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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 16 Dec 2007 14:11:43 -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/2007/Dec/16/t1197838504miulstm21hq6wmb.htm/, Retrieved Thu, 02 May 2024 04:50:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4270, Retrieved Thu, 02 May 2024 04:50:39 +0000

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No (this computation is public)

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Estimated Impact

188

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

-       [(Partial) Autocorrelation Function] [] [2007-12-16 21:11:43] [ba3202e2798d2e4685d19d988e9c69df] [Current]

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Summary of compuational 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 compuational 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=4270&T=0

[TABLE]
[ROW][C]Summary of compuational 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=4270&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4270&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 compuational 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
0	1	8.4853	0
1	0.945246	8.0207	0
2	0.878157	7.4514	0
3	0.818132	6.9421	0
4	0.748774	6.3536	0
5	0.687404	5.8328	0
6	0.643097	5.4569	0
7	0.60078	5.0978	1e-06
8	0.560921	4.7596	5e-06
9	0.503617	4.2733	2.9e-05
10	0.436805	3.7064	0.000205
11	0.35889	3.0453	0.001623
12	0.256669	2.1779	0.016345
13	0.14862	1.2611	0.105675
14	0.059104	0.5015	0.30877
15	-0.027721	-0.2352	0.592646
16	-0.089697	-0.7611	0.775459
17	-0.140045	-1.1883	0.880693

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & 0.945246 & 8.0207 & 0 \tabularnewline
2 & 0.878157 & 7.4514 & 0 \tabularnewline
3 & 0.818132 & 6.9421 & 0 \tabularnewline
4 & 0.748774 & 6.3536 & 0 \tabularnewline
5 & 0.687404 & 5.8328 & 0 \tabularnewline
6 & 0.643097 & 5.4569 & 0 \tabularnewline
7 & 0.60078 & 5.0978 & 1e-06 \tabularnewline
8 & 0.560921 & 4.7596 & 5e-06 \tabularnewline
9 & 0.503617 & 4.2733 & 2.9e-05 \tabularnewline
10 & 0.436805 & 3.7064 & 0.000205 \tabularnewline
11 & 0.35889 & 3.0453 & 0.001623 \tabularnewline
12 & 0.256669 & 2.1779 & 0.016345 \tabularnewline
13 & 0.14862 & 1.2611 & 0.105675 \tabularnewline
14 & 0.059104 & 0.5015 & 0.30877 \tabularnewline
15 & -0.027721 & -0.2352 & 0.592646 \tabularnewline
16 & -0.089697 & -0.7611 & 0.775459 \tabularnewline
17 & -0.140045 & -1.1883 & 0.880693 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4270&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]0[/C][C]1[/C][C]8.4853[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.945246[/C][C]8.0207[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.878157[/C][C]7.4514[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.818132[/C][C]6.9421[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.748774[/C][C]6.3536[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.687404[/C][C]5.8328[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.643097[/C][C]5.4569[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.60078[/C][C]5.0978[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]0.560921[/C][C]4.7596[/C][C]5e-06[/C][/ROW]
[ROW][C]9[/C][C]0.503617[/C][C]4.2733[/C][C]2.9e-05[/C][/ROW]
[ROW][C]10[/C][C]0.436805[/C][C]3.7064[/C][C]0.000205[/C][/ROW]
[ROW][C]11[/C][C]0.35889[/C][C]3.0453[/C][C]0.001623[/C][/ROW]
[ROW][C]12[/C][C]0.256669[/C][C]2.1779[/C][C]0.016345[/C][/ROW]
[ROW][C]13[/C][C]0.14862[/C][C]1.2611[/C][C]0.105675[/C][/ROW]
[ROW][C]14[/C][C]0.059104[/C][C]0.5015[/C][C]0.30877[/C][/ROW]
[ROW][C]15[/C][C]-0.027721[/C][C]-0.2352[/C][C]0.592646[/C][/ROW]
[ROW][C]16[/C][C]-0.089697[/C][C]-0.7611[/C][C]0.775459[/C][/ROW]
[ROW][C]17[/C][C]-0.140045[/C][C]-1.1883[/C][C]0.880693[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4270&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4270&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
0	1	8.4853	0
1	0.945246	8.0207	0
2	0.878157	7.4514	0
3	0.818132	6.9421	0
4	0.748774	6.3536	0
5	0.687404	5.8328	0
6	0.643097	5.4569	0
7	0.60078	5.0978	1e-06
8	0.560921	4.7596	5e-06
9	0.503617	4.2733	2.9e-05
10	0.436805	3.7064	0.000205
11	0.35889	3.0453	0.001623
12	0.256669	2.1779	0.016345
13	0.14862	1.2611	0.105675
14	0.059104	0.5015	0.30877
15	-0.027721	-0.2352	0.592646
16	-0.089697	-0.7611	0.775459
17	-0.140045	-1.1883	0.880693

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.945246	8.0207	0
1	-0.143963	-1.2216	0.887072
2	0.044463	0.3773	0.353536
3	-0.139455	-1.1833	0.879712
4	0.06752	0.5729	0.284239
5	0.092085	0.7814	0.218573
6	-0.022106	-0.1876	0.574131
7	-0.000508	-0.0043	0.501715
8	-0.227625	-1.9315	0.971319
9	-0.063771	-0.5411	0.704949
10	-0.160585	-1.3626	0.911374
11	-0.254319	-2.158	0.982867
12	-0.131526	-1.116	0.865941
13	0.017049	0.1447	0.442688
14	-0.097605	-0.8282	0.794854
15	0.145594	1.2354	0.110348
16	-0.0684	-0.5804	0.718268
17	0.155316	1.3179	0.095857

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.945246 & 8.0207 & 0 \tabularnewline
1 & -0.143963 & -1.2216 & 0.887072 \tabularnewline
2 & 0.044463 & 0.3773 & 0.353536 \tabularnewline
3 & -0.139455 & -1.1833 & 0.879712 \tabularnewline
4 & 0.06752 & 0.5729 & 0.284239 \tabularnewline
5 & 0.092085 & 0.7814 & 0.218573 \tabularnewline
6 & -0.022106 & -0.1876 & 0.574131 \tabularnewline
7 & -0.000508 & -0.0043 & 0.501715 \tabularnewline
8 & -0.227625 & -1.9315 & 0.971319 \tabularnewline
9 & -0.063771 & -0.5411 & 0.704949 \tabularnewline
10 & -0.160585 & -1.3626 & 0.911374 \tabularnewline
11 & -0.254319 & -2.158 & 0.982867 \tabularnewline
12 & -0.131526 & -1.116 & 0.865941 \tabularnewline
13 & 0.017049 & 0.1447 & 0.442688 \tabularnewline
14 & -0.097605 & -0.8282 & 0.794854 \tabularnewline
15 & 0.145594 & 1.2354 & 0.110348 \tabularnewline
16 & -0.0684 & -0.5804 & 0.718268 \tabularnewline
17 & 0.155316 & 1.3179 & 0.095857 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4270&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]0[/C][C]0.945246[/C][C]8.0207[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.143963[/C][C]-1.2216[/C][C]0.887072[/C][/ROW]
[ROW][C]2[/C][C]0.044463[/C][C]0.3773[/C][C]0.353536[/C][/ROW]
[ROW][C]3[/C][C]-0.139455[/C][C]-1.1833[/C][C]0.879712[/C][/ROW]
[ROW][C]4[/C][C]0.06752[/C][C]0.5729[/C][C]0.284239[/C][/ROW]
[ROW][C]5[/C][C]0.092085[/C][C]0.7814[/C][C]0.218573[/C][/ROW]
[ROW][C]6[/C][C]-0.022106[/C][C]-0.1876[/C][C]0.574131[/C][/ROW]
[ROW][C]7[/C][C]-0.000508[/C][C]-0.0043[/C][C]0.501715[/C][/ROW]
[ROW][C]8[/C][C]-0.227625[/C][C]-1.9315[/C][C]0.971319[/C][/ROW]
[ROW][C]9[/C][C]-0.063771[/C][C]-0.5411[/C][C]0.704949[/C][/ROW]
[ROW][C]10[/C][C]-0.160585[/C][C]-1.3626[/C][C]0.911374[/C][/ROW]
[ROW][C]11[/C][C]-0.254319[/C][C]-2.158[/C][C]0.982867[/C][/ROW]
[ROW][C]12[/C][C]-0.131526[/C][C]-1.116[/C][C]0.865941[/C][/ROW]
[ROW][C]13[/C][C]0.017049[/C][C]0.1447[/C][C]0.442688[/C][/ROW]
[ROW][C]14[/C][C]-0.097605[/C][C]-0.8282[/C][C]0.794854[/C][/ROW]
[ROW][C]15[/C][C]0.145594[/C][C]1.2354[/C][C]0.110348[/C][/ROW]
[ROW][C]16[/C][C]-0.0684[/C][C]-0.5804[/C][C]0.718268[/C][/ROW]
[ROW][C]17[/C][C]0.155316[/C][C]1.3179[/C][C]0.095857[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4270&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4270&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
0	0.945246	8.0207	0
1	-0.143963	-1.2216	0.887072
2	0.044463	0.3773	0.353536
3	-0.139455	-1.1833	0.879712
4	0.06752	0.5729	0.284239
5	0.092085	0.7814	0.218573
6	-0.022106	-0.1876	0.574131
7	-0.000508	-0.0043	0.501715
8	-0.227625	-1.9315	0.971319
9	-0.063771	-0.5411	0.704949
10	-0.160585	-1.3626	0.911374
11	-0.254319	-2.158	0.982867
12	-0.131526	-1.116	0.865941
13	0.017049	0.1447	0.442688
14	-0.097605	-0.8282	0.794854
15	0.145594	1.2354	0.110348
16	-0.0684	-0.5804	0.718268
17	0.155316	1.3179	0.095857

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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