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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 27 Nov 2009 15:09:54 -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/2009/Nov/27/t12593598813kym75lxfjiio67.htm/, Retrieved Sun, 28 Apr 2024 20:38:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61307, Retrieved Sun, 28 Apr 2024 20:38:46 +0000

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No (this computation is public)

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Estimated Impact

120

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

-       [(Partial) Autocorrelation Function] [ACF 1] [2009-11-27 22:09:54] [b42c0aeada8a5fa89825c81e73c10645] [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=61307&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=61307&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61307&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	0.860096	6.6623	0
2	0.674123	5.2217	1e-06
3	0.424552	3.2886	0.000844
4	0.289644	2.2436	0.014282
5	0.210164	1.6279	0.05439
6	0.18596	1.4404	0.07747
7	0.128191	0.993	0.162358
8	0.036333	0.2814	0.389671
9	-0.115435	-0.8942	0.187405
10	-0.278605	-2.1581	0.017467
11	-0.418153	-3.239	0.000979
12	-0.48201	-3.7336	0.000211
13	-0.473253	-3.6658	0.000262
14	-0.397888	-3.082	0.001552
15	-0.299048	-2.3164	0.011984
16	-0.223066	-1.7279	0.044579
17	-0.173174	-1.3414	0.092424

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.860096 & 6.6623 & 0 \tabularnewline
2 & 0.674123 & 5.2217 & 1e-06 \tabularnewline
3 & 0.424552 & 3.2886 & 0.000844 \tabularnewline
4 & 0.289644 & 2.2436 & 0.014282 \tabularnewline
5 & 0.210164 & 1.6279 & 0.05439 \tabularnewline
6 & 0.18596 & 1.4404 & 0.07747 \tabularnewline
7 & 0.128191 & 0.993 & 0.162358 \tabularnewline
8 & 0.036333 & 0.2814 & 0.389671 \tabularnewline
9 & -0.115435 & -0.8942 & 0.187405 \tabularnewline
10 & -0.278605 & -2.1581 & 0.017467 \tabularnewline
11 & -0.418153 & -3.239 & 0.000979 \tabularnewline
12 & -0.48201 & -3.7336 & 0.000211 \tabularnewline
13 & -0.473253 & -3.6658 & 0.000262 \tabularnewline
14 & -0.397888 & -3.082 & 0.001552 \tabularnewline
15 & -0.299048 & -2.3164 & 0.011984 \tabularnewline
16 & -0.223066 & -1.7279 & 0.044579 \tabularnewline
17 & -0.173174 & -1.3414 & 0.092424 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61307&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]0.860096[/C][C]6.6623[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.674123[/C][C]5.2217[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.424552[/C][C]3.2886[/C][C]0.000844[/C][/ROW]
[ROW][C]4[/C][C]0.289644[/C][C]2.2436[/C][C]0.014282[/C][/ROW]
[ROW][C]5[/C][C]0.210164[/C][C]1.6279[/C][C]0.05439[/C][/ROW]
[ROW][C]6[/C][C]0.18596[/C][C]1.4404[/C][C]0.07747[/C][/ROW]
[ROW][C]7[/C][C]0.128191[/C][C]0.993[/C][C]0.162358[/C][/ROW]
[ROW][C]8[/C][C]0.036333[/C][C]0.2814[/C][C]0.389671[/C][/ROW]
[ROW][C]9[/C][C]-0.115435[/C][C]-0.8942[/C][C]0.187405[/C][/ROW]
[ROW][C]10[/C][C]-0.278605[/C][C]-2.1581[/C][C]0.017467[/C][/ROW]
[ROW][C]11[/C][C]-0.418153[/C][C]-3.239[/C][C]0.000979[/C][/ROW]
[ROW][C]12[/C][C]-0.48201[/C][C]-3.7336[/C][C]0.000211[/C][/ROW]
[ROW][C]13[/C][C]-0.473253[/C][C]-3.6658[/C][C]0.000262[/C][/ROW]
[ROW][C]14[/C][C]-0.397888[/C][C]-3.082[/C][C]0.001552[/C][/ROW]
[ROW][C]15[/C][C]-0.299048[/C][C]-2.3164[/C][C]0.011984[/C][/ROW]
[ROW][C]16[/C][C]-0.223066[/C][C]-1.7279[/C][C]0.044579[/C][/ROW]
[ROW][C]17[/C][C]-0.173174[/C][C]-1.3414[/C][C]0.092424[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61307&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61307&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	0.860096	6.6623	0
2	0.674123	5.2217	1e-06
3	0.424552	3.2886	0.000844
4	0.289644	2.2436	0.014282
5	0.210164	1.6279	0.05439
6	0.18596	1.4404	0.07747
7	0.128191	0.993	0.162358
8	0.036333	0.2814	0.389671
9	-0.115435	-0.8942	0.187405
10	-0.278605	-2.1581	0.017467
11	-0.418153	-3.239	0.000979
12	-0.48201	-3.7336	0.000211
13	-0.473253	-3.6658	0.000262
14	-0.397888	-3.082	0.001552
15	-0.299048	-2.3164	0.011984
16	-0.223066	-1.7279	0.044579
17	-0.173174	-1.3414	0.092424

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.860096	6.6623	0
2	-0.252239	-1.9538	0.027693
3	-0.347016	-2.688	0.004645
4	0.401692	3.1115	0.001424
5	0.048432	0.3752	0.354435
6	-0.204793	-1.5863	0.058962
7	-0.134967	-1.0455	0.150004
8	-0.070036	-0.5425	0.294742
9	-0.220104	-1.7049	0.046692
10	-0.201184	-1.5584	0.062203
11	-0.025441	-0.1971	0.422223
12	0.042477	0.329	0.371641
13	-0.019677	-0.1524	0.439683
14	0.077042	0.5968	0.276456
15	0.140773	1.0904	0.139943
16	-0.074771	-0.5792	0.28232
17	0.023455	0.1817	0.428224

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.860096 & 6.6623 & 0 \tabularnewline
2 & -0.252239 & -1.9538 & 0.027693 \tabularnewline
3 & -0.347016 & -2.688 & 0.004645 \tabularnewline
4 & 0.401692 & 3.1115 & 0.001424 \tabularnewline
5 & 0.048432 & 0.3752 & 0.354435 \tabularnewline
6 & -0.204793 & -1.5863 & 0.058962 \tabularnewline
7 & -0.134967 & -1.0455 & 0.150004 \tabularnewline
8 & -0.070036 & -0.5425 & 0.294742 \tabularnewline
9 & -0.220104 & -1.7049 & 0.046692 \tabularnewline
10 & -0.201184 & -1.5584 & 0.062203 \tabularnewline
11 & -0.025441 & -0.1971 & 0.422223 \tabularnewline
12 & 0.042477 & 0.329 & 0.371641 \tabularnewline
13 & -0.019677 & -0.1524 & 0.439683 \tabularnewline
14 & 0.077042 & 0.5968 & 0.276456 \tabularnewline
15 & 0.140773 & 1.0904 & 0.139943 \tabularnewline
16 & -0.074771 & -0.5792 & 0.28232 \tabularnewline
17 & 0.023455 & 0.1817 & 0.428224 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61307&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]0.860096[/C][C]6.6623[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.252239[/C][C]-1.9538[/C][C]0.027693[/C][/ROW]
[ROW][C]3[/C][C]-0.347016[/C][C]-2.688[/C][C]0.004645[/C][/ROW]
[ROW][C]4[/C][C]0.401692[/C][C]3.1115[/C][C]0.001424[/C][/ROW]
[ROW][C]5[/C][C]0.048432[/C][C]0.3752[/C][C]0.354435[/C][/ROW]
[ROW][C]6[/C][C]-0.204793[/C][C]-1.5863[/C][C]0.058962[/C][/ROW]
[ROW][C]7[/C][C]-0.134967[/C][C]-1.0455[/C][C]0.150004[/C][/ROW]
[ROW][C]8[/C][C]-0.070036[/C][C]-0.5425[/C][C]0.294742[/C][/ROW]
[ROW][C]9[/C][C]-0.220104[/C][C]-1.7049[/C][C]0.046692[/C][/ROW]
[ROW][C]10[/C][C]-0.201184[/C][C]-1.5584[/C][C]0.062203[/C][/ROW]
[ROW][C]11[/C][C]-0.025441[/C][C]-0.1971[/C][C]0.422223[/C][/ROW]
[ROW][C]12[/C][C]0.042477[/C][C]0.329[/C][C]0.371641[/C][/ROW]
[ROW][C]13[/C][C]-0.019677[/C][C]-0.1524[/C][C]0.439683[/C][/ROW]
[ROW][C]14[/C][C]0.077042[/C][C]0.5968[/C][C]0.276456[/C][/ROW]
[ROW][C]15[/C][C]0.140773[/C][C]1.0904[/C][C]0.139943[/C][/ROW]
[ROW][C]16[/C][C]-0.074771[/C][C]-0.5792[/C][C]0.28232[/C][/ROW]
[ROW][C]17[/C][C]0.023455[/C][C]0.1817[/C][C]0.428224[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61307&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61307&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	0.860096	6.6623	0
2	-0.252239	-1.9538	0.027693
3	-0.347016	-2.688	0.004645
4	0.401692	3.1115	0.001424
5	0.048432	0.3752	0.354435
6	-0.204793	-1.5863	0.058962
7	-0.134967	-1.0455	0.150004
8	-0.070036	-0.5425	0.294742
9	-0.220104	-1.7049	0.046692
10	-0.201184	-1.5584	0.062203
11	-0.025441	-0.1971	0.422223
12	0.042477	0.329	0.371641
13	-0.019677	-0.1524	0.439683
14	0.077042	0.5968	0.276456
15	0.140773	1.0904	0.139943
16	-0.074771	-0.5792	0.28232
17	0.023455	0.1817	0.428224

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 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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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Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code