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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

Mon, 14 Dec 2009 02:45:47 -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/2009/Dec/14/t1260784015d3cd6mmdaaeg6mp.htm/, Retrieved Sun, 05 May 2024 19:36:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67476, Retrieved Sun, 05 May 2024 19:36:59 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

162

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

-     [Variance Reduction Matrix] [VRM invoer] [2008-12-17 15:09:52] [74be16979710d4c4e7c6647856088456]
- RMPD    [(Partial) Autocorrelation Function] [Autocorrelation F...] [2009-12-14 09:45:47] [91da2e1ebdd83187f2515f461585cbee] [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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67476&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67476&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67476&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.283156	-3.491	0.000315
2	-0.362701	-4.4717	8e-06
3	0.150021	1.8496	0.033158
4	0.044324	0.5465	0.292775
5	-0.077949	-0.961	0.169036
6	0.191847	2.3652	0.00964
7	-0.195471	-2.4099	0.008575
8	0.183407	2.2612	0.012583
9	0.043789	0.5399	0.295039
10	-0.415362	-5.1209	0
11	-0.123196	-1.5189	0.065437
12	0.730979	9.0121	0
13	-0.231622	-2.8556	0.002448
14	-0.274471	-3.3839	0.000455
15	0.056396	0.6953	0.243965
16	0.026546	0.3273	0.371953
17	-0.001	-0.0123	0.495089
18	0.107793	1.329	0.092927
19	-0.133416	-1.6449	0.051033
20	0.212291	2.6173	0.004879
21	-0.057271	-0.7061	0.240607

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.283156 & -3.491 & 0.000315 \tabularnewline
2 & -0.362701 & -4.4717 & 8e-06 \tabularnewline
3 & 0.150021 & 1.8496 & 0.033158 \tabularnewline
4 & 0.044324 & 0.5465 & 0.292775 \tabularnewline
5 & -0.077949 & -0.961 & 0.169036 \tabularnewline
6 & 0.191847 & 2.3652 & 0.00964 \tabularnewline
7 & -0.195471 & -2.4099 & 0.008575 \tabularnewline
8 & 0.183407 & 2.2612 & 0.012583 \tabularnewline
9 & 0.043789 & 0.5399 & 0.295039 \tabularnewline
10 & -0.415362 & -5.1209 & 0 \tabularnewline
11 & -0.123196 & -1.5189 & 0.065437 \tabularnewline
12 & 0.730979 & 9.0121 & 0 \tabularnewline
13 & -0.231622 & -2.8556 & 0.002448 \tabularnewline
14 & -0.274471 & -3.3839 & 0.000455 \tabularnewline
15 & 0.056396 & 0.6953 & 0.243965 \tabularnewline
16 & 0.026546 & 0.3273 & 0.371953 \tabularnewline
17 & -0.001 & -0.0123 & 0.495089 \tabularnewline
18 & 0.107793 & 1.329 & 0.092927 \tabularnewline
19 & -0.133416 & -1.6449 & 0.051033 \tabularnewline
20 & 0.212291 & 2.6173 & 0.004879 \tabularnewline
21 & -0.057271 & -0.7061 & 0.240607 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67476&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]-0.283156[/C][C]-3.491[/C][C]0.000315[/C][/ROW]
[ROW][C]2[/C][C]-0.362701[/C][C]-4.4717[/C][C]8e-06[/C][/ROW]
[ROW][C]3[/C][C]0.150021[/C][C]1.8496[/C][C]0.033158[/C][/ROW]
[ROW][C]4[/C][C]0.044324[/C][C]0.5465[/C][C]0.292775[/C][/ROW]
[ROW][C]5[/C][C]-0.077949[/C][C]-0.961[/C][C]0.169036[/C][/ROW]
[ROW][C]6[/C][C]0.191847[/C][C]2.3652[/C][C]0.00964[/C][/ROW]
[ROW][C]7[/C][C]-0.195471[/C][C]-2.4099[/C][C]0.008575[/C][/ROW]
[ROW][C]8[/C][C]0.183407[/C][C]2.2612[/C][C]0.012583[/C][/ROW]
[ROW][C]9[/C][C]0.043789[/C][C]0.5399[/C][C]0.295039[/C][/ROW]
[ROW][C]10[/C][C]-0.415362[/C][C]-5.1209[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]-0.123196[/C][C]-1.5189[/C][C]0.065437[/C][/ROW]
[ROW][C]12[/C][C]0.730979[/C][C]9.0121[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.231622[/C][C]-2.8556[/C][C]0.002448[/C][/ROW]
[ROW][C]14[/C][C]-0.274471[/C][C]-3.3839[/C][C]0.000455[/C][/ROW]
[ROW][C]15[/C][C]0.056396[/C][C]0.6953[/C][C]0.243965[/C][/ROW]
[ROW][C]16[/C][C]0.026546[/C][C]0.3273[/C][C]0.371953[/C][/ROW]
[ROW][C]17[/C][C]-0.001[/C][C]-0.0123[/C][C]0.495089[/C][/ROW]
[ROW][C]18[/C][C]0.107793[/C][C]1.329[/C][C]0.092927[/C][/ROW]
[ROW][C]19[/C][C]-0.133416[/C][C]-1.6449[/C][C]0.051033[/C][/ROW]
[ROW][C]20[/C][C]0.212291[/C][C]2.6173[/C][C]0.004879[/C][/ROW]
[ROW][C]21[/C][C]-0.057271[/C][C]-0.7061[/C][C]0.240607[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67476&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67476&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	-0.283156	-3.491	0.000315
2	-0.362701	-4.4717	8e-06
3	0.150021	1.8496	0.033158
4	0.044324	0.5465	0.292775
5	-0.077949	-0.961	0.169036
6	0.191847	2.3652	0.00964
7	-0.195471	-2.4099	0.008575
8	0.183407	2.2612	0.012583
9	0.043789	0.5399	0.295039
10	-0.415362	-5.1209	0
11	-0.123196	-1.5189	0.065437
12	0.730979	9.0121	0
13	-0.231622	-2.8556	0.002448
14	-0.274471	-3.3839	0.000455
15	0.056396	0.6953	0.243965
16	0.026546	0.3273	0.371953
17	-0.001	-0.0123	0.495089
18	0.107793	1.329	0.092927
19	-0.133416	-1.6449	0.051033
20	0.212291	2.6173	0.004879
21	-0.057271	-0.7061	0.240607

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.283156	-3.491	0.000315
2	-0.481482	-5.9361	0
3	-0.195961	-2.416	0.00844
4	-0.203879	-2.5136	0.006496
5	-0.181813	-2.2415	0.01322
6	0.126998	1.5657	0.059746
7	-0.153868	-1.897	0.029861
8	0.324066	3.9954	5e-05
9	0.19785	2.4393	0.007934
10	-0.260314	-3.2094	0.000811
11	-0.658249	-8.1154	0
12	0.172521	2.127	0.017518
13	0.12716	1.5677	0.059512
14	0.105982	1.3066	0.096655
15	-0.121521	-1.4982	0.068076
16	-0.085579	-1.0551	0.14653
17	-0.058714	-0.7239	0.235128
18	-0.12515	-1.543	0.06246
19	0.085358	1.0524	0.147151
20	-0.015109	-0.1863	0.42624
21	-0.180461	-2.2249	0.013781

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.283156 & -3.491 & 0.000315 \tabularnewline
2 & -0.481482 & -5.9361 & 0 \tabularnewline
3 & -0.195961 & -2.416 & 0.00844 \tabularnewline
4 & -0.203879 & -2.5136 & 0.006496 \tabularnewline
5 & -0.181813 & -2.2415 & 0.01322 \tabularnewline
6 & 0.126998 & 1.5657 & 0.059746 \tabularnewline
7 & -0.153868 & -1.897 & 0.029861 \tabularnewline
8 & 0.324066 & 3.9954 & 5e-05 \tabularnewline
9 & 0.19785 & 2.4393 & 0.007934 \tabularnewline
10 & -0.260314 & -3.2094 & 0.000811 \tabularnewline
11 & -0.658249 & -8.1154 & 0 \tabularnewline
12 & 0.172521 & 2.127 & 0.017518 \tabularnewline
13 & 0.12716 & 1.5677 & 0.059512 \tabularnewline
14 & 0.105982 & 1.3066 & 0.096655 \tabularnewline
15 & -0.121521 & -1.4982 & 0.068076 \tabularnewline
16 & -0.085579 & -1.0551 & 0.14653 \tabularnewline
17 & -0.058714 & -0.7239 & 0.235128 \tabularnewline
18 & -0.12515 & -1.543 & 0.06246 \tabularnewline
19 & 0.085358 & 1.0524 & 0.147151 \tabularnewline
20 & -0.015109 & -0.1863 & 0.42624 \tabularnewline
21 & -0.180461 & -2.2249 & 0.013781 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67476&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]-0.283156[/C][C]-3.491[/C][C]0.000315[/C][/ROW]
[ROW][C]2[/C][C]-0.481482[/C][C]-5.9361[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.195961[/C][C]-2.416[/C][C]0.00844[/C][/ROW]
[ROW][C]4[/C][C]-0.203879[/C][C]-2.5136[/C][C]0.006496[/C][/ROW]
[ROW][C]5[/C][C]-0.181813[/C][C]-2.2415[/C][C]0.01322[/C][/ROW]
[ROW][C]6[/C][C]0.126998[/C][C]1.5657[/C][C]0.059746[/C][/ROW]
[ROW][C]7[/C][C]-0.153868[/C][C]-1.897[/C][C]0.029861[/C][/ROW]
[ROW][C]8[/C][C]0.324066[/C][C]3.9954[/C][C]5e-05[/C][/ROW]
[ROW][C]9[/C][C]0.19785[/C][C]2.4393[/C][C]0.007934[/C][/ROW]
[ROW][C]10[/C][C]-0.260314[/C][C]-3.2094[/C][C]0.000811[/C][/ROW]
[ROW][C]11[/C][C]-0.658249[/C][C]-8.1154[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.172521[/C][C]2.127[/C][C]0.017518[/C][/ROW]
[ROW][C]13[/C][C]0.12716[/C][C]1.5677[/C][C]0.059512[/C][/ROW]
[ROW][C]14[/C][C]0.105982[/C][C]1.3066[/C][C]0.096655[/C][/ROW]
[ROW][C]15[/C][C]-0.121521[/C][C]-1.4982[/C][C]0.068076[/C][/ROW]
[ROW][C]16[/C][C]-0.085579[/C][C]-1.0551[/C][C]0.14653[/C][/ROW]
[ROW][C]17[/C][C]-0.058714[/C][C]-0.7239[/C][C]0.235128[/C][/ROW]
[ROW][C]18[/C][C]-0.12515[/C][C]-1.543[/C][C]0.06246[/C][/ROW]
[ROW][C]19[/C][C]0.085358[/C][C]1.0524[/C][C]0.147151[/C][/ROW]
[ROW][C]20[/C][C]-0.015109[/C][C]-0.1863[/C][C]0.42624[/C][/ROW]
[ROW][C]21[/C][C]-0.180461[/C][C]-2.2249[/C][C]0.013781[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67476&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67476&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	-0.283156	-3.491	0.000315
2	-0.481482	-5.9361	0
3	-0.195961	-2.416	0.00844
4	-0.203879	-2.5136	0.006496
5	-0.181813	-2.2415	0.01322
6	0.126998	1.5657	0.059746
7	-0.153868	-1.897	0.029861
8	0.324066	3.9954	5e-05
9	0.19785	2.4393	0.007934
10	-0.260314	-3.2094	0.000811
11	-0.658249	-8.1154	0
12	0.172521	2.127	0.017518
13	0.12716	1.5677	0.059512
14	0.105982	1.3066	0.096655
15	-0.121521	-1.4982	0.068076
16	-0.085579	-1.0551	0.14653
17	-0.058714	-0.7239	0.235128
18	-0.12515	-1.543	0.06246
19	0.085358	1.0524	0.147151
20	-0.015109	-0.1863	0.42624
21	-0.180461	-2.2249	0.013781

Figure 1

PNG link

Postscript link

PDF link

Figure 2

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 ;

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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code