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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 20 Oct 2016 16:14:06 +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/Oct/20/t1476976498cj97hp20ib7u53i.htm/, Retrieved Sat, 04 May 2024 23:08:08 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 23:08:08 +0200

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No (this computation is public)

User-defined keywords

Estimated Impact

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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	1 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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1 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=&T=0

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

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.223294	1.7152	0.045783
2	-0.000191	-0.0015	0.499417
3	-0.068329	-0.5248	0.300828
4	-0.068651	-0.5273	0.299974
5	-0.17695	-1.3592	0.089632
6	-0.227617	-1.7484	0.042802
7	-0.174547	-1.3407	0.092575
8	-0.094756	-0.7278	0.234796
9	-0.07568	-0.5813	0.281624
10	-0.043067	-0.3308	0.370982
11	0.208208	1.5993	0.057551
12	0.211472	1.6243	0.054817
13	0.042778	0.3286	0.371818
14	-0.01208	-0.0928	0.463193
15	-0.017592	-0.1351	0.446485
16	-0.045295	-0.3479	0.364571
17	-0.11259	-0.8648	0.19532
18	-0.126208	-0.9694	0.168146
19	-0.062142	-0.4773	0.317447
20	-0.081951	-0.6295	0.265733
21	-0.000587	-0.0045	0.49821
22	-0.049801	-0.3825	0.351723
23	0.151356	1.1626	0.124839
24	0.053666	0.4122	0.340837

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.223294 & 1.7152 & 0.045783 \tabularnewline
2 & -0.000191 & -0.0015 & 0.499417 \tabularnewline
3 & -0.068329 & -0.5248 & 0.300828 \tabularnewline
4 & -0.068651 & -0.5273 & 0.299974 \tabularnewline
5 & -0.17695 & -1.3592 & 0.089632 \tabularnewline
6 & -0.227617 & -1.7484 & 0.042802 \tabularnewline
7 & -0.174547 & -1.3407 & 0.092575 \tabularnewline
8 & -0.094756 & -0.7278 & 0.234796 \tabularnewline
9 & -0.07568 & -0.5813 & 0.281624 \tabularnewline
10 & -0.043067 & -0.3308 & 0.370982 \tabularnewline
11 & 0.208208 & 1.5993 & 0.057551 \tabularnewline
12 & 0.211472 & 1.6243 & 0.054817 \tabularnewline
13 & 0.042778 & 0.3286 & 0.371818 \tabularnewline
14 & -0.01208 & -0.0928 & 0.463193 \tabularnewline
15 & -0.017592 & -0.1351 & 0.446485 \tabularnewline
16 & -0.045295 & -0.3479 & 0.364571 \tabularnewline
17 & -0.11259 & -0.8648 & 0.19532 \tabularnewline
18 & -0.126208 & -0.9694 & 0.168146 \tabularnewline
19 & -0.062142 & -0.4773 & 0.317447 \tabularnewline
20 & -0.081951 & -0.6295 & 0.265733 \tabularnewline
21 & -0.000587 & -0.0045 & 0.49821 \tabularnewline
22 & -0.049801 & -0.3825 & 0.351723 \tabularnewline
23 & 0.151356 & 1.1626 & 0.124839 \tabularnewline
24 & 0.053666 & 0.4122 & 0.340837 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.223294[/C][C]1.7152[/C][C]0.045783[/C][/ROW]
[ROW][C]2[/C][C]-0.000191[/C][C]-0.0015[/C][C]0.499417[/C][/ROW]
[ROW][C]3[/C][C]-0.068329[/C][C]-0.5248[/C][C]0.300828[/C][/ROW]
[ROW][C]4[/C][C]-0.068651[/C][C]-0.5273[/C][C]0.299974[/C][/ROW]
[ROW][C]5[/C][C]-0.17695[/C][C]-1.3592[/C][C]0.089632[/C][/ROW]
[ROW][C]6[/C][C]-0.227617[/C][C]-1.7484[/C][C]0.042802[/C][/ROW]
[ROW][C]7[/C][C]-0.174547[/C][C]-1.3407[/C][C]0.092575[/C][/ROW]
[ROW][C]8[/C][C]-0.094756[/C][C]-0.7278[/C][C]0.234796[/C][/ROW]
[ROW][C]9[/C][C]-0.07568[/C][C]-0.5813[/C][C]0.281624[/C][/ROW]
[ROW][C]10[/C][C]-0.043067[/C][C]-0.3308[/C][C]0.370982[/C][/ROW]
[ROW][C]11[/C][C]0.208208[/C][C]1.5993[/C][C]0.057551[/C][/ROW]
[ROW][C]12[/C][C]0.211472[/C][C]1.6243[/C][C]0.054817[/C][/ROW]
[ROW][C]13[/C][C]0.042778[/C][C]0.3286[/C][C]0.371818[/C][/ROW]
[ROW][C]14[/C][C]-0.01208[/C][C]-0.0928[/C][C]0.463193[/C][/ROW]
[ROW][C]15[/C][C]-0.017592[/C][C]-0.1351[/C][C]0.446485[/C][/ROW]
[ROW][C]16[/C][C]-0.045295[/C][C]-0.3479[/C][C]0.364571[/C][/ROW]
[ROW][C]17[/C][C]-0.11259[/C][C]-0.8648[/C][C]0.19532[/C][/ROW]
[ROW][C]18[/C][C]-0.126208[/C][C]-0.9694[/C][C]0.168146[/C][/ROW]
[ROW][C]19[/C][C]-0.062142[/C][C]-0.4773[/C][C]0.317447[/C][/ROW]
[ROW][C]20[/C][C]-0.081951[/C][C]-0.6295[/C][C]0.265733[/C][/ROW]
[ROW][C]21[/C][C]-0.000587[/C][C]-0.0045[/C][C]0.49821[/C][/ROW]
[ROW][C]22[/C][C]-0.049801[/C][C]-0.3825[/C][C]0.351723[/C][/ROW]
[ROW][C]23[/C][C]0.151356[/C][C]1.1626[/C][C]0.124839[/C][/ROW]
[ROW][C]24[/C][C]0.053666[/C][C]0.4122[/C][C]0.340837[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.223294	1.7152	0.045783
2	-0.000191	-0.0015	0.499417
3	-0.068329	-0.5248	0.300828
4	-0.068651	-0.5273	0.299974
5	-0.17695	-1.3592	0.089632
6	-0.227617	-1.7484	0.042802
7	-0.174547	-1.3407	0.092575
8	-0.094756	-0.7278	0.234796
9	-0.07568	-0.5813	0.281624
10	-0.043067	-0.3308	0.370982
11	0.208208	1.5993	0.057551
12	0.211472	1.6243	0.054817
13	0.042778	0.3286	0.371818
14	-0.01208	-0.0928	0.463193
15	-0.017592	-0.1351	0.446485
16	-0.045295	-0.3479	0.364571
17	-0.11259	-0.8648	0.19532
18	-0.126208	-0.9694	0.168146
19	-0.062142	-0.4773	0.317447
20	-0.081951	-0.6295	0.265733
21	-0.000587	-0.0045	0.49821
22	-0.049801	-0.3825	0.351723
23	0.151356	1.1626	0.124839
24	0.053666	0.4122	0.340837

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.223294	1.7152	0.045783
2	-0.052678	-0.4046	0.343608
3	-0.059653	-0.4582	0.324244
4	-0.041829	-0.3213	0.374561
5	-0.164057	-1.2601	0.106289
6	-0.173147	-1.33	0.094324
7	-0.118968	-0.9138	0.182268
8	-0.085416	-0.6561	0.257158
9	-0.110897	-0.8518	0.198881
10	-0.09777	-0.751	0.227823
11	0.154158	1.1841	0.120558
12	0.054433	0.4181	0.338692
13	-0.090336	-0.6939	0.24524
14	-0.047357	-0.3638	0.358671
15	-0.052688	-0.4047	0.34358
16	-0.049305	-0.3787	0.353128
17	-0.062883	-0.483	0.315437
18	-0.063605	-0.4886	0.313484
19	-0.033799	-0.2596	0.398033
20	-0.106457	-0.8177	0.208405
21	0.011055	0.0849	0.466309
22	-0.16422	-1.2614	0.106064
23	0.051696	0.3971	0.346368
24	-0.100155	-0.7693	0.222392

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.223294 & 1.7152 & 0.045783 \tabularnewline
2 & -0.052678 & -0.4046 & 0.343608 \tabularnewline
3 & -0.059653 & -0.4582 & 0.324244 \tabularnewline
4 & -0.041829 & -0.3213 & 0.374561 \tabularnewline
5 & -0.164057 & -1.2601 & 0.106289 \tabularnewline
6 & -0.173147 & -1.33 & 0.094324 \tabularnewline
7 & -0.118968 & -0.9138 & 0.182268 \tabularnewline
8 & -0.085416 & -0.6561 & 0.257158 \tabularnewline
9 & -0.110897 & -0.8518 & 0.198881 \tabularnewline
10 & -0.09777 & -0.751 & 0.227823 \tabularnewline
11 & 0.154158 & 1.1841 & 0.120558 \tabularnewline
12 & 0.054433 & 0.4181 & 0.338692 \tabularnewline
13 & -0.090336 & -0.6939 & 0.24524 \tabularnewline
14 & -0.047357 & -0.3638 & 0.358671 \tabularnewline
15 & -0.052688 & -0.4047 & 0.34358 \tabularnewline
16 & -0.049305 & -0.3787 & 0.353128 \tabularnewline
17 & -0.062883 & -0.483 & 0.315437 \tabularnewline
18 & -0.063605 & -0.4886 & 0.313484 \tabularnewline
19 & -0.033799 & -0.2596 & 0.398033 \tabularnewline
20 & -0.106457 & -0.8177 & 0.208405 \tabularnewline
21 & 0.011055 & 0.0849 & 0.466309 \tabularnewline
22 & -0.16422 & -1.2614 & 0.106064 \tabularnewline
23 & 0.051696 & 0.3971 & 0.346368 \tabularnewline
24 & -0.100155 & -0.7693 & 0.222392 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.223294[/C][C]1.7152[/C][C]0.045783[/C][/ROW]
[ROW][C]2[/C][C]-0.052678[/C][C]-0.4046[/C][C]0.343608[/C][/ROW]
[ROW][C]3[/C][C]-0.059653[/C][C]-0.4582[/C][C]0.324244[/C][/ROW]
[ROW][C]4[/C][C]-0.041829[/C][C]-0.3213[/C][C]0.374561[/C][/ROW]
[ROW][C]5[/C][C]-0.164057[/C][C]-1.2601[/C][C]0.106289[/C][/ROW]
[ROW][C]6[/C][C]-0.173147[/C][C]-1.33[/C][C]0.094324[/C][/ROW]
[ROW][C]7[/C][C]-0.118968[/C][C]-0.9138[/C][C]0.182268[/C][/ROW]
[ROW][C]8[/C][C]-0.085416[/C][C]-0.6561[/C][C]0.257158[/C][/ROW]
[ROW][C]9[/C][C]-0.110897[/C][C]-0.8518[/C][C]0.198881[/C][/ROW]
[ROW][C]10[/C][C]-0.09777[/C][C]-0.751[/C][C]0.227823[/C][/ROW]
[ROW][C]11[/C][C]0.154158[/C][C]1.1841[/C][C]0.120558[/C][/ROW]
[ROW][C]12[/C][C]0.054433[/C][C]0.4181[/C][C]0.338692[/C][/ROW]
[ROW][C]13[/C][C]-0.090336[/C][C]-0.6939[/C][C]0.24524[/C][/ROW]
[ROW][C]14[/C][C]-0.047357[/C][C]-0.3638[/C][C]0.358671[/C][/ROW]
[ROW][C]15[/C][C]-0.052688[/C][C]-0.4047[/C][C]0.34358[/C][/ROW]
[ROW][C]16[/C][C]-0.049305[/C][C]-0.3787[/C][C]0.353128[/C][/ROW]
[ROW][C]17[/C][C]-0.062883[/C][C]-0.483[/C][C]0.315437[/C][/ROW]
[ROW][C]18[/C][C]-0.063605[/C][C]-0.4886[/C][C]0.313484[/C][/ROW]
[ROW][C]19[/C][C]-0.033799[/C][C]-0.2596[/C][C]0.398033[/C][/ROW]
[ROW][C]20[/C][C]-0.106457[/C][C]-0.8177[/C][C]0.208405[/C][/ROW]
[ROW][C]21[/C][C]0.011055[/C][C]0.0849[/C][C]0.466309[/C][/ROW]
[ROW][C]22[/C][C]-0.16422[/C][C]-1.2614[/C][C]0.106064[/C][/ROW]
[ROW][C]23[/C][C]0.051696[/C][C]0.3971[/C][C]0.346368[/C][/ROW]
[ROW][C]24[/C][C]-0.100155[/C][C]-0.7693[/C][C]0.222392[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.223294	1.7152	0.045783
2	-0.052678	-0.4046	0.343608
3	-0.059653	-0.4582	0.324244
4	-0.041829	-0.3213	0.374561
5	-0.164057	-1.2601	0.106289
6	-0.173147	-1.33	0.094324
7	-0.118968	-0.9138	0.182268
8	-0.085416	-0.6561	0.257158
9	-0.110897	-0.8518	0.198881
10	-0.09777	-0.751	0.227823
11	0.154158	1.1841	0.120558
12	0.054433	0.4181	0.338692
13	-0.090336	-0.6939	0.24524
14	-0.047357	-0.3638	0.358671
15	-0.052688	-0.4047	0.34358
16	-0.049305	-0.3787	0.353128
17	-0.062883	-0.483	0.315437
18	-0.063605	-0.4886	0.313484
19	-0.033799	-0.2596	0.398033
20	-0.106457	-0.8177	0.208405
21	0.011055	0.0849	0.466309
22	-0.16422	-1.2614	0.106064
23	0.051696	0.3971	0.346368
24	-0.100155	-0.7693	0.222392

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 24 ; 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)
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,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