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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 04 Dec 2012 14:34:44 -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/2012/Dec/04/t1354649699p0vnxdu7zx5tyvt.htm/, Retrieved Wed, 24 Apr 2024 08:23:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=196551, Retrieved Wed, 24 Apr 2024 08:23:39 +0000

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

-     [(Partial) Autocorrelation Function] [Workshop 9 ] [2012-12-04 19:22:06] [a4b60d76ea6b846adbf54f7861413bce]
-   P     [(Partial) Autocorrelation Function] [Workshop 9] [2012-12-04 19:34:44] [ab4290de075ebbfc5b460761b0110080] [Current]

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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	'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196551&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196551&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196551&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.047793	-0.3311	0.370998
2	0.033962	0.2353	0.407489
3	-0.043016	-0.298	0.383485
4	-0.005729	-0.0397	0.484251
5	-0.095004	-0.6582	0.256776
6	-0.029796	-0.2064	0.418664
7	0.030275	0.2098	0.417375
8	0.096671	0.6698	0.253112
9	-0.059499	-0.4122	0.341005
10	-0.048032	-0.3328	0.370377
11	0.120509	0.8349	0.203952
12	-0.498852	-3.4561	0.000578
13	-0.09624	-0.6668	0.254056
14	0.041545	0.2878	0.387356
15	-0.043148	-0.2989	0.38314
16	-0.025227	-0.1748	0.430994
17	-0.121968	-0.845	0.201146
18	0.051287	0.3553	0.361952

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.047793 & -0.3311 & 0.370998 \tabularnewline
2 & 0.033962 & 0.2353 & 0.407489 \tabularnewline
3 & -0.043016 & -0.298 & 0.383485 \tabularnewline
4 & -0.005729 & -0.0397 & 0.484251 \tabularnewline
5 & -0.095004 & -0.6582 & 0.256776 \tabularnewline
6 & -0.029796 & -0.2064 & 0.418664 \tabularnewline
7 & 0.030275 & 0.2098 & 0.417375 \tabularnewline
8 & 0.096671 & 0.6698 & 0.253112 \tabularnewline
9 & -0.059499 & -0.4122 & 0.341005 \tabularnewline
10 & -0.048032 & -0.3328 & 0.370377 \tabularnewline
11 & 0.120509 & 0.8349 & 0.203952 \tabularnewline
12 & -0.498852 & -3.4561 & 0.000578 \tabularnewline
13 & -0.09624 & -0.6668 & 0.254056 \tabularnewline
14 & 0.041545 & 0.2878 & 0.387356 \tabularnewline
15 & -0.043148 & -0.2989 & 0.38314 \tabularnewline
16 & -0.025227 & -0.1748 & 0.430994 \tabularnewline
17 & -0.121968 & -0.845 & 0.201146 \tabularnewline
18 & 0.051287 & 0.3553 & 0.361952 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196551&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]-0.047793[/C][C]-0.3311[/C][C]0.370998[/C][/ROW]
[ROW][C]2[/C][C]0.033962[/C][C]0.2353[/C][C]0.407489[/C][/ROW]
[ROW][C]3[/C][C]-0.043016[/C][C]-0.298[/C][C]0.383485[/C][/ROW]
[ROW][C]4[/C][C]-0.005729[/C][C]-0.0397[/C][C]0.484251[/C][/ROW]
[ROW][C]5[/C][C]-0.095004[/C][C]-0.6582[/C][C]0.256776[/C][/ROW]
[ROW][C]6[/C][C]-0.029796[/C][C]-0.2064[/C][C]0.418664[/C][/ROW]
[ROW][C]7[/C][C]0.030275[/C][C]0.2098[/C][C]0.417375[/C][/ROW]
[ROW][C]8[/C][C]0.096671[/C][C]0.6698[/C][C]0.253112[/C][/ROW]
[ROW][C]9[/C][C]-0.059499[/C][C]-0.4122[/C][C]0.341005[/C][/ROW]
[ROW][C]10[/C][C]-0.048032[/C][C]-0.3328[/C][C]0.370377[/C][/ROW]
[ROW][C]11[/C][C]0.120509[/C][C]0.8349[/C][C]0.203952[/C][/ROW]
[ROW][C]12[/C][C]-0.498852[/C][C]-3.4561[/C][C]0.000578[/C][/ROW]
[ROW][C]13[/C][C]-0.09624[/C][C]-0.6668[/C][C]0.254056[/C][/ROW]
[ROW][C]14[/C][C]0.041545[/C][C]0.2878[/C][C]0.387356[/C][/ROW]
[ROW][C]15[/C][C]-0.043148[/C][C]-0.2989[/C][C]0.38314[/C][/ROW]
[ROW][C]16[/C][C]-0.025227[/C][C]-0.1748[/C][C]0.430994[/C][/ROW]
[ROW][C]17[/C][C]-0.121968[/C][C]-0.845[/C][C]0.201146[/C][/ROW]
[ROW][C]18[/C][C]0.051287[/C][C]0.3553[/C][C]0.361952[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196551&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196551&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	-0.047793	-0.3311	0.370998
2	0.033962	0.2353	0.407489
3	-0.043016	-0.298	0.383485
4	-0.005729	-0.0397	0.484251
5	-0.095004	-0.6582	0.256776
6	-0.029796	-0.2064	0.418664
7	0.030275	0.2098	0.417375
8	0.096671	0.6698	0.253112
9	-0.059499	-0.4122	0.341005
10	-0.048032	-0.3328	0.370377
11	0.120509	0.8349	0.203952
12	-0.498852	-3.4561	0.000578
13	-0.09624	-0.6668	0.254056
14	0.041545	0.2878	0.387356
15	-0.043148	-0.2989	0.38314
16	-0.025227	-0.1748	0.430994
17	-0.121968	-0.845	0.201146
18	0.051287	0.3553	0.361952

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.047793	-0.3311	0.370998
2	0.031751	0.22	0.413411
3	-0.040059	-0.2775	0.39128
4	-0.010647	-0.0738	0.470752
5	-0.093564	-0.6482	0.259962
6	-0.040194	-0.2785	0.390923
7	0.032226	0.2233	0.412136
8	0.095525	0.6618	0.255627
9	-0.057885	-0.401	0.345087
10	-0.068996	-0.478	0.317404
11	0.123978	0.8589	0.19732
12	-0.504425	-3.4948	0.000516
13	-0.145394	-1.0073	0.159416
14	0.10493	0.727	0.235386
15	-0.154956	-1.0736	0.144192
16	-0.056963	-0.3946	0.347425
17	-0.231854	-1.6063	0.057381
18	-0.05817	-0.403	0.344363

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.047793 & -0.3311 & 0.370998 \tabularnewline
2 & 0.031751 & 0.22 & 0.413411 \tabularnewline
3 & -0.040059 & -0.2775 & 0.39128 \tabularnewline
4 & -0.010647 & -0.0738 & 0.470752 \tabularnewline
5 & -0.093564 & -0.6482 & 0.259962 \tabularnewline
6 & -0.040194 & -0.2785 & 0.390923 \tabularnewline
7 & 0.032226 & 0.2233 & 0.412136 \tabularnewline
8 & 0.095525 & 0.6618 & 0.255627 \tabularnewline
9 & -0.057885 & -0.401 & 0.345087 \tabularnewline
10 & -0.068996 & -0.478 & 0.317404 \tabularnewline
11 & 0.123978 & 0.8589 & 0.19732 \tabularnewline
12 & -0.504425 & -3.4948 & 0.000516 \tabularnewline
13 & -0.145394 & -1.0073 & 0.159416 \tabularnewline
14 & 0.10493 & 0.727 & 0.235386 \tabularnewline
15 & -0.154956 & -1.0736 & 0.144192 \tabularnewline
16 & -0.056963 & -0.3946 & 0.347425 \tabularnewline
17 & -0.231854 & -1.6063 & 0.057381 \tabularnewline
18 & -0.05817 & -0.403 & 0.344363 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196551&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]-0.047793[/C][C]-0.3311[/C][C]0.370998[/C][/ROW]
[ROW][C]2[/C][C]0.031751[/C][C]0.22[/C][C]0.413411[/C][/ROW]
[ROW][C]3[/C][C]-0.040059[/C][C]-0.2775[/C][C]0.39128[/C][/ROW]
[ROW][C]4[/C][C]-0.010647[/C][C]-0.0738[/C][C]0.470752[/C][/ROW]
[ROW][C]5[/C][C]-0.093564[/C][C]-0.6482[/C][C]0.259962[/C][/ROW]
[ROW][C]6[/C][C]-0.040194[/C][C]-0.2785[/C][C]0.390923[/C][/ROW]
[ROW][C]7[/C][C]0.032226[/C][C]0.2233[/C][C]0.412136[/C][/ROW]
[ROW][C]8[/C][C]0.095525[/C][C]0.6618[/C][C]0.255627[/C][/ROW]
[ROW][C]9[/C][C]-0.057885[/C][C]-0.401[/C][C]0.345087[/C][/ROW]
[ROW][C]10[/C][C]-0.068996[/C][C]-0.478[/C][C]0.317404[/C][/ROW]
[ROW][C]11[/C][C]0.123978[/C][C]0.8589[/C][C]0.19732[/C][/ROW]
[ROW][C]12[/C][C]-0.504425[/C][C]-3.4948[/C][C]0.000516[/C][/ROW]
[ROW][C]13[/C][C]-0.145394[/C][C]-1.0073[/C][C]0.159416[/C][/ROW]
[ROW][C]14[/C][C]0.10493[/C][C]0.727[/C][C]0.235386[/C][/ROW]
[ROW][C]15[/C][C]-0.154956[/C][C]-1.0736[/C][C]0.144192[/C][/ROW]
[ROW][C]16[/C][C]-0.056963[/C][C]-0.3946[/C][C]0.347425[/C][/ROW]
[ROW][C]17[/C][C]-0.231854[/C][C]-1.6063[/C][C]0.057381[/C][/ROW]
[ROW][C]18[/C][C]-0.05817[/C][C]-0.403[/C][C]0.344363[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196551&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196551&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	-0.047793	-0.3311	0.370998
2	0.031751	0.22	0.413411
3	-0.040059	-0.2775	0.39128
4	-0.010647	-0.0738	0.470752
5	-0.093564	-0.6482	0.259962
6	-0.040194	-0.2785	0.390923
7	0.032226	0.2233	0.412136
8	0.095525	0.6618	0.255627
9	-0.057885	-0.401	0.345087
10	-0.068996	-0.478	0.317404
11	0.123978	0.8589	0.19732
12	-0.504425	-3.4948	0.000516
13	-0.145394	-1.0073	0.159416
14	0.10493	0.727	0.235386
15	-0.154956	-1.0736	0.144192
16	-0.056963	-0.3946	0.347425
17	-0.231854	-1.6063	0.057381
18	-0.05817	-0.403	0.344363

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 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 2 ; 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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code