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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 24 Nov 2007 07:16:20 -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/Nov/24/t11959132789vp33xym7gnp2ww.htm/, Retrieved Fri, 03 May 2024 08:44:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6308, Retrieved Fri, 03 May 2024 08:44:57 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

209

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

-       [(Partial) Autocorrelation Function] [Partial Autocorre...] [2007-11-24 14:16:20] [6b5c00822e2ce0f7cf73539c28d95782] [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=6308&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=6308&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6308&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	7.746	0
1	0.907995	7.0333	0
2	0.815358	6.3157	0
3	0.725638	5.6208	0
4	0.667576	5.171	1e-06
5	0.620909	4.8095	5e-06
6	0.587637	4.5518	1.3e-05
7	0.546682	4.2346	4e-05
8	0.509746	3.9485	0.000105
9	0.469618	3.6376	0.000287
10	0.434378	3.3647	0.00067
11	0.397876	3.0819	0.001552
12	0.356464	2.7612	0.003815
13	0.329283	2.5506	0.006662
14	0.286502	2.2192	0.015132
15	0.250975	1.944	0.028292
16	0.223065	1.7279	0.044579

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.907995 & 7.0333 & 0 \tabularnewline
2 & 0.815358 & 6.3157 & 0 \tabularnewline
3 & 0.725638 & 5.6208 & 0 \tabularnewline
4 & 0.667576 & 5.171 & 1e-06 \tabularnewline
5 & 0.620909 & 4.8095 & 5e-06 \tabularnewline
6 & 0.587637 & 4.5518 & 1.3e-05 \tabularnewline
7 & 0.546682 & 4.2346 & 4e-05 \tabularnewline
8 & 0.509746 & 3.9485 & 0.000105 \tabularnewline
9 & 0.469618 & 3.6376 & 0.000287 \tabularnewline
10 & 0.434378 & 3.3647 & 0.00067 \tabularnewline
11 & 0.397876 & 3.0819 & 0.001552 \tabularnewline
12 & 0.356464 & 2.7612 & 0.003815 \tabularnewline
13 & 0.329283 & 2.5506 & 0.006662 \tabularnewline
14 & 0.286502 & 2.2192 & 0.015132 \tabularnewline
15 & 0.250975 & 1.944 & 0.028292 \tabularnewline
16 & 0.223065 & 1.7279 & 0.044579 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6308&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.907995[/C][C]7.0333[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.815358[/C][C]6.3157[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.725638[/C][C]5.6208[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.667576[/C][C]5.171[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]0.620909[/C][C]4.8095[/C][C]5e-06[/C][/ROW]
[ROW][C]6[/C][C]0.587637[/C][C]4.5518[/C][C]1.3e-05[/C][/ROW]
[ROW][C]7[/C][C]0.546682[/C][C]4.2346[/C][C]4e-05[/C][/ROW]
[ROW][C]8[/C][C]0.509746[/C][C]3.9485[/C][C]0.000105[/C][/ROW]
[ROW][C]9[/C][C]0.469618[/C][C]3.6376[/C][C]0.000287[/C][/ROW]
[ROW][C]10[/C][C]0.434378[/C][C]3.3647[/C][C]0.00067[/C][/ROW]
[ROW][C]11[/C][C]0.397876[/C][C]3.0819[/C][C]0.001552[/C][/ROW]
[ROW][C]12[/C][C]0.356464[/C][C]2.7612[/C][C]0.003815[/C][/ROW]
[ROW][C]13[/C][C]0.329283[/C][C]2.5506[/C][C]0.006662[/C][/ROW]
[ROW][C]14[/C][C]0.286502[/C][C]2.2192[/C][C]0.015132[/C][/ROW]
[ROW][C]15[/C][C]0.250975[/C][C]1.944[/C][C]0.028292[/C][/ROW]
[ROW][C]16[/C][C]0.223065[/C][C]1.7279[/C][C]0.044579[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6308&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6308&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	7.746	0
1	0.907995	7.0333	0
2	0.815358	6.3157	0
3	0.725638	5.6208	0
4	0.667576	5.171	1e-06
5	0.620909	4.8095	5e-06
6	0.587637	4.5518	1.3e-05
7	0.546682	4.2346	4e-05
8	0.509746	3.9485	0.000105
9	0.469618	3.6376	0.000287
10	0.434378	3.3647	0.00067
11	0.397876	3.0819	0.001552
12	0.356464	2.7612	0.003815
13	0.329283	2.5506	0.006662
14	0.286502	2.2192	0.015132
15	0.250975	1.944	0.028292
16	0.223065	1.7279	0.044579

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.907995	7.0333	0
1	-0.051827	-0.4014	0.655242
2	-0.034349	-0.2661	0.604451
3	0.128915	0.9986	0.161006
4	0.027604	0.2138	0.415707
5	0.049533	0.3837	0.351285
6	-0.039255	-0.3041	0.618935
7	0.017881	0.1385	0.445152
8	-0.016204	-0.1255	0.549733
9	0.002036	0.0158	0.493736
10	-0.019845	-0.1537	0.560825
11	-0.056187	-0.4352	0.667518
12	0.067195	0.5205	0.302318
13	-0.116582	-0.903	0.814941
14	0.010723	0.0831	0.467039
15	0.03434	0.266	0.395576
16	-0.011783	-0.0913	0.53621

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.907995 & 7.0333 & 0 \tabularnewline
1 & -0.051827 & -0.4014 & 0.655242 \tabularnewline
2 & -0.034349 & -0.2661 & 0.604451 \tabularnewline
3 & 0.128915 & 0.9986 & 0.161006 \tabularnewline
4 & 0.027604 & 0.2138 & 0.415707 \tabularnewline
5 & 0.049533 & 0.3837 & 0.351285 \tabularnewline
6 & -0.039255 & -0.3041 & 0.618935 \tabularnewline
7 & 0.017881 & 0.1385 & 0.445152 \tabularnewline
8 & -0.016204 & -0.1255 & 0.549733 \tabularnewline
9 & 0.002036 & 0.0158 & 0.493736 \tabularnewline
10 & -0.019845 & -0.1537 & 0.560825 \tabularnewline
11 & -0.056187 & -0.4352 & 0.667518 \tabularnewline
12 & 0.067195 & 0.5205 & 0.302318 \tabularnewline
13 & -0.116582 & -0.903 & 0.814941 \tabularnewline
14 & 0.010723 & 0.0831 & 0.467039 \tabularnewline
15 & 0.03434 & 0.266 & 0.395576 \tabularnewline
16 & -0.011783 & -0.0913 & 0.53621 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6308&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]0.907995[/C][C]7.0333[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.051827[/C][C]-0.4014[/C][C]0.655242[/C][/ROW]
[ROW][C]2[/C][C]-0.034349[/C][C]-0.2661[/C][C]0.604451[/C][/ROW]
[ROW][C]3[/C][C]0.128915[/C][C]0.9986[/C][C]0.161006[/C][/ROW]
[ROW][C]4[/C][C]0.027604[/C][C]0.2138[/C][C]0.415707[/C][/ROW]
[ROW][C]5[/C][C]0.049533[/C][C]0.3837[/C][C]0.351285[/C][/ROW]
[ROW][C]6[/C][C]-0.039255[/C][C]-0.3041[/C][C]0.618935[/C][/ROW]
[ROW][C]7[/C][C]0.017881[/C][C]0.1385[/C][C]0.445152[/C][/ROW]
[ROW][C]8[/C][C]-0.016204[/C][C]-0.1255[/C][C]0.549733[/C][/ROW]
[ROW][C]9[/C][C]0.002036[/C][C]0.0158[/C][C]0.493736[/C][/ROW]
[ROW][C]10[/C][C]-0.019845[/C][C]-0.1537[/C][C]0.560825[/C][/ROW]
[ROW][C]11[/C][C]-0.056187[/C][C]-0.4352[/C][C]0.667518[/C][/ROW]
[ROW][C]12[/C][C]0.067195[/C][C]0.5205[/C][C]0.302318[/C][/ROW]
[ROW][C]13[/C][C]-0.116582[/C][C]-0.903[/C][C]0.814941[/C][/ROW]
[ROW][C]14[/C][C]0.010723[/C][C]0.0831[/C][C]0.467039[/C][/ROW]
[ROW][C]15[/C][C]0.03434[/C][C]0.266[/C][C]0.395576[/C][/ROW]
[ROW][C]16[/C][C]-0.011783[/C][C]-0.0913[/C][C]0.53621[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6308&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6308&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	0.907995	7.0333	0
1	-0.051827	-0.4014	0.655242
2	-0.034349	-0.2661	0.604451
3	0.128915	0.9986	0.161006
4	0.027604	0.2138	0.415707
5	0.049533	0.3837	0.351285
6	-0.039255	-0.3041	0.618935
7	0.017881	0.1385	0.445152
8	-0.016204	-0.1255	0.549733
9	0.002036	0.0158	0.493736
10	-0.019845	-0.1537	0.560825
11	-0.056187	-0.4352	0.667518
12	0.067195	0.5205	0.302318
13	-0.116582	-0.903	0.814941
14	0.010723	0.0831	0.467039
15	0.03434	0.266	0.395576
16	-0.011783	-0.0913	0.53621

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 = 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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