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

Sun, 04 Dec 2016 15:15:05 +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/04/t1480860950sdd5aa2k9cb2vxn.htm/, Retrieved Fri, 17 May 2024 13:24:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297671, Retrieved Fri, 17 May 2024 13:24:57 +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

121

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

-       [(Partial) Autocorrelation Function] [] [2016-12-04 14:15:05] [6deb082de88ded72ec069288c69f9f98] [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	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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297671&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]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=297671&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297671&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.965969	10.6257	0
2	0.944159	10.3857	0
3	0.925309	10.1784	0
4	0.90557	9.9613	0
5	0.883303	9.7163	0
6	0.860731	9.468	0
7	0.843184	9.275	0
8	0.832533	9.1579	0
9	0.811405	8.9255	0
10	0.793427	8.7277	0
11	0.775239	8.5276	0
12	0.751002	8.261	0
13	0.728196	8.0102	0
14	0.706803	7.7748	0
15	0.677351	7.4509	0
16	0.64161	7.0577	0
17	0.613805	6.7519	0
18	0.587086	6.4579	0
19	0.570126	6.2714	0
20	0.544807	5.9929	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.965969 & 10.6257 & 0 \tabularnewline
2 & 0.944159 & 10.3857 & 0 \tabularnewline
3 & 0.925309 & 10.1784 & 0 \tabularnewline
4 & 0.90557 & 9.9613 & 0 \tabularnewline
5 & 0.883303 & 9.7163 & 0 \tabularnewline
6 & 0.860731 & 9.468 & 0 \tabularnewline
7 & 0.843184 & 9.275 & 0 \tabularnewline
8 & 0.832533 & 9.1579 & 0 \tabularnewline
9 & 0.811405 & 8.9255 & 0 \tabularnewline
10 & 0.793427 & 8.7277 & 0 \tabularnewline
11 & 0.775239 & 8.5276 & 0 \tabularnewline
12 & 0.751002 & 8.261 & 0 \tabularnewline
13 & 0.728196 & 8.0102 & 0 \tabularnewline
14 & 0.706803 & 7.7748 & 0 \tabularnewline
15 & 0.677351 & 7.4509 & 0 \tabularnewline
16 & 0.64161 & 7.0577 & 0 \tabularnewline
17 & 0.613805 & 6.7519 & 0 \tabularnewline
18 & 0.587086 & 6.4579 & 0 \tabularnewline
19 & 0.570126 & 6.2714 & 0 \tabularnewline
20 & 0.544807 & 5.9929 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297671&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]0.965969[/C][C]10.6257[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.944159[/C][C]10.3857[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.925309[/C][C]10.1784[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.90557[/C][C]9.9613[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.883303[/C][C]9.7163[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.860731[/C][C]9.468[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.843184[/C][C]9.275[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.832533[/C][C]9.1579[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.811405[/C][C]8.9255[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.793427[/C][C]8.7277[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.775239[/C][C]8.5276[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.751002[/C][C]8.261[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.728196[/C][C]8.0102[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.706803[/C][C]7.7748[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.677351[/C][C]7.4509[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.64161[/C][C]7.0577[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.613805[/C][C]6.7519[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.587086[/C][C]6.4579[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.570126[/C][C]6.2714[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.544807[/C][C]5.9929[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297671&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297671&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	0.965969	10.6257	0
2	0.944159	10.3857	0
3	0.925309	10.1784	0
4	0.90557	9.9613	0
5	0.883303	9.7163	0
6	0.860731	9.468	0
7	0.843184	9.275	0
8	0.832533	9.1579	0
9	0.811405	8.9255	0
10	0.793427	8.7277	0
11	0.775239	8.5276	0
12	0.751002	8.261	0
13	0.728196	8.0102	0
14	0.706803	7.7748	0
15	0.677351	7.4509	0
16	0.64161	7.0577	0
17	0.613805	6.7519	0
18	0.587086	6.4579	0
19	0.570126	6.2714	0
20	0.544807	5.9929	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.965969	10.6257	0
2	0.165341	1.8188	0.035711
3	0.067035	0.7374	0.231156
4	-0.000642	-0.0071	0.49719
5	-0.046624	-0.5129	0.304492
6	-0.031341	-0.3448	0.365438
7	0.056362	0.62	0.268218
8	0.124257	1.3668	0.087106
9	-0.114137	-1.2555	0.105858
10	-0.001034	-0.0114	0.495472
11	-0.025797	-0.2838	0.388538
12	-0.113285	-1.2461	0.107562
13	-0.012611	-0.1387	0.44495
14	0.021569	0.2373	0.40643
15	-0.138584	-1.5244	0.065006
16	-0.185252	-2.0378	0.021877
17	0.06606	0.7267	0.234419
18	0.001846	0.0203	0.491918
19	0.158287	1.7412	0.042098
20	-0.041773	-0.4595	0.323348

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.965969 & 10.6257 & 0 \tabularnewline
2 & 0.165341 & 1.8188 & 0.035711 \tabularnewline
3 & 0.067035 & 0.7374 & 0.231156 \tabularnewline
4 & -0.000642 & -0.0071 & 0.49719 \tabularnewline
5 & -0.046624 & -0.5129 & 0.304492 \tabularnewline
6 & -0.031341 & -0.3448 & 0.365438 \tabularnewline
7 & 0.056362 & 0.62 & 0.268218 \tabularnewline
8 & 0.124257 & 1.3668 & 0.087106 \tabularnewline
9 & -0.114137 & -1.2555 & 0.105858 \tabularnewline
10 & -0.001034 & -0.0114 & 0.495472 \tabularnewline
11 & -0.025797 & -0.2838 & 0.388538 \tabularnewline
12 & -0.113285 & -1.2461 & 0.107562 \tabularnewline
13 & -0.012611 & -0.1387 & 0.44495 \tabularnewline
14 & 0.021569 & 0.2373 & 0.40643 \tabularnewline
15 & -0.138584 & -1.5244 & 0.065006 \tabularnewline
16 & -0.185252 & -2.0378 & 0.021877 \tabularnewline
17 & 0.06606 & 0.7267 & 0.234419 \tabularnewline
18 & 0.001846 & 0.0203 & 0.491918 \tabularnewline
19 & 0.158287 & 1.7412 & 0.042098 \tabularnewline
20 & -0.041773 & -0.4595 & 0.323348 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297671&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]0.965969[/C][C]10.6257[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.165341[/C][C]1.8188[/C][C]0.035711[/C][/ROW]
[ROW][C]3[/C][C]0.067035[/C][C]0.7374[/C][C]0.231156[/C][/ROW]
[ROW][C]4[/C][C]-0.000642[/C][C]-0.0071[/C][C]0.49719[/C][/ROW]
[ROW][C]5[/C][C]-0.046624[/C][C]-0.5129[/C][C]0.304492[/C][/ROW]
[ROW][C]6[/C][C]-0.031341[/C][C]-0.3448[/C][C]0.365438[/C][/ROW]
[ROW][C]7[/C][C]0.056362[/C][C]0.62[/C][C]0.268218[/C][/ROW]
[ROW][C]8[/C][C]0.124257[/C][C]1.3668[/C][C]0.087106[/C][/ROW]
[ROW][C]9[/C][C]-0.114137[/C][C]-1.2555[/C][C]0.105858[/C][/ROW]
[ROW][C]10[/C][C]-0.001034[/C][C]-0.0114[/C][C]0.495472[/C][/ROW]
[ROW][C]11[/C][C]-0.025797[/C][C]-0.2838[/C][C]0.388538[/C][/ROW]
[ROW][C]12[/C][C]-0.113285[/C][C]-1.2461[/C][C]0.107562[/C][/ROW]
[ROW][C]13[/C][C]-0.012611[/C][C]-0.1387[/C][C]0.44495[/C][/ROW]
[ROW][C]14[/C][C]0.021569[/C][C]0.2373[/C][C]0.40643[/C][/ROW]
[ROW][C]15[/C][C]-0.138584[/C][C]-1.5244[/C][C]0.065006[/C][/ROW]
[ROW][C]16[/C][C]-0.185252[/C][C]-2.0378[/C][C]0.021877[/C][/ROW]
[ROW][C]17[/C][C]0.06606[/C][C]0.7267[/C][C]0.234419[/C][/ROW]
[ROW][C]18[/C][C]0.001846[/C][C]0.0203[/C][C]0.491918[/C][/ROW]
[ROW][C]19[/C][C]0.158287[/C][C]1.7412[/C][C]0.042098[/C][/ROW]
[ROW][C]20[/C][C]-0.041773[/C][C]-0.4595[/C][C]0.323348[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297671&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297671&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	0.965969	10.6257	0
2	0.165341	1.8188	0.035711
3	0.067035	0.7374	0.231156
4	-0.000642	-0.0071	0.49719
5	-0.046624	-0.5129	0.304492
6	-0.031341	-0.3448	0.365438
7	0.056362	0.62	0.268218
8	0.124257	1.3668	0.087106
9	-0.114137	-1.2555	0.105858
10	-0.001034	-0.0114	0.495472
11	-0.025797	-0.2838	0.388538
12	-0.113285	-1.2461	0.107562
13	-0.012611	-0.1387	0.44495
14	0.021569	0.2373	0.40643
15	-0.138584	-1.5244	0.065006
16	-0.185252	-2.0378	0.021877
17	0.06606	0.7267	0.234419
18	0.001846	0.0203	0.491918
19	0.158287	1.7412	0.042098
20	-0.041773	-0.4595	0.323348

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)
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