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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

Wed, 29 Dec 2010 13:40:49 +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/2010/Dec/29/t1293629927bnmd1v5xyg44q25.htm/, Retrieved Fri, 03 May 2024 04:22:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116822, Retrieved Fri, 03 May 2024 04:22:09 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

124

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

-     [Univariate Explorative Data Analysis] [] [2010-12-26 15:53:52] [70635d2e8be5a44e0387ac70a19b85b5]
-   PD  [Univariate Explorative Data Analysis] [] [2010-12-27 12:40:14] [70635d2e8be5a44e0387ac70a19b85b5]
-    D    [Univariate Explorative Data Analysis] [] [2010-12-27 15:32:59] [70635d2e8be5a44e0387ac70a19b85b5]
- RMPD        [(Partial) Autocorrelation Function] [] [2010-12-29 13:40:49] [5e4b6b538311b7e958647ef5010fb0e5] [Current]
-   P           [(Partial) Autocorrelation Function] [] [2010-12-29 13:46:42] [70635d2e8be5a44e0387ac70a19b85b5] 
-   P             [(Partial) Autocorrelation Function] [] [2010-12-29 18:35:21] [70635d2e8be5a44e0387ac70a19b85b5] 

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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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116822&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116822&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116822&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.07797	-0.9356	0.175511
2	0.082368	0.9884	0.162303
3	0.358326	4.2999	1.6e-05
4	-0.021532	-0.2584	0.398238
5	0.165306	1.9837	0.024597
6	0.335937	4.0312	4.5e-05
7	-0.196072	-2.3529	0.009991
8	0.196043	2.3525	0.01
9	0.273313	3.2798	0.000652
10	-0.132214	-1.5866	0.057402
11	0.15768	1.8922	0.030238
12	-0.106264	-1.2752	0.102152
13	-0.118954	-1.4274	0.077808
14	0.130769	1.5692	0.059395
15	-0.013639	-0.1637	0.435112
16	-0.208098	-2.4972	0.006822
17	0.156978	1.8837	0.030809
18	-0.11155	-1.3386	0.091405
19	-0.153151	-1.8378	0.034076
20	0.125545	1.5065	0.067059
21	-0.218096	-2.6172	0.004907

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.07797 & -0.9356 & 0.175511 \tabularnewline
2 & 0.082368 & 0.9884 & 0.162303 \tabularnewline
3 & 0.358326 & 4.2999 & 1.6e-05 \tabularnewline
4 & -0.021532 & -0.2584 & 0.398238 \tabularnewline
5 & 0.165306 & 1.9837 & 0.024597 \tabularnewline
6 & 0.335937 & 4.0312 & 4.5e-05 \tabularnewline
7 & -0.196072 & -2.3529 & 0.009991 \tabularnewline
8 & 0.196043 & 2.3525 & 0.01 \tabularnewline
9 & 0.273313 & 3.2798 & 0.000652 \tabularnewline
10 & -0.132214 & -1.5866 & 0.057402 \tabularnewline
11 & 0.15768 & 1.8922 & 0.030238 \tabularnewline
12 & -0.106264 & -1.2752 & 0.102152 \tabularnewline
13 & -0.118954 & -1.4274 & 0.077808 \tabularnewline
14 & 0.130769 & 1.5692 & 0.059395 \tabularnewline
15 & -0.013639 & -0.1637 & 0.435112 \tabularnewline
16 & -0.208098 & -2.4972 & 0.006822 \tabularnewline
17 & 0.156978 & 1.8837 & 0.030809 \tabularnewline
18 & -0.11155 & -1.3386 & 0.091405 \tabularnewline
19 & -0.153151 & -1.8378 & 0.034076 \tabularnewline
20 & 0.125545 & 1.5065 & 0.067059 \tabularnewline
21 & -0.218096 & -2.6172 & 0.004907 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116822&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]-0.07797[/C][C]-0.9356[/C][C]0.175511[/C][/ROW]
[ROW][C]2[/C][C]0.082368[/C][C]0.9884[/C][C]0.162303[/C][/ROW]
[ROW][C]3[/C][C]0.358326[/C][C]4.2999[/C][C]1.6e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.021532[/C][C]-0.2584[/C][C]0.398238[/C][/ROW]
[ROW][C]5[/C][C]0.165306[/C][C]1.9837[/C][C]0.024597[/C][/ROW]
[ROW][C]6[/C][C]0.335937[/C][C]4.0312[/C][C]4.5e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.196072[/C][C]-2.3529[/C][C]0.009991[/C][/ROW]
[ROW][C]8[/C][C]0.196043[/C][C]2.3525[/C][C]0.01[/C][/ROW]
[ROW][C]9[/C][C]0.273313[/C][C]3.2798[/C][C]0.000652[/C][/ROW]
[ROW][C]10[/C][C]-0.132214[/C][C]-1.5866[/C][C]0.057402[/C][/ROW]
[ROW][C]11[/C][C]0.15768[/C][C]1.8922[/C][C]0.030238[/C][/ROW]
[ROW][C]12[/C][C]-0.106264[/C][C]-1.2752[/C][C]0.102152[/C][/ROW]
[ROW][C]13[/C][C]-0.118954[/C][C]-1.4274[/C][C]0.077808[/C][/ROW]
[ROW][C]14[/C][C]0.130769[/C][C]1.5692[/C][C]0.059395[/C][/ROW]
[ROW][C]15[/C][C]-0.013639[/C][C]-0.1637[/C][C]0.435112[/C][/ROW]
[ROW][C]16[/C][C]-0.208098[/C][C]-2.4972[/C][C]0.006822[/C][/ROW]
[ROW][C]17[/C][C]0.156978[/C][C]1.8837[/C][C]0.030809[/C][/ROW]
[ROW][C]18[/C][C]-0.11155[/C][C]-1.3386[/C][C]0.091405[/C][/ROW]
[ROW][C]19[/C][C]-0.153151[/C][C]-1.8378[/C][C]0.034076[/C][/ROW]
[ROW][C]20[/C][C]0.125545[/C][C]1.5065[/C][C]0.067059[/C][/ROW]
[ROW][C]21[/C][C]-0.218096[/C][C]-2.6172[/C][C]0.004907[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116822&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116822&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	-0.07797	-0.9356	0.175511
2	0.082368	0.9884	0.162303
3	0.358326	4.2999	1.6e-05
4	-0.021532	-0.2584	0.398238
5	0.165306	1.9837	0.024597
6	0.335937	4.0312	4.5e-05
7	-0.196072	-2.3529	0.009991
8	0.196043	2.3525	0.01
9	0.273313	3.2798	0.000652
10	-0.132214	-1.5866	0.057402
11	0.15768	1.8922	0.030238
12	-0.106264	-1.2752	0.102152
13	-0.118954	-1.4274	0.077808
14	0.130769	1.5692	0.059395
15	-0.013639	-0.1637	0.435112
16	-0.208098	-2.4972	0.006822
17	0.156978	1.8837	0.030809
18	-0.11155	-1.3386	0.091405
19	-0.153151	-1.8378	0.034076
20	0.125545	1.5065	0.067059
21	-0.218096	-2.6172	0.004907

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.07797	-0.9356	0.175511
2	0.076756	0.9211	0.179278
3	0.374712	4.4965	7e-06
4	0.041492	0.4979	0.309656
5	0.117001	1.404	0.081234
6	0.275196	3.3023	0.000605
7	-0.194924	-2.3391	0.010353
8	0.024017	0.2882	0.386802
9	0.178267	2.1392	0.017053
10	-0.049244	-0.5909	0.277746
11	-0.040587	-0.487	0.313485
12	-0.305537	-3.6664	0.000173
13	-0.10136	-1.2163	0.112925
14	-0.054378	-0.6525	0.257547
15	0.061007	0.7321	0.232653
16	-0.077135	-0.9256	0.178095
17	0.09544	1.1453	0.126996
18	0.045056	0.5407	0.294786
19	-0.160754	-1.929	0.027846
20	0.084791	1.0175	0.155313
21	-0.008696	-0.1043	0.458518

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.07797 & -0.9356 & 0.175511 \tabularnewline
2 & 0.076756 & 0.9211 & 0.179278 \tabularnewline
3 & 0.374712 & 4.4965 & 7e-06 \tabularnewline
4 & 0.041492 & 0.4979 & 0.309656 \tabularnewline
5 & 0.117001 & 1.404 & 0.081234 \tabularnewline
6 & 0.275196 & 3.3023 & 0.000605 \tabularnewline
7 & -0.194924 & -2.3391 & 0.010353 \tabularnewline
8 & 0.024017 & 0.2882 & 0.386802 \tabularnewline
9 & 0.178267 & 2.1392 & 0.017053 \tabularnewline
10 & -0.049244 & -0.5909 & 0.277746 \tabularnewline
11 & -0.040587 & -0.487 & 0.313485 \tabularnewline
12 & -0.305537 & -3.6664 & 0.000173 \tabularnewline
13 & -0.10136 & -1.2163 & 0.112925 \tabularnewline
14 & -0.054378 & -0.6525 & 0.257547 \tabularnewline
15 & 0.061007 & 0.7321 & 0.232653 \tabularnewline
16 & -0.077135 & -0.9256 & 0.178095 \tabularnewline
17 & 0.09544 & 1.1453 & 0.126996 \tabularnewline
18 & 0.045056 & 0.5407 & 0.294786 \tabularnewline
19 & -0.160754 & -1.929 & 0.027846 \tabularnewline
20 & 0.084791 & 1.0175 & 0.155313 \tabularnewline
21 & -0.008696 & -0.1043 & 0.458518 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116822&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]-0.07797[/C][C]-0.9356[/C][C]0.175511[/C][/ROW]
[ROW][C]2[/C][C]0.076756[/C][C]0.9211[/C][C]0.179278[/C][/ROW]
[ROW][C]3[/C][C]0.374712[/C][C]4.4965[/C][C]7e-06[/C][/ROW]
[ROW][C]4[/C][C]0.041492[/C][C]0.4979[/C][C]0.309656[/C][/ROW]
[ROW][C]5[/C][C]0.117001[/C][C]1.404[/C][C]0.081234[/C][/ROW]
[ROW][C]6[/C][C]0.275196[/C][C]3.3023[/C][C]0.000605[/C][/ROW]
[ROW][C]7[/C][C]-0.194924[/C][C]-2.3391[/C][C]0.010353[/C][/ROW]
[ROW][C]8[/C][C]0.024017[/C][C]0.2882[/C][C]0.386802[/C][/ROW]
[ROW][C]9[/C][C]0.178267[/C][C]2.1392[/C][C]0.017053[/C][/ROW]
[ROW][C]10[/C][C]-0.049244[/C][C]-0.5909[/C][C]0.277746[/C][/ROW]
[ROW][C]11[/C][C]-0.040587[/C][C]-0.487[/C][C]0.313485[/C][/ROW]
[ROW][C]12[/C][C]-0.305537[/C][C]-3.6664[/C][C]0.000173[/C][/ROW]
[ROW][C]13[/C][C]-0.10136[/C][C]-1.2163[/C][C]0.112925[/C][/ROW]
[ROW][C]14[/C][C]-0.054378[/C][C]-0.6525[/C][C]0.257547[/C][/ROW]
[ROW][C]15[/C][C]0.061007[/C][C]0.7321[/C][C]0.232653[/C][/ROW]
[ROW][C]16[/C][C]-0.077135[/C][C]-0.9256[/C][C]0.178095[/C][/ROW]
[ROW][C]17[/C][C]0.09544[/C][C]1.1453[/C][C]0.126996[/C][/ROW]
[ROW][C]18[/C][C]0.045056[/C][C]0.5407[/C][C]0.294786[/C][/ROW]
[ROW][C]19[/C][C]-0.160754[/C][C]-1.929[/C][C]0.027846[/C][/ROW]
[ROW][C]20[/C][C]0.084791[/C][C]1.0175[/C][C]0.155313[/C][/ROW]
[ROW][C]21[/C][C]-0.008696[/C][C]-0.1043[/C][C]0.458518[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116822&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116822&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	-0.07797	-0.9356	0.175511
2	0.076756	0.9211	0.179278
3	0.374712	4.4965	7e-06
4	0.041492	0.4979	0.309656
5	0.117001	1.404	0.081234
6	0.275196	3.3023	0.000605
7	-0.194924	-2.3391	0.010353
8	0.024017	0.2882	0.386802
9	0.178267	2.1392	0.017053
10	-0.049244	-0.5909	0.277746
11	-0.040587	-0.487	0.313485
12	-0.305537	-3.6664	0.000173
13	-0.10136	-1.2163	0.112925
14	-0.054378	-0.6525	0.257547
15	0.061007	0.7321	0.232653
16	-0.077135	-0.9256	0.178095
17	0.09544	1.1453	0.126996
18	0.045056	0.5407	0.294786
19	-0.160754	-1.929	0.027846
20	0.084791	1.0175	0.155313
21	-0.008696	-0.1043	0.458518

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 = -0.2 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = -0.2 ; par3 = 0 ; par4 = 1 ; 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