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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 27 Dec 2014 14:02:35 +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/2014/Dec/27/t141968908041og7agw54c7kwz.htm/, Retrieved Thu, 16 May 2024 07:25:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271589, Retrieved Thu, 16 May 2024 07:25:59 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

155

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

-     [(Partial) Autocorrelation Function] [Gemiddelde consum...] [2014-10-19 19:56:14] [aab2fa127edf87899d1b292d8eac77df]
-   PD    [(Partial) Autocorrelation Function] [Autocorrelatie we...] [2014-12-27 14:02:35] [be7d2a6a6c016378f31f309d9b06695b] [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=271589&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=271589&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271589&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	0.004347	0.0366	0.485442
2	-0.38997	-3.2859	0.000791
3	-0.105358	-0.8878	0.188833
4	0.225458	1.8997	0.030764
5	-0.010189	-0.0859	0.465913
6	-0.215808	-1.8184	0.036608
7	-0.030217	-0.2546	0.399879
8	0.213376	1.7979	0.038219
9	-0.133195	-1.1223	0.132753
10	-0.351537	-2.9621	0.002077
11	-0.002242	-0.0189	0.492491
12	0.74289	6.2597	0
13	-0.010548	-0.0889	0.464716
14	-0.346369	-2.9186	0.002354
15	-0.103222	-0.8698	0.19368
16	0.186016	1.5674	0.060734
17	-0.038194	-0.3218	0.374264
18	-0.195484	-1.6472	0.051971

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.004347 & 0.0366 & 0.485442 \tabularnewline
2 & -0.38997 & -3.2859 & 0.000791 \tabularnewline
3 & -0.105358 & -0.8878 & 0.188833 \tabularnewline
4 & 0.225458 & 1.8997 & 0.030764 \tabularnewline
5 & -0.010189 & -0.0859 & 0.465913 \tabularnewline
6 & -0.215808 & -1.8184 & 0.036608 \tabularnewline
7 & -0.030217 & -0.2546 & 0.399879 \tabularnewline
8 & 0.213376 & 1.7979 & 0.038219 \tabularnewline
9 & -0.133195 & -1.1223 & 0.132753 \tabularnewline
10 & -0.351537 & -2.9621 & 0.002077 \tabularnewline
11 & -0.002242 & -0.0189 & 0.492491 \tabularnewline
12 & 0.74289 & 6.2597 & 0 \tabularnewline
13 & -0.010548 & -0.0889 & 0.464716 \tabularnewline
14 & -0.346369 & -2.9186 & 0.002354 \tabularnewline
15 & -0.103222 & -0.8698 & 0.19368 \tabularnewline
16 & 0.186016 & 1.5674 & 0.060734 \tabularnewline
17 & -0.038194 & -0.3218 & 0.374264 \tabularnewline
18 & -0.195484 & -1.6472 & 0.051971 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271589&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]0.004347[/C][C]0.0366[/C][C]0.485442[/C][/ROW]
[ROW][C]2[/C][C]-0.38997[/C][C]-3.2859[/C][C]0.000791[/C][/ROW]
[ROW][C]3[/C][C]-0.105358[/C][C]-0.8878[/C][C]0.188833[/C][/ROW]
[ROW][C]4[/C][C]0.225458[/C][C]1.8997[/C][C]0.030764[/C][/ROW]
[ROW][C]5[/C][C]-0.010189[/C][C]-0.0859[/C][C]0.465913[/C][/ROW]
[ROW][C]6[/C][C]-0.215808[/C][C]-1.8184[/C][C]0.036608[/C][/ROW]
[ROW][C]7[/C][C]-0.030217[/C][C]-0.2546[/C][C]0.399879[/C][/ROW]
[ROW][C]8[/C][C]0.213376[/C][C]1.7979[/C][C]0.038219[/C][/ROW]
[ROW][C]9[/C][C]-0.133195[/C][C]-1.1223[/C][C]0.132753[/C][/ROW]
[ROW][C]10[/C][C]-0.351537[/C][C]-2.9621[/C][C]0.002077[/C][/ROW]
[ROW][C]11[/C][C]-0.002242[/C][C]-0.0189[/C][C]0.492491[/C][/ROW]
[ROW][C]12[/C][C]0.74289[/C][C]6.2597[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.010548[/C][C]-0.0889[/C][C]0.464716[/C][/ROW]
[ROW][C]14[/C][C]-0.346369[/C][C]-2.9186[/C][C]0.002354[/C][/ROW]
[ROW][C]15[/C][C]-0.103222[/C][C]-0.8698[/C][C]0.19368[/C][/ROW]
[ROW][C]16[/C][C]0.186016[/C][C]1.5674[/C][C]0.060734[/C][/ROW]
[ROW][C]17[/C][C]-0.038194[/C][C]-0.3218[/C][C]0.374264[/C][/ROW]
[ROW][C]18[/C][C]-0.195484[/C][C]-1.6472[/C][C]0.051971[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271589&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271589&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	0.004347	0.0366	0.485442
2	-0.38997	-3.2859	0.000791
3	-0.105358	-0.8878	0.188833
4	0.225458	1.8997	0.030764
5	-0.010189	-0.0859	0.465913
6	-0.215808	-1.8184	0.036608
7	-0.030217	-0.2546	0.399879
8	0.213376	1.7979	0.038219
9	-0.133195	-1.1223	0.132753
10	-0.351537	-2.9621	0.002077
11	-0.002242	-0.0189	0.492491
12	0.74289	6.2597	0
13	-0.010548	-0.0889	0.464716
14	-0.346369	-2.9186	0.002354
15	-0.103222	-0.8698	0.19368
16	0.186016	1.5674	0.060734
17	-0.038194	-0.3218	0.374264
18	-0.195484	-1.6472	0.051971

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.004347	0.0366	0.485442
2	-0.389996	-3.2862	0.00079
3	-0.119481	-1.0068	0.158733
4	0.083634	0.7047	0.241648
5	-0.104244	-0.8784	0.191351
6	-0.142768	-1.203	0.11649
7	-0.050501	-0.4255	0.335868
8	0.072718	0.6127	0.271007
9	-0.221075	-1.8628	0.033313
10	-0.314017	-2.646	0.005012
11	-0.171357	-1.4439	0.076586
12	0.61883	5.2144	1e-06
13	-0.071758	-0.6046	0.273671
14	0.059348	0.5001	0.309283
15	-0.092047	-0.7756	0.220279
16	-0.1101	-0.9277	0.178347
17	-0.1492	-1.2572	0.106404
18	-0.058552	-0.4934	0.311639

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.004347 & 0.0366 & 0.485442 \tabularnewline
2 & -0.389996 & -3.2862 & 0.00079 \tabularnewline
3 & -0.119481 & -1.0068 & 0.158733 \tabularnewline
4 & 0.083634 & 0.7047 & 0.241648 \tabularnewline
5 & -0.104244 & -0.8784 & 0.191351 \tabularnewline
6 & -0.142768 & -1.203 & 0.11649 \tabularnewline
7 & -0.050501 & -0.4255 & 0.335868 \tabularnewline
8 & 0.072718 & 0.6127 & 0.271007 \tabularnewline
9 & -0.221075 & -1.8628 & 0.033313 \tabularnewline
10 & -0.314017 & -2.646 & 0.005012 \tabularnewline
11 & -0.171357 & -1.4439 & 0.076586 \tabularnewline
12 & 0.61883 & 5.2144 & 1e-06 \tabularnewline
13 & -0.071758 & -0.6046 & 0.273671 \tabularnewline
14 & 0.059348 & 0.5001 & 0.309283 \tabularnewline
15 & -0.092047 & -0.7756 & 0.220279 \tabularnewline
16 & -0.1101 & -0.9277 & 0.178347 \tabularnewline
17 & -0.1492 & -1.2572 & 0.106404 \tabularnewline
18 & -0.058552 & -0.4934 & 0.311639 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271589&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]0.004347[/C][C]0.0366[/C][C]0.485442[/C][/ROW]
[ROW][C]2[/C][C]-0.389996[/C][C]-3.2862[/C][C]0.00079[/C][/ROW]
[ROW][C]3[/C][C]-0.119481[/C][C]-1.0068[/C][C]0.158733[/C][/ROW]
[ROW][C]4[/C][C]0.083634[/C][C]0.7047[/C][C]0.241648[/C][/ROW]
[ROW][C]5[/C][C]-0.104244[/C][C]-0.8784[/C][C]0.191351[/C][/ROW]
[ROW][C]6[/C][C]-0.142768[/C][C]-1.203[/C][C]0.11649[/C][/ROW]
[ROW][C]7[/C][C]-0.050501[/C][C]-0.4255[/C][C]0.335868[/C][/ROW]
[ROW][C]8[/C][C]0.072718[/C][C]0.6127[/C][C]0.271007[/C][/ROW]
[ROW][C]9[/C][C]-0.221075[/C][C]-1.8628[/C][C]0.033313[/C][/ROW]
[ROW][C]10[/C][C]-0.314017[/C][C]-2.646[/C][C]0.005012[/C][/ROW]
[ROW][C]11[/C][C]-0.171357[/C][C]-1.4439[/C][C]0.076586[/C][/ROW]
[ROW][C]12[/C][C]0.61883[/C][C]5.2144[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.071758[/C][C]-0.6046[/C][C]0.273671[/C][/ROW]
[ROW][C]14[/C][C]0.059348[/C][C]0.5001[/C][C]0.309283[/C][/ROW]
[ROW][C]15[/C][C]-0.092047[/C][C]-0.7756[/C][C]0.220279[/C][/ROW]
[ROW][C]16[/C][C]-0.1101[/C][C]-0.9277[/C][C]0.178347[/C][/ROW]
[ROW][C]17[/C][C]-0.1492[/C][C]-1.2572[/C][C]0.106404[/C][/ROW]
[ROW][C]18[/C][C]-0.058552[/C][C]-0.4934[/C][C]0.311639[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271589&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271589&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	0.004347	0.0366	0.485442
2	-0.389996	-3.2862	0.00079
3	-0.119481	-1.0068	0.158733
4	0.083634	0.7047	0.241648
5	-0.104244	-0.8784	0.191351
6	-0.142768	-1.203	0.11649
7	-0.050501	-0.4255	0.335868
8	0.072718	0.6127	0.271007
9	-0.221075	-1.8628	0.033313
10	-0.314017	-2.646	0.005012
11	-0.171357	-1.4439	0.076586
12	0.61883	5.2144	1e-06
13	-0.071758	-0.6046	0.273671
14	0.059348	0.5001	0.309283
15	-0.092047	-0.7756	0.220279
16	-0.1101	-0.9277	0.178347
17	-0.1492	-1.2572	0.106404
18	-0.058552	-0.4934	0.311639

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