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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 27 Nov 2009 12:18:00 -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/Nov/27/t1259349527eq12zqzrq5n8a9u.htm/, Retrieved Sun, 28 Apr 2024 23:29:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61158, Retrieved Sun, 28 Apr 2024 23:29:30 +0000

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No (this computation is public)

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Estimated Impact

118

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-       [(Partial) Autocorrelation Function] [] [2009-11-27 19:18:00] [7cc673c2b3a8ab442a3ec6ca430f2445] [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	'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61158&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61158&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61158&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.304786	-2.3609	0.01075
2	-0.3005	-2.3277	0.01166
3	0.128536	0.9956	0.161713
4	0.087461	0.6775	0.250355
5	-0.082458	-0.6387	0.26272
6	0.176328	1.3658	0.088545
7	-0.296479	-2.2965	0.012577
8	0.225164	1.7441	0.04313
9	0.000873	0.0068	0.497313
10	-0.290895	-2.2533	0.013955
11	-0.079252	-0.6139	0.270806
12	0.524362	4.0617	7.2e-05
13	-0.172532	-1.3364	0.093227
14	-0.195589	-1.515	0.067508
15	-0.017257	-0.1337	0.447055
16	0.187292	1.4508	0.076028
17	-0.088249	-0.6836	0.248437

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.304786 & -2.3609 & 0.01075 \tabularnewline
2 & -0.3005 & -2.3277 & 0.01166 \tabularnewline
3 & 0.128536 & 0.9956 & 0.161713 \tabularnewline
4 & 0.087461 & 0.6775 & 0.250355 \tabularnewline
5 & -0.082458 & -0.6387 & 0.26272 \tabularnewline
6 & 0.176328 & 1.3658 & 0.088545 \tabularnewline
7 & -0.296479 & -2.2965 & 0.012577 \tabularnewline
8 & 0.225164 & 1.7441 & 0.04313 \tabularnewline
9 & 0.000873 & 0.0068 & 0.497313 \tabularnewline
10 & -0.290895 & -2.2533 & 0.013955 \tabularnewline
11 & -0.079252 & -0.6139 & 0.270806 \tabularnewline
12 & 0.524362 & 4.0617 & 7.2e-05 \tabularnewline
13 & -0.172532 & -1.3364 & 0.093227 \tabularnewline
14 & -0.195589 & -1.515 & 0.067508 \tabularnewline
15 & -0.017257 & -0.1337 & 0.447055 \tabularnewline
16 & 0.187292 & 1.4508 & 0.076028 \tabularnewline
17 & -0.088249 & -0.6836 & 0.248437 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61158&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]-0.304786[/C][C]-2.3609[/C][C]0.01075[/C][/ROW]
[ROW][C]2[/C][C]-0.3005[/C][C]-2.3277[/C][C]0.01166[/C][/ROW]
[ROW][C]3[/C][C]0.128536[/C][C]0.9956[/C][C]0.161713[/C][/ROW]
[ROW][C]4[/C][C]0.087461[/C][C]0.6775[/C][C]0.250355[/C][/ROW]
[ROW][C]5[/C][C]-0.082458[/C][C]-0.6387[/C][C]0.26272[/C][/ROW]
[ROW][C]6[/C][C]0.176328[/C][C]1.3658[/C][C]0.088545[/C][/ROW]
[ROW][C]7[/C][C]-0.296479[/C][C]-2.2965[/C][C]0.012577[/C][/ROW]
[ROW][C]8[/C][C]0.225164[/C][C]1.7441[/C][C]0.04313[/C][/ROW]
[ROW][C]9[/C][C]0.000873[/C][C]0.0068[/C][C]0.497313[/C][/ROW]
[ROW][C]10[/C][C]-0.290895[/C][C]-2.2533[/C][C]0.013955[/C][/ROW]
[ROW][C]11[/C][C]-0.079252[/C][C]-0.6139[/C][C]0.270806[/C][/ROW]
[ROW][C]12[/C][C]0.524362[/C][C]4.0617[/C][C]7.2e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.172532[/C][C]-1.3364[/C][C]0.093227[/C][/ROW]
[ROW][C]14[/C][C]-0.195589[/C][C]-1.515[/C][C]0.067508[/C][/ROW]
[ROW][C]15[/C][C]-0.017257[/C][C]-0.1337[/C][C]0.447055[/C][/ROW]
[ROW][C]16[/C][C]0.187292[/C][C]1.4508[/C][C]0.076028[/C][/ROW]
[ROW][C]17[/C][C]-0.088249[/C][C]-0.6836[/C][C]0.248437[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61158&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61158&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	-0.304786	-2.3609	0.01075
2	-0.3005	-2.3277	0.01166
3	0.128536	0.9956	0.161713
4	0.087461	0.6775	0.250355
5	-0.082458	-0.6387	0.26272
6	0.176328	1.3658	0.088545
7	-0.296479	-2.2965	0.012577
8	0.225164	1.7441	0.04313
9	0.000873	0.0068	0.497313
10	-0.290895	-2.2533	0.013955
11	-0.079252	-0.6139	0.270806
12	0.524362	4.0617	7.2e-05
13	-0.172532	-1.3364	0.093227
14	-0.195589	-1.515	0.067508
15	-0.017257	-0.1337	0.447055
16	0.187292	1.4508	0.076028
17	-0.088249	-0.6836	0.248437

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.304786	-2.3609	0.01075
2	-0.433681	-3.3593	0.000681
3	-0.183235	-1.4193	0.080488
4	-0.079222	-0.6137	0.270883
5	-0.079536	-0.6161	0.270085
6	0.221707	1.7173	0.045538
7	-0.228641	-1.771	0.040816
8	0.220205	1.7057	0.046618
9	-0.058993	-0.457	0.324676
10	-0.282309	-2.1868	0.016335
11	-0.440825	-3.4146	0.000575
12	0.157313	1.2185	0.113894
13	0.180275	1.3964	0.083869
14	0.032811	0.2541	0.400124
15	-0.030045	-0.2327	0.408384
16	0.081265	0.6295	0.265713
17	-0.16288	-1.2617	0.105976

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.304786 & -2.3609 & 0.01075 \tabularnewline
2 & -0.433681 & -3.3593 & 0.000681 \tabularnewline
3 & -0.183235 & -1.4193 & 0.080488 \tabularnewline
4 & -0.079222 & -0.6137 & 0.270883 \tabularnewline
5 & -0.079536 & -0.6161 & 0.270085 \tabularnewline
6 & 0.221707 & 1.7173 & 0.045538 \tabularnewline
7 & -0.228641 & -1.771 & 0.040816 \tabularnewline
8 & 0.220205 & 1.7057 & 0.046618 \tabularnewline
9 & -0.058993 & -0.457 & 0.324676 \tabularnewline
10 & -0.282309 & -2.1868 & 0.016335 \tabularnewline
11 & -0.440825 & -3.4146 & 0.000575 \tabularnewline
12 & 0.157313 & 1.2185 & 0.113894 \tabularnewline
13 & 0.180275 & 1.3964 & 0.083869 \tabularnewline
14 & 0.032811 & 0.2541 & 0.400124 \tabularnewline
15 & -0.030045 & -0.2327 & 0.408384 \tabularnewline
16 & 0.081265 & 0.6295 & 0.265713 \tabularnewline
17 & -0.16288 & -1.2617 & 0.105976 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61158&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]-0.304786[/C][C]-2.3609[/C][C]0.01075[/C][/ROW]
[ROW][C]2[/C][C]-0.433681[/C][C]-3.3593[/C][C]0.000681[/C][/ROW]
[ROW][C]3[/C][C]-0.183235[/C][C]-1.4193[/C][C]0.080488[/C][/ROW]
[ROW][C]4[/C][C]-0.079222[/C][C]-0.6137[/C][C]0.270883[/C][/ROW]
[ROW][C]5[/C][C]-0.079536[/C][C]-0.6161[/C][C]0.270085[/C][/ROW]
[ROW][C]6[/C][C]0.221707[/C][C]1.7173[/C][C]0.045538[/C][/ROW]
[ROW][C]7[/C][C]-0.228641[/C][C]-1.771[/C][C]0.040816[/C][/ROW]
[ROW][C]8[/C][C]0.220205[/C][C]1.7057[/C][C]0.046618[/C][/ROW]
[ROW][C]9[/C][C]-0.058993[/C][C]-0.457[/C][C]0.324676[/C][/ROW]
[ROW][C]10[/C][C]-0.282309[/C][C]-2.1868[/C][C]0.016335[/C][/ROW]
[ROW][C]11[/C][C]-0.440825[/C][C]-3.4146[/C][C]0.000575[/C][/ROW]
[ROW][C]12[/C][C]0.157313[/C][C]1.2185[/C][C]0.113894[/C][/ROW]
[ROW][C]13[/C][C]0.180275[/C][C]1.3964[/C][C]0.083869[/C][/ROW]
[ROW][C]14[/C][C]0.032811[/C][C]0.2541[/C][C]0.400124[/C][/ROW]
[ROW][C]15[/C][C]-0.030045[/C][C]-0.2327[/C][C]0.408384[/C][/ROW]
[ROW][C]16[/C][C]0.081265[/C][C]0.6295[/C][C]0.265713[/C][/ROW]
[ROW][C]17[/C][C]-0.16288[/C][C]-1.2617[/C][C]0.105976[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61158&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61158&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	-0.304786	-2.3609	0.01075
2	-0.433681	-3.3593	0.000681
3	-0.183235	-1.4193	0.080488
4	-0.079222	-0.6137	0.270883
5	-0.079536	-0.6161	0.270085
6	0.221707	1.7173	0.045538
7	-0.228641	-1.771	0.040816
8	0.220205	1.7057	0.046618
9	-0.058993	-0.457	0.324676
10	-0.282309	-2.1868	0.016335
11	-0.440825	-3.4146	0.000575
12	0.157313	1.2185	0.113894
13	0.180275	1.3964	0.083869
14	0.032811	0.2541	0.400124
15	-0.030045	-0.2327	0.408384
16	0.081265	0.6295	0.265713
17	-0.16288	-1.2617	0.105976

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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code