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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 17 Dec 2008 10:58:54 -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/17/t1229536761whpq0axqo2mhi67.htm/, Retrieved Sun, 19 May 2024 07:23:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34458, Retrieved Sun, 19 May 2024 07:23:22 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

149

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

-       [(Partial) Autocorrelation Function] [Japan d=0; D=0] [2008-12-17 17:58:54] [d41d8cd98f00b204e9800998ecf8427e] [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	'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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34458&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34458&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34458&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.981949	19.5159	0
2	0.968622	19.251	0
3	0.954498	18.9703	0
4	0.941885	18.7196	0
5	0.927859	18.4408	0
6	0.914078	18.1669	0
7	0.900661	17.9003	0
8	0.890024	17.6889	0
9	0.876797	17.426	0
10	0.865277	17.197	0
11	0.854454	16.9819	0
12	0.841555	16.7256	0
13	0.828539	16.4669	0
14	0.814226	16.1824	0
15	0.803104	15.9614	0
16	0.791972	15.7401	0
17	0.778483	15.472	0
18	0.765724	15.2185	0
19	0.752009	14.9459	0
20	0.74053	14.7177	0
21	0.729557	14.4997	0
22	0.716945	14.249	0
23	0.706561	14.0426	0
24	0.695628	13.8253	0
25	0.683736	13.589	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.981949 & 19.5159 & 0 \tabularnewline
2 & 0.968622 & 19.251 & 0 \tabularnewline
3 & 0.954498 & 18.9703 & 0 \tabularnewline
4 & 0.941885 & 18.7196 & 0 \tabularnewline
5 & 0.927859 & 18.4408 & 0 \tabularnewline
6 & 0.914078 & 18.1669 & 0 \tabularnewline
7 & 0.900661 & 17.9003 & 0 \tabularnewline
8 & 0.890024 & 17.6889 & 0 \tabularnewline
9 & 0.876797 & 17.426 & 0 \tabularnewline
10 & 0.865277 & 17.197 & 0 \tabularnewline
11 & 0.854454 & 16.9819 & 0 \tabularnewline
12 & 0.841555 & 16.7256 & 0 \tabularnewline
13 & 0.828539 & 16.4669 & 0 \tabularnewline
14 & 0.814226 & 16.1824 & 0 \tabularnewline
15 & 0.803104 & 15.9614 & 0 \tabularnewline
16 & 0.791972 & 15.7401 & 0 \tabularnewline
17 & 0.778483 & 15.472 & 0 \tabularnewline
18 & 0.765724 & 15.2185 & 0 \tabularnewline
19 & 0.752009 & 14.9459 & 0 \tabularnewline
20 & 0.74053 & 14.7177 & 0 \tabularnewline
21 & 0.729557 & 14.4997 & 0 \tabularnewline
22 & 0.716945 & 14.249 & 0 \tabularnewline
23 & 0.706561 & 14.0426 & 0 \tabularnewline
24 & 0.695628 & 13.8253 & 0 \tabularnewline
25 & 0.683736 & 13.589 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34458&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]0.981949[/C][C]19.5159[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.968622[/C][C]19.251[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.954498[/C][C]18.9703[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.941885[/C][C]18.7196[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.927859[/C][C]18.4408[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.914078[/C][C]18.1669[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.900661[/C][C]17.9003[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.890024[/C][C]17.6889[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.876797[/C][C]17.426[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.865277[/C][C]17.197[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.854454[/C][C]16.9819[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.841555[/C][C]16.7256[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.828539[/C][C]16.4669[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.814226[/C][C]16.1824[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.803104[/C][C]15.9614[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.791972[/C][C]15.7401[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.778483[/C][C]15.472[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.765724[/C][C]15.2185[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.752009[/C][C]14.9459[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.74053[/C][C]14.7177[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.729557[/C][C]14.4997[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.716945[/C][C]14.249[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.706561[/C][C]14.0426[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]0.695628[/C][C]13.8253[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]0.683736[/C][C]13.589[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34458&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34458&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	0.981949	19.5159	0
2	0.968622	19.251	0
3	0.954498	18.9703	0
4	0.941885	18.7196	0
5	0.927859	18.4408	0
6	0.914078	18.1669	0
7	0.900661	17.9003	0
8	0.890024	17.6889	0
9	0.876797	17.426	0
10	0.865277	17.197	0
11	0.854454	16.9819	0
12	0.841555	16.7256	0
13	0.828539	16.4669	0
14	0.814226	16.1824	0
15	0.803104	15.9614	0
16	0.791972	15.7401	0
17	0.778483	15.472	0
18	0.765724	15.2185	0
19	0.752009	14.9459	0
20	0.74053	14.7177	0
21	0.729557	14.4997	0
22	0.716945	14.249	0
23	0.706561	14.0426	0
24	0.695628	13.8253	0
25	0.683736	13.589	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.981949	19.5159	0
2	0.122929	2.4432	0.007498
3	-0.012109	-0.2407	0.404972
4	0.032071	0.6374	0.262116
5	-0.035992	-0.7153	0.237414
6	-0.010066	-0.2001	0.420767
7	0.005838	0.116	0.453844
8	0.072414	1.4392	0.075444
9	-0.058462	-1.1619	0.122987
10	0.025316	0.5031	0.307574
11	0.029621	0.5887	0.278196
12	-0.068834	-1.368	0.086038
13	-0.01871	-0.3718	0.355103
14	-0.042984	-0.8543	0.196733
15	0.072709	1.4451	0.074616
16	0.010839	0.2154	0.414775
17	-0.065777	-1.3073	0.095937
18	0.003474	0.0691	0.472492
19	-0.046004	-0.9143	0.180558
20	0.051478	1.0231	0.153441
21	0.023333	0.4637	0.321548
22	-0.040707	-0.809	0.209493
23	0.044243	0.8793	0.189883
24	-0.014805	-0.2942	0.384363
25	-0.025017	-0.4972	0.309664

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.981949 & 19.5159 & 0 \tabularnewline
2 & 0.122929 & 2.4432 & 0.007498 \tabularnewline
3 & -0.012109 & -0.2407 & 0.404972 \tabularnewline
4 & 0.032071 & 0.6374 & 0.262116 \tabularnewline
5 & -0.035992 & -0.7153 & 0.237414 \tabularnewline
6 & -0.010066 & -0.2001 & 0.420767 \tabularnewline
7 & 0.005838 & 0.116 & 0.453844 \tabularnewline
8 & 0.072414 & 1.4392 & 0.075444 \tabularnewline
9 & -0.058462 & -1.1619 & 0.122987 \tabularnewline
10 & 0.025316 & 0.5031 & 0.307574 \tabularnewline
11 & 0.029621 & 0.5887 & 0.278196 \tabularnewline
12 & -0.068834 & -1.368 & 0.086038 \tabularnewline
13 & -0.01871 & -0.3718 & 0.355103 \tabularnewline
14 & -0.042984 & -0.8543 & 0.196733 \tabularnewline
15 & 0.072709 & 1.4451 & 0.074616 \tabularnewline
16 & 0.010839 & 0.2154 & 0.414775 \tabularnewline
17 & -0.065777 & -1.3073 & 0.095937 \tabularnewline
18 & 0.003474 & 0.0691 & 0.472492 \tabularnewline
19 & -0.046004 & -0.9143 & 0.180558 \tabularnewline
20 & 0.051478 & 1.0231 & 0.153441 \tabularnewline
21 & 0.023333 & 0.4637 & 0.321548 \tabularnewline
22 & -0.040707 & -0.809 & 0.209493 \tabularnewline
23 & 0.044243 & 0.8793 & 0.189883 \tabularnewline
24 & -0.014805 & -0.2942 & 0.384363 \tabularnewline
25 & -0.025017 & -0.4972 & 0.309664 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34458&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]0.981949[/C][C]19.5159[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.122929[/C][C]2.4432[/C][C]0.007498[/C][/ROW]
[ROW][C]3[/C][C]-0.012109[/C][C]-0.2407[/C][C]0.404972[/C][/ROW]
[ROW][C]4[/C][C]0.032071[/C][C]0.6374[/C][C]0.262116[/C][/ROW]
[ROW][C]5[/C][C]-0.035992[/C][C]-0.7153[/C][C]0.237414[/C][/ROW]
[ROW][C]6[/C][C]-0.010066[/C][C]-0.2001[/C][C]0.420767[/C][/ROW]
[ROW][C]7[/C][C]0.005838[/C][C]0.116[/C][C]0.453844[/C][/ROW]
[ROW][C]8[/C][C]0.072414[/C][C]1.4392[/C][C]0.075444[/C][/ROW]
[ROW][C]9[/C][C]-0.058462[/C][C]-1.1619[/C][C]0.122987[/C][/ROW]
[ROW][C]10[/C][C]0.025316[/C][C]0.5031[/C][C]0.307574[/C][/ROW]
[ROW][C]11[/C][C]0.029621[/C][C]0.5887[/C][C]0.278196[/C][/ROW]
[ROW][C]12[/C][C]-0.068834[/C][C]-1.368[/C][C]0.086038[/C][/ROW]
[ROW][C]13[/C][C]-0.01871[/C][C]-0.3718[/C][C]0.355103[/C][/ROW]
[ROW][C]14[/C][C]-0.042984[/C][C]-0.8543[/C][C]0.196733[/C][/ROW]
[ROW][C]15[/C][C]0.072709[/C][C]1.4451[/C][C]0.074616[/C][/ROW]
[ROW][C]16[/C][C]0.010839[/C][C]0.2154[/C][C]0.414775[/C][/ROW]
[ROW][C]17[/C][C]-0.065777[/C][C]-1.3073[/C][C]0.095937[/C][/ROW]
[ROW][C]18[/C][C]0.003474[/C][C]0.0691[/C][C]0.472492[/C][/ROW]
[ROW][C]19[/C][C]-0.046004[/C][C]-0.9143[/C][C]0.180558[/C][/ROW]
[ROW][C]20[/C][C]0.051478[/C][C]1.0231[/C][C]0.153441[/C][/ROW]
[ROW][C]21[/C][C]0.023333[/C][C]0.4637[/C][C]0.321548[/C][/ROW]
[ROW][C]22[/C][C]-0.040707[/C][C]-0.809[/C][C]0.209493[/C][/ROW]
[ROW][C]23[/C][C]0.044243[/C][C]0.8793[/C][C]0.189883[/C][/ROW]
[ROW][C]24[/C][C]-0.014805[/C][C]-0.2942[/C][C]0.384363[/C][/ROW]
[ROW][C]25[/C][C]-0.025017[/C][C]-0.4972[/C][C]0.309664[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34458&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34458&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	0.981949	19.5159	0
2	0.122929	2.4432	0.007498
3	-0.012109	-0.2407	0.404972
4	0.032071	0.6374	0.262116
5	-0.035992	-0.7153	0.237414
6	-0.010066	-0.2001	0.420767
7	0.005838	0.116	0.453844
8	0.072414	1.4392	0.075444
9	-0.058462	-1.1619	0.122987
10	0.025316	0.5031	0.307574
11	0.029621	0.5887	0.278196
12	-0.068834	-1.368	0.086038
13	-0.01871	-0.3718	0.355103
14	-0.042984	-0.8543	0.196733
15	0.072709	1.4451	0.074616
16	0.010839	0.2154	0.414775
17	-0.065777	-1.3073	0.095937
18	0.003474	0.0691	0.472492
19	-0.046004	-0.9143	0.180558
20	0.051478	1.0231	0.153441
21	0.023333	0.4637	0.321548
22	-0.040707	-0.809	0.209493
23	0.044243	0.8793	0.189883
24	-0.014805	-0.2942	0.384363
25	-0.025017	-0.4972	0.309664

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code