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

Fri, 16 Dec 2016 09:17:35 +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/2016/Dec/16/t1481876351zvfjgxl56gfqji8.htm/, Retrieved Thu, 02 May 2024 23:33:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300099, Retrieved Thu, 02 May 2024 23:33:05 +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] [Partial autocorel...] [2016-12-16 08:17:35] [f07fac15bca656f595926f3a45d3c842] [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	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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300099&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300099&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300099&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.632763	-4.4293	2.6e-05
2	0.091659	0.6416	0.262057
3	-0.004037	-0.0283	0.488784
4	0.205492	1.4384	0.078332
5	-0.316936	-2.2186	0.015591
6	0.268038	1.8763	0.033291
7	-0.209988	-1.4699	0.073988
8	0.199289	1.395	0.084651
9	-0.129233	-0.9046	0.185043
10	-0.006161	-0.0431	0.482889
11	0.003663	0.0256	0.489824
12	0.201621	1.4113	0.082231
13	-0.323586	-2.2651	0.013981
14	0.127197	0.8904	0.188808
15	0.168268	1.1779	0.122268
16	-0.199446	-1.3961	0.084486
17	-0.001221	-0.0085	0.496607

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.632763 & -4.4293 & 2.6e-05 \tabularnewline
2 & 0.091659 & 0.6416 & 0.262057 \tabularnewline
3 & -0.004037 & -0.0283 & 0.488784 \tabularnewline
4 & 0.205492 & 1.4384 & 0.078332 \tabularnewline
5 & -0.316936 & -2.2186 & 0.015591 \tabularnewline
6 & 0.268038 & 1.8763 & 0.033291 \tabularnewline
7 & -0.209988 & -1.4699 & 0.073988 \tabularnewline
8 & 0.199289 & 1.395 & 0.084651 \tabularnewline
9 & -0.129233 & -0.9046 & 0.185043 \tabularnewline
10 & -0.006161 & -0.0431 & 0.482889 \tabularnewline
11 & 0.003663 & 0.0256 & 0.489824 \tabularnewline
12 & 0.201621 & 1.4113 & 0.082231 \tabularnewline
13 & -0.323586 & -2.2651 & 0.013981 \tabularnewline
14 & 0.127197 & 0.8904 & 0.188808 \tabularnewline
15 & 0.168268 & 1.1779 & 0.122268 \tabularnewline
16 & -0.199446 & -1.3961 & 0.084486 \tabularnewline
17 & -0.001221 & -0.0085 & 0.496607 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300099&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]-0.632763[/C][C]-4.4293[/C][C]2.6e-05[/C][/ROW]
[ROW][C]2[/C][C]0.091659[/C][C]0.6416[/C][C]0.262057[/C][/ROW]
[ROW][C]3[/C][C]-0.004037[/C][C]-0.0283[/C][C]0.488784[/C][/ROW]
[ROW][C]4[/C][C]0.205492[/C][C]1.4384[/C][C]0.078332[/C][/ROW]
[ROW][C]5[/C][C]-0.316936[/C][C]-2.2186[/C][C]0.015591[/C][/ROW]
[ROW][C]6[/C][C]0.268038[/C][C]1.8763[/C][C]0.033291[/C][/ROW]
[ROW][C]7[/C][C]-0.209988[/C][C]-1.4699[/C][C]0.073988[/C][/ROW]
[ROW][C]8[/C][C]0.199289[/C][C]1.395[/C][C]0.084651[/C][/ROW]
[ROW][C]9[/C][C]-0.129233[/C][C]-0.9046[/C][C]0.185043[/C][/ROW]
[ROW][C]10[/C][C]-0.006161[/C][C]-0.0431[/C][C]0.482889[/C][/ROW]
[ROW][C]11[/C][C]0.003663[/C][C]0.0256[/C][C]0.489824[/C][/ROW]
[ROW][C]12[/C][C]0.201621[/C][C]1.4113[/C][C]0.082231[/C][/ROW]
[ROW][C]13[/C][C]-0.323586[/C][C]-2.2651[/C][C]0.013981[/C][/ROW]
[ROW][C]14[/C][C]0.127197[/C][C]0.8904[/C][C]0.188808[/C][/ROW]
[ROW][C]15[/C][C]0.168268[/C][C]1.1779[/C][C]0.122268[/C][/ROW]
[ROW][C]16[/C][C]-0.199446[/C][C]-1.3961[/C][C]0.084486[/C][/ROW]
[ROW][C]17[/C][C]-0.001221[/C][C]-0.0085[/C][C]0.496607[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300099&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300099&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	-0.632763	-4.4293	2.6e-05
2	0.091659	0.6416	0.262057
3	-0.004037	-0.0283	0.488784
4	0.205492	1.4384	0.078332
5	-0.316936	-2.2186	0.015591
6	0.268038	1.8763	0.033291
7	-0.209988	-1.4699	0.073988
8	0.199289	1.395	0.084651
9	-0.129233	-0.9046	0.185043
10	-0.006161	-0.0431	0.482889
11	0.003663	0.0256	0.489824
12	0.201621	1.4113	0.082231
13	-0.323586	-2.2651	0.013981
14	0.127197	0.8904	0.188808
15	0.168268	1.1779	0.122268
16	-0.199446	-1.3961	0.084486
17	-0.001221	-0.0085	0.496607

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.632763	-4.4293	2.6e-05
2	-0.514884	-3.6042	0.000366
3	-0.549134	-3.8439	0.000175
4	-0.167491	-1.1724	0.123345
5	-0.282336	-1.9764	0.026879
6	-0.032765	-0.2294	0.409773
7	-0.20266	-1.4186	0.081169
8	-0.074077	-0.5185	0.303208
9	0.095284	0.667	0.253954
10	-0.066504	-0.4655	0.321808
11	-0.178703	-1.2509	0.108451
12	0.10271	0.719	0.237787
13	0.071371	0.4996	0.309798
14	-0.18407	-1.2885	0.101813
15	0.049315	0.3452	0.365708
16	0.010601	0.0742	0.470573
17	0.020694	0.1449	0.442709

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.632763 & -4.4293 & 2.6e-05 \tabularnewline
2 & -0.514884 & -3.6042 & 0.000366 \tabularnewline
3 & -0.549134 & -3.8439 & 0.000175 \tabularnewline
4 & -0.167491 & -1.1724 & 0.123345 \tabularnewline
5 & -0.282336 & -1.9764 & 0.026879 \tabularnewline
6 & -0.032765 & -0.2294 & 0.409773 \tabularnewline
7 & -0.20266 & -1.4186 & 0.081169 \tabularnewline
8 & -0.074077 & -0.5185 & 0.303208 \tabularnewline
9 & 0.095284 & 0.667 & 0.253954 \tabularnewline
10 & -0.066504 & -0.4655 & 0.321808 \tabularnewline
11 & -0.178703 & -1.2509 & 0.108451 \tabularnewline
12 & 0.10271 & 0.719 & 0.237787 \tabularnewline
13 & 0.071371 & 0.4996 & 0.309798 \tabularnewline
14 & -0.18407 & -1.2885 & 0.101813 \tabularnewline
15 & 0.049315 & 0.3452 & 0.365708 \tabularnewline
16 & 0.010601 & 0.0742 & 0.470573 \tabularnewline
17 & 0.020694 & 0.1449 & 0.442709 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300099&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]-0.632763[/C][C]-4.4293[/C][C]2.6e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.514884[/C][C]-3.6042[/C][C]0.000366[/C][/ROW]
[ROW][C]3[/C][C]-0.549134[/C][C]-3.8439[/C][C]0.000175[/C][/ROW]
[ROW][C]4[/C][C]-0.167491[/C][C]-1.1724[/C][C]0.123345[/C][/ROW]
[ROW][C]5[/C][C]-0.282336[/C][C]-1.9764[/C][C]0.026879[/C][/ROW]
[ROW][C]6[/C][C]-0.032765[/C][C]-0.2294[/C][C]0.409773[/C][/ROW]
[ROW][C]7[/C][C]-0.20266[/C][C]-1.4186[/C][C]0.081169[/C][/ROW]
[ROW][C]8[/C][C]-0.074077[/C][C]-0.5185[/C][C]0.303208[/C][/ROW]
[ROW][C]9[/C][C]0.095284[/C][C]0.667[/C][C]0.253954[/C][/ROW]
[ROW][C]10[/C][C]-0.066504[/C][C]-0.4655[/C][C]0.321808[/C][/ROW]
[ROW][C]11[/C][C]-0.178703[/C][C]-1.2509[/C][C]0.108451[/C][/ROW]
[ROW][C]12[/C][C]0.10271[/C][C]0.719[/C][C]0.237787[/C][/ROW]
[ROW][C]13[/C][C]0.071371[/C][C]0.4996[/C][C]0.309798[/C][/ROW]
[ROW][C]14[/C][C]-0.18407[/C][C]-1.2885[/C][C]0.101813[/C][/ROW]
[ROW][C]15[/C][C]0.049315[/C][C]0.3452[/C][C]0.365708[/C][/ROW]
[ROW][C]16[/C][C]0.010601[/C][C]0.0742[/C][C]0.470573[/C][/ROW]
[ROW][C]17[/C][C]0.020694[/C][C]0.1449[/C][C]0.442709[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300099&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300099&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	-0.632763	-4.4293	2.6e-05
2	-0.514884	-3.6042	0.000366
3	-0.549134	-3.8439	0.000175
4	-0.167491	-1.1724	0.123345
5	-0.282336	-1.9764	0.026879
6	-0.032765	-0.2294	0.409773
7	-0.20266	-1.4186	0.081169
8	-0.074077	-0.5185	0.303208
9	0.095284	0.667	0.253954
10	-0.066504	-0.4655	0.321808
11	-0.178703	-1.2509	0.108451
12	0.10271	0.719	0.237787
13	0.071371	0.4996	0.309798
14	-0.18407	-1.2885	0.101813
15	0.049315	0.3452	0.365708
16	0.010601	0.0742	0.470573
17	0.020694	0.1449	0.442709

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 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code