232[/C][/ROW]
[ROW][C]7[/C][C]-0.021145[/C][C]-0.1794[/C][C]0.429055[/C][/ROW]
[ROW][C]8[/C][C]-0.021198[/C][C]-0.1799[/C][C]0.42888[/C][/ROW]
[ROW][C]9[/C][C]-0.02125[/C][C]-0.1803[/C][C]0.428707[/C][/ROW]
[ROW][C]10[/C][C]-0.0213[/C][C]-0.1807[/C][C]0.42854[/C][/ROW]
[ROW][C]11[/C][C]-0.021349[/C][C]-0.1811[/C][C]0.42838[/C][/ROW]
[ROW][C]12[/C][C]-0.021394[/C][C]-0.1815[/C][C]0.428228[/C][/ROW]
[ROW][C]13[/C][C]-0.021437[/C][C]-0.1819[/C][C]0.428087[/C][/ROW]
[ROW][C]14[/C][C]-0.021475[/C][C]-0.1822[/C][C]0.42796[/C][/ROW]
[ROW][C]15[/C][C]-0.021509[/C][C]-0.1825[/C][C]0.427848[/C][/ROW]
[ROW][C]16[/C][C]-0.021537[/C][C]-0.1827[/C][C]0.427754[/C][/ROW]
[ROW][C]17[/C][C]-0.021559[/C][C]-0.1829[/C][C]0.427681[/C][/ROW]
[ROW][C]18[/C][C]-0.021574[/C][C]-0.1831[/C][C]0.427632[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=227432&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=227432&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	0.958333	8.1317	0
2	-0.020883	-0.1772	0.429927
3	-0.020933	-0.1776	0.429758
4	-0.020985	-0.1781	0.429585
5	-0.021038	-0.1785	0.429409
6	-0.021092	-0.179	0.429232
7	-0.021145	-0.1794	0.429055
8	-0.021198	-0.1799	0.42888
9	-0.02125	-0.1803	0.428707
10	-0.0213	-0.1807	0.42854
11	-0.021349	-0.1811	0.42838
12	-0.021394	-0.1815	0.428228
13	-0.021437	-0.1819	0.428087
14	-0.021475	-0.1822	0.42796
15	-0.021509	-0.1825	0.427848
16	-0.021537	-0.1827	0.427754
17	-0.021559	-0.1829	0.427681
18	-0.021574	-0.1831	0.427632

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 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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