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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 21 Dec 2008 11:00:26 -0700

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/2008/Dec/21/t12298824558otox84c46kq0p0.htm/, Retrieved Sun, 19 May 2024 11:29:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35720, Retrieved Sun, 19 May 2024 11:29:58 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

116

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

-       [(Partial) Autocorrelation Function] [] [2008-12-21 18:00:26] [a2d5a6282476ec2b5afae6fb53d308f8] [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	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35720&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35720&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35720&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.946684	7.333	0
2	0.903823	7.001	0
3	0.873053	6.7626	0
4	0.829824	6.4278	0
5	0.779384	6.0371	0
6	0.731647	5.6673	0
7	0.677545	5.2482	1e-06
8	0.617878	4.7861	6e-06
9	0.55822	4.324	2.9e-05
10	0.507634	3.9321	0.00011
11	0.460407	3.5663	0.000359
12	0.403291	3.1239	0.001374
13	0.360953	2.7959	0.003471
14	0.315473	2.4436	0.008749
15	0.257396	1.9938	0.025364
16	0.197344	1.5286	0.065807
17	0.153065	1.1856	0.12022

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.946684 & 7.333 & 0 \tabularnewline
2 & 0.903823 & 7.001 & 0 \tabularnewline
3 & 0.873053 & 6.7626 & 0 \tabularnewline
4 & 0.829824 & 6.4278 & 0 \tabularnewline
5 & 0.779384 & 6.0371 & 0 \tabularnewline
6 & 0.731647 & 5.6673 & 0 \tabularnewline
7 & 0.677545 & 5.2482 & 1e-06 \tabularnewline
8 & 0.617878 & 4.7861 & 6e-06 \tabularnewline
9 & 0.55822 & 4.324 & 2.9e-05 \tabularnewline
10 & 0.507634 & 3.9321 & 0.00011 \tabularnewline
11 & 0.460407 & 3.5663 & 0.000359 \tabularnewline
12 & 0.403291 & 3.1239 & 0.001374 \tabularnewline
13 & 0.360953 & 2.7959 & 0.003471 \tabularnewline
14 & 0.315473 & 2.4436 & 0.008749 \tabularnewline
15 & 0.257396 & 1.9938 & 0.025364 \tabularnewline
16 & 0.197344 & 1.5286 & 0.065807 \tabularnewline
17 & 0.153065 & 1.1856 & 0.12022 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35720&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]0.946684[/C][C]7.333[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.903823[/C][C]7.001[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.873053[/C][C]6.7626[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.829824[/C][C]6.4278[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.779384[/C][C]6.0371[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.731647[/C][C]5.6673[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.677545[/C][C]5.2482[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]0.617878[/C][C]4.7861[/C][C]6e-06[/C][/ROW]
[ROW][C]9[/C][C]0.55822[/C][C]4.324[/C][C]2.9e-05[/C][/ROW]
[ROW][C]10[/C][C]0.507634[/C][C]3.9321[/C][C]0.00011[/C][/ROW]
[ROW][C]11[/C][C]0.460407[/C][C]3.5663[/C][C]0.000359[/C][/ROW]
[ROW][C]12[/C][C]0.403291[/C][C]3.1239[/C][C]0.001374[/C][/ROW]
[ROW][C]13[/C][C]0.360953[/C][C]2.7959[/C][C]0.003471[/C][/ROW]
[ROW][C]14[/C][C]0.315473[/C][C]2.4436[/C][C]0.008749[/C][/ROW]
[ROW][C]15[/C][C]0.257396[/C][C]1.9938[/C][C]0.025364[/C][/ROW]
[ROW][C]16[/C][C]0.197344[/C][C]1.5286[/C][C]0.065807[/C][/ROW]
[ROW][C]17[/C][C]0.153065[/C][C]1.1856[/C][C]0.12022[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35720&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35720&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	0.946684	7.333	0
2	0.903823	7.001	0
3	0.873053	6.7626	0
4	0.829824	6.4278	0
5	0.779384	6.0371	0
6	0.731647	5.6673	0
7	0.677545	5.2482	1e-06
8	0.617878	4.7861	6e-06
9	0.55822	4.324	2.9e-05
10	0.507634	3.9321	0.00011
11	0.460407	3.5663	0.000359
12	0.403291	3.1239	0.001374
13	0.360953	2.7959	0.003471
14	0.315473	2.4436	0.008749
15	0.257396	1.9938	0.025364
16	0.197344	1.5286	0.065807
17	0.153065	1.1856	0.12022

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.946684	7.333	0
2	0.073347	0.5681	0.286029
3	0.104035	0.8059	0.211755
4	-0.114494	-0.8869	0.189346
5	-0.102456	-0.7936	0.215271
6	-0.041349	-0.3203	0.374932
7	-0.095554	-0.7402	0.231045
8	-0.085512	-0.6624	0.255135
9	-0.059522	-0.4611	0.323213
10	0.050717	0.3929	0.34791
11	0.0382	0.2959	0.384167
12	-0.091586	-0.7094	0.240405
13	0.093947	0.7277	0.23481
14	-0.068655	-0.5318	0.298414
15	-0.131905	-1.0217	0.155506
16	-0.127615	-0.9885	0.163439
17	0.050558	0.3916	0.348363

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.946684 & 7.333 & 0 \tabularnewline
2 & 0.073347 & 0.5681 & 0.286029 \tabularnewline
3 & 0.104035 & 0.8059 & 0.211755 \tabularnewline
4 & -0.114494 & -0.8869 & 0.189346 \tabularnewline
5 & -0.102456 & -0.7936 & 0.215271 \tabularnewline
6 & -0.041349 & -0.3203 & 0.374932 \tabularnewline
7 & -0.095554 & -0.7402 & 0.231045 \tabularnewline
8 & -0.085512 & -0.6624 & 0.255135 \tabularnewline
9 & -0.059522 & -0.4611 & 0.323213 \tabularnewline
10 & 0.050717 & 0.3929 & 0.34791 \tabularnewline
11 & 0.0382 & 0.2959 & 0.384167 \tabularnewline
12 & -0.091586 & -0.7094 & 0.240405 \tabularnewline
13 & 0.093947 & 0.7277 & 0.23481 \tabularnewline
14 & -0.068655 & -0.5318 & 0.298414 \tabularnewline
15 & -0.131905 & -1.0217 & 0.155506 \tabularnewline
16 & -0.127615 & -0.9885 & 0.163439 \tabularnewline
17 & 0.050558 & 0.3916 & 0.348363 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35720&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]0.946684[/C][C]7.333[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.073347[/C][C]0.5681[/C][C]0.286029[/C][/ROW]
[ROW][C]3[/C][C]0.104035[/C][C]0.8059[/C][C]0.211755[/C][/ROW]
[ROW][C]4[/C][C]-0.114494[/C][C]-0.8869[/C][C]0.189346[/C][/ROW]
[ROW][C]5[/C][C]-0.102456[/C][C]-0.7936[/C][C]0.215271[/C][/ROW]
[ROW][C]6[/C][C]-0.041349[/C][C]-0.3203[/C][C]0.374932[/C][/ROW]
[ROW][C]7[/C][C]-0.095554[/C][C]-0.7402[/C][C]0.231045[/C][/ROW]
[ROW][C]8[/C][C]-0.085512[/C][C]-0.6624[/C][C]0.255135[/C][/ROW]
[ROW][C]9[/C][C]-0.059522[/C][C]-0.4611[/C][C]0.323213[/C][/ROW]
[ROW][C]10[/C][C]0.050717[/C][C]0.3929[/C][C]0.34791[/C][/ROW]
[ROW][C]11[/C][C]0.0382[/C][C]0.2959[/C][C]0.384167[/C][/ROW]
[ROW][C]12[/C][C]-0.091586[/C][C]-0.7094[/C][C]0.240405[/C][/ROW]
[ROW][C]13[/C][C]0.093947[/C][C]0.7277[/C][C]0.23481[/C][/ROW]
[ROW][C]14[/C][C]-0.068655[/C][C]-0.5318[/C][C]0.298414[/C][/ROW]
[ROW][C]15[/C][C]-0.131905[/C][C]-1.0217[/C][C]0.155506[/C][/ROW]
[ROW][C]16[/C][C]-0.127615[/C][C]-0.9885[/C][C]0.163439[/C][/ROW]
[ROW][C]17[/C][C]0.050558[/C][C]0.3916[/C][C]0.348363[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35720&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35720&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	0.946684	7.333	0
2	0.073347	0.5681	0.286029
3	0.104035	0.8059	0.211755
4	-0.114494	-0.8869	0.189346
5	-0.102456	-0.7936	0.215271
6	-0.041349	-0.3203	0.374932
7	-0.095554	-0.7402	0.231045
8	-0.085512	-0.6624	0.255135
9	-0.059522	-0.4611	0.323213
10	0.050717	0.3929	0.34791
11	0.0382	0.2959	0.384167
12	-0.091586	-0.7094	0.240405
13	0.093947	0.7277	0.23481
14	-0.068655	-0.5318	0.298414
15	-0.131905	-1.0217	0.155506
16	-0.127615	-0.9885	0.163439
17	0.050558	0.3916	0.348363

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 4 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x,par1,main='Autocorrelation',xlab='lags',ylab='ACF')
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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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Dataset

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Figures (Output of Computation)

Input Parameters & R Code