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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 14 Dec 2009 02:13:20 -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/2009/Dec/14/t1260782390qxr1l27a0pbm15w.htm/, Retrieved Sun, 05 May 2024 15:05:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67459, Retrieved Sun, 05 May 2024 15:05:46 +0000

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Estimated Impact

155

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-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2009-12-14 09:13:20] [6df9bd2792d60592b4a24994398a86db] [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=67459&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=67459&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67459&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	0.866153	9.9513	0
2	0.813116	9.342	0
3	0.84548	9.7138	0
4	0.780119	8.9629	0
5	0.749567	8.6119	0
6	0.76594	8.8	0
7	0.679469	7.8065	0
8	0.656726	7.5452	0
9	0.650334	7.4718	0
10	0.569898	6.5476	0
11	0.591933	6.8008	0
12	0.638942	7.3409	0
13	0.526045	6.0438	0
14	0.473033	5.4347	0
15	0.494245	5.6784	0
16	0.443334	5.0935	1e-06
17	0.429284	4.9321	1e-06
18	0.441211	5.0691	1e-06
19	0.38193	4.388	1.2e-05
20	0.361799	4.1568	2.9e-05
21	0.356766	4.0989	3.6e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.866153 & 9.9513 & 0 \tabularnewline
2 & 0.813116 & 9.342 & 0 \tabularnewline
3 & 0.84548 & 9.7138 & 0 \tabularnewline
4 & 0.780119 & 8.9629 & 0 \tabularnewline
5 & 0.749567 & 8.6119 & 0 \tabularnewline
6 & 0.76594 & 8.8 & 0 \tabularnewline
7 & 0.679469 & 7.8065 & 0 \tabularnewline
8 & 0.656726 & 7.5452 & 0 \tabularnewline
9 & 0.650334 & 7.4718 & 0 \tabularnewline
10 & 0.569898 & 6.5476 & 0 \tabularnewline
11 & 0.591933 & 6.8008 & 0 \tabularnewline
12 & 0.638942 & 7.3409 & 0 \tabularnewline
13 & 0.526045 & 6.0438 & 0 \tabularnewline
14 & 0.473033 & 5.4347 & 0 \tabularnewline
15 & 0.494245 & 5.6784 & 0 \tabularnewline
16 & 0.443334 & 5.0935 & 1e-06 \tabularnewline
17 & 0.429284 & 4.9321 & 1e-06 \tabularnewline
18 & 0.441211 & 5.0691 & 1e-06 \tabularnewline
19 & 0.38193 & 4.388 & 1.2e-05 \tabularnewline
20 & 0.361799 & 4.1568 & 2.9e-05 \tabularnewline
21 & 0.356766 & 4.0989 & 3.6e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67459&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]0.866153[/C][C]9.9513[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.813116[/C][C]9.342[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.84548[/C][C]9.7138[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.780119[/C][C]8.9629[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.749567[/C][C]8.6119[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.76594[/C][C]8.8[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.679469[/C][C]7.8065[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.656726[/C][C]7.5452[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.650334[/C][C]7.4718[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.569898[/C][C]6.5476[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.591933[/C][C]6.8008[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.638942[/C][C]7.3409[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.526045[/C][C]6.0438[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.473033[/C][C]5.4347[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.494245[/C][C]5.6784[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.443334[/C][C]5.0935[/C][C]1e-06[/C][/ROW]
[ROW][C]17[/C][C]0.429284[/C][C]4.9321[/C][C]1e-06[/C][/ROW]
[ROW][C]18[/C][C]0.441211[/C][C]5.0691[/C][C]1e-06[/C][/ROW]
[ROW][C]19[/C][C]0.38193[/C][C]4.388[/C][C]1.2e-05[/C][/ROW]
[ROW][C]20[/C][C]0.361799[/C][C]4.1568[/C][C]2.9e-05[/C][/ROW]
[ROW][C]21[/C][C]0.356766[/C][C]4.0989[/C][C]3.6e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67459&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67459&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	0.866153	9.9513	0
2	0.813116	9.342	0
3	0.84548	9.7138	0
4	0.780119	8.9629	0
5	0.749567	8.6119	0
6	0.76594	8.8	0
7	0.679469	7.8065	0
8	0.656726	7.5452	0
9	0.650334	7.4718	0
10	0.569898	6.5476	0
11	0.591933	6.8008	0
12	0.638942	7.3409	0
13	0.526045	6.0438	0
14	0.473033	5.4347	0
15	0.494245	5.6784	0
16	0.443334	5.0935	1e-06
17	0.429284	4.9321	1e-06
18	0.441211	5.0691	1e-06
19	0.38193	4.388	1.2e-05
20	0.361799	4.1568	2.9e-05
21	0.356766	4.0989	3.6e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.866153	9.9513	0
2	0.251803	2.893	0.002233
3	0.429327	4.9326	1e-06
4	-0.140305	-1.612	0.054678
5	0.094409	1.0847	0.140021
6	0.085112	0.9779	0.164967
7	-0.26125	-3.0015	0.001607
8	0.102653	1.1794	0.120181
9	-0.113586	-1.305	0.09708
10	-0.095581	-1.0981	0.137071
11	0.299422	3.4401	0.000389
12	0.224896	2.5839	0.005429
13	-0.335144	-3.8505	9.1e-05
14	-0.264878	-3.0432	0.001413
15	0.040929	0.4702	0.319479
16	0.132566	1.5231	0.065067
17	0.066904	0.7687	0.22173
18	0.026699	0.3067	0.379759
19	0.016705	0.1919	0.42405
20	-0.076344	-0.8771	0.191005
21	-0.017032	-0.1957	0.422582

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.866153 & 9.9513 & 0 \tabularnewline
2 & 0.251803 & 2.893 & 0.002233 \tabularnewline
3 & 0.429327 & 4.9326 & 1e-06 \tabularnewline
4 & -0.140305 & -1.612 & 0.054678 \tabularnewline
5 & 0.094409 & 1.0847 & 0.140021 \tabularnewline
6 & 0.085112 & 0.9779 & 0.164967 \tabularnewline
7 & -0.26125 & -3.0015 & 0.001607 \tabularnewline
8 & 0.102653 & 1.1794 & 0.120181 \tabularnewline
9 & -0.113586 & -1.305 & 0.09708 \tabularnewline
10 & -0.095581 & -1.0981 & 0.137071 \tabularnewline
11 & 0.299422 & 3.4401 & 0.000389 \tabularnewline
12 & 0.224896 & 2.5839 & 0.005429 \tabularnewline
13 & -0.335144 & -3.8505 & 9.1e-05 \tabularnewline
14 & -0.264878 & -3.0432 & 0.001413 \tabularnewline
15 & 0.040929 & 0.4702 & 0.319479 \tabularnewline
16 & 0.132566 & 1.5231 & 0.065067 \tabularnewline
17 & 0.066904 & 0.7687 & 0.22173 \tabularnewline
18 & 0.026699 & 0.3067 & 0.379759 \tabularnewline
19 & 0.016705 & 0.1919 & 0.42405 \tabularnewline
20 & -0.076344 & -0.8771 & 0.191005 \tabularnewline
21 & -0.017032 & -0.1957 & 0.422582 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67459&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]0.866153[/C][C]9.9513[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.251803[/C][C]2.893[/C][C]0.002233[/C][/ROW]
[ROW][C]3[/C][C]0.429327[/C][C]4.9326[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]-0.140305[/C][C]-1.612[/C][C]0.054678[/C][/ROW]
[ROW][C]5[/C][C]0.094409[/C][C]1.0847[/C][C]0.140021[/C][/ROW]
[ROW][C]6[/C][C]0.085112[/C][C]0.9779[/C][C]0.164967[/C][/ROW]
[ROW][C]7[/C][C]-0.26125[/C][C]-3.0015[/C][C]0.001607[/C][/ROW]
[ROW][C]8[/C][C]0.102653[/C][C]1.1794[/C][C]0.120181[/C][/ROW]
[ROW][C]9[/C][C]-0.113586[/C][C]-1.305[/C][C]0.09708[/C][/ROW]
[ROW][C]10[/C][C]-0.095581[/C][C]-1.0981[/C][C]0.137071[/C][/ROW]
[ROW][C]11[/C][C]0.299422[/C][C]3.4401[/C][C]0.000389[/C][/ROW]
[ROW][C]12[/C][C]0.224896[/C][C]2.5839[/C][C]0.005429[/C][/ROW]
[ROW][C]13[/C][C]-0.335144[/C][C]-3.8505[/C][C]9.1e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.264878[/C][C]-3.0432[/C][C]0.001413[/C][/ROW]
[ROW][C]15[/C][C]0.040929[/C][C]0.4702[/C][C]0.319479[/C][/ROW]
[ROW][C]16[/C][C]0.132566[/C][C]1.5231[/C][C]0.065067[/C][/ROW]
[ROW][C]17[/C][C]0.066904[/C][C]0.7687[/C][C]0.22173[/C][/ROW]
[ROW][C]18[/C][C]0.026699[/C][C]0.3067[/C][C]0.379759[/C][/ROW]
[ROW][C]19[/C][C]0.016705[/C][C]0.1919[/C][C]0.42405[/C][/ROW]
[ROW][C]20[/C][C]-0.076344[/C][C]-0.8771[/C][C]0.191005[/C][/ROW]
[ROW][C]21[/C][C]-0.017032[/C][C]-0.1957[/C][C]0.422582[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67459&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67459&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	0.866153	9.9513	0
2	0.251803	2.893	0.002233
3	0.429327	4.9326	1e-06
4	-0.140305	-1.612	0.054678
5	0.094409	1.0847	0.140021
6	0.085112	0.9779	0.164967
7	-0.26125	-3.0015	0.001607
8	0.102653	1.1794	0.120181
9	-0.113586	-1.305	0.09708
10	-0.095581	-1.0981	0.137071
11	0.299422	3.4401	0.000389
12	0.224896	2.5839	0.005429
13	-0.335144	-3.8505	9.1e-05
14	-0.264878	-3.0432	0.001413
15	0.040929	0.4702	0.319479
16	0.132566	1.5231	0.065067
17	0.066904	0.7687	0.22173
18	0.026699	0.3067	0.379759
19	0.016705	0.1919	0.42405
20	-0.076344	-0.8771	0.191005
21	-0.017032	-0.1957	0.422582

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Invoer (België 1998-2008) ; par2 = Belgostat ; par3 = u ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code