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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 27 Nov 2009 13:12:03 -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/t125935296854otu6au86l7lnn.htm/, Retrieved Sun, 28 Apr 2024 21:07:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61235, Retrieved Sun, 28 Apr 2024 21:07:19 +0000

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No (this computation is public)

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Estimated Impact

115

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

-       [(Partial) Autocorrelation Function] [Autocorrelatie] [2009-11-27 20:12:03] [4c76f32a7a0cc9034048c3cdcdaf547e] [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=61235&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=61235&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61235&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	0.541656	3.7527	0.000236
2	0.634169	4.3937	3.1e-05
3	0.688982	4.7734	9e-06
4	0.411417	2.8504	0.003209
5	0.413627	2.8657	0.003079
6	0.386508	2.6778	0.005057
7	0.173631	1.2029	0.117448
8	0.216429	1.4995	0.070151
9	0.081256	0.563	0.288043
10	0.049604	0.3437	0.3663
11	0.072731	0.5039	0.308321
12	-0.045702	-0.3166	0.376447
13	0.009447	0.0655	0.474043
14	0.006136	0.0425	0.483135
15	-0.042984	-0.2978	0.383569
16	-0.071508	-0.4954	0.311281
17	-0.002043	-0.0142	0.494383

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.541656 & 3.7527 & 0.000236 \tabularnewline
2 & 0.634169 & 4.3937 & 3.1e-05 \tabularnewline
3 & 0.688982 & 4.7734 & 9e-06 \tabularnewline
4 & 0.411417 & 2.8504 & 0.003209 \tabularnewline
5 & 0.413627 & 2.8657 & 0.003079 \tabularnewline
6 & 0.386508 & 2.6778 & 0.005057 \tabularnewline
7 & 0.173631 & 1.2029 & 0.117448 \tabularnewline
8 & 0.216429 & 1.4995 & 0.070151 \tabularnewline
9 & 0.081256 & 0.563 & 0.288043 \tabularnewline
10 & 0.049604 & 0.3437 & 0.3663 \tabularnewline
11 & 0.072731 & 0.5039 & 0.308321 \tabularnewline
12 & -0.045702 & -0.3166 & 0.376447 \tabularnewline
13 & 0.009447 & 0.0655 & 0.474043 \tabularnewline
14 & 0.006136 & 0.0425 & 0.483135 \tabularnewline
15 & -0.042984 & -0.2978 & 0.383569 \tabularnewline
16 & -0.071508 & -0.4954 & 0.311281 \tabularnewline
17 & -0.002043 & -0.0142 & 0.494383 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61235&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]0.541656[/C][C]3.7527[/C][C]0.000236[/C][/ROW]
[ROW][C]2[/C][C]0.634169[/C][C]4.3937[/C][C]3.1e-05[/C][/ROW]
[ROW][C]3[/C][C]0.688982[/C][C]4.7734[/C][C]9e-06[/C][/ROW]
[ROW][C]4[/C][C]0.411417[/C][C]2.8504[/C][C]0.003209[/C][/ROW]
[ROW][C]5[/C][C]0.413627[/C][C]2.8657[/C][C]0.003079[/C][/ROW]
[ROW][C]6[/C][C]0.386508[/C][C]2.6778[/C][C]0.005057[/C][/ROW]
[ROW][C]7[/C][C]0.173631[/C][C]1.2029[/C][C]0.117448[/C][/ROW]
[ROW][C]8[/C][C]0.216429[/C][C]1.4995[/C][C]0.070151[/C][/ROW]
[ROW][C]9[/C][C]0.081256[/C][C]0.563[/C][C]0.288043[/C][/ROW]
[ROW][C]10[/C][C]0.049604[/C][C]0.3437[/C][C]0.3663[/C][/ROW]
[ROW][C]11[/C][C]0.072731[/C][C]0.5039[/C][C]0.308321[/C][/ROW]
[ROW][C]12[/C][C]-0.045702[/C][C]-0.3166[/C][C]0.376447[/C][/ROW]
[ROW][C]13[/C][C]0.009447[/C][C]0.0655[/C][C]0.474043[/C][/ROW]
[ROW][C]14[/C][C]0.006136[/C][C]0.0425[/C][C]0.483135[/C][/ROW]
[ROW][C]15[/C][C]-0.042984[/C][C]-0.2978[/C][C]0.383569[/C][/ROW]
[ROW][C]16[/C][C]-0.071508[/C][C]-0.4954[/C][C]0.311281[/C][/ROW]
[ROW][C]17[/C][C]-0.002043[/C][C]-0.0142[/C][C]0.494383[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61235&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61235&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	0.541656	3.7527	0.000236
2	0.634169	4.3937	3.1e-05
3	0.688982	4.7734	9e-06
4	0.411417	2.8504	0.003209
5	0.413627	2.8657	0.003079
6	0.386508	2.6778	0.005057
7	0.173631	1.2029	0.117448
8	0.216429	1.4995	0.070151
9	0.081256	0.563	0.288043
10	0.049604	0.3437	0.3663
11	0.072731	0.5039	0.308321
12	-0.045702	-0.3166	0.376447
13	0.009447	0.0655	0.474043
14	0.006136	0.0425	0.483135
15	-0.042984	-0.2978	0.383569
16	-0.071508	-0.4954	0.311281
17	-0.002043	-0.0142	0.494383

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.541656	3.7527	0.000236
2	0.482273	3.3413	0.000811
3	0.460879	3.1931	0.001243
4	-0.239235	-1.6575	0.051974
5	-0.319394	-2.2128	0.015849
6	-0.073901	-0.512	0.305498
7	-0.073118	-0.5066	0.307385
8	0.087943	0.6093	0.272604
9	-0.106209	-0.7358	0.232704
10	0.069572	0.482	0.315995
11	0.167938	1.1635	0.125187
12	-0.019071	-0.1321	0.447717
13	-0.024675	-0.171	0.43249
14	-0.031159	-0.2159	0.415
15	0.056314	0.3902	0.349074
16	-0.261906	-1.8145	0.037923
17	-0.010366	-0.0718	0.471522

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.541656 & 3.7527 & 0.000236 \tabularnewline
2 & 0.482273 & 3.3413 & 0.000811 \tabularnewline
3 & 0.460879 & 3.1931 & 0.001243 \tabularnewline
4 & -0.239235 & -1.6575 & 0.051974 \tabularnewline
5 & -0.319394 & -2.2128 & 0.015849 \tabularnewline
6 & -0.073901 & -0.512 & 0.305498 \tabularnewline
7 & -0.073118 & -0.5066 & 0.307385 \tabularnewline
8 & 0.087943 & 0.6093 & 0.272604 \tabularnewline
9 & -0.106209 & -0.7358 & 0.232704 \tabularnewline
10 & 0.069572 & 0.482 & 0.315995 \tabularnewline
11 & 0.167938 & 1.1635 & 0.125187 \tabularnewline
12 & -0.019071 & -0.1321 & 0.447717 \tabularnewline
13 & -0.024675 & -0.171 & 0.43249 \tabularnewline
14 & -0.031159 & -0.2159 & 0.415 \tabularnewline
15 & 0.056314 & 0.3902 & 0.349074 \tabularnewline
16 & -0.261906 & -1.8145 & 0.037923 \tabularnewline
17 & -0.010366 & -0.0718 & 0.471522 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61235&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]0.541656[/C][C]3.7527[/C][C]0.000236[/C][/ROW]
[ROW][C]2[/C][C]0.482273[/C][C]3.3413[/C][C]0.000811[/C][/ROW]
[ROW][C]3[/C][C]0.460879[/C][C]3.1931[/C][C]0.001243[/C][/ROW]
[ROW][C]4[/C][C]-0.239235[/C][C]-1.6575[/C][C]0.051974[/C][/ROW]
[ROW][C]5[/C][C]-0.319394[/C][C]-2.2128[/C][C]0.015849[/C][/ROW]
[ROW][C]6[/C][C]-0.073901[/C][C]-0.512[/C][C]0.305498[/C][/ROW]
[ROW][C]7[/C][C]-0.073118[/C][C]-0.5066[/C][C]0.307385[/C][/ROW]
[ROW][C]8[/C][C]0.087943[/C][C]0.6093[/C][C]0.272604[/C][/ROW]
[ROW][C]9[/C][C]-0.106209[/C][C]-0.7358[/C][C]0.232704[/C][/ROW]
[ROW][C]10[/C][C]0.069572[/C][C]0.482[/C][C]0.315995[/C][/ROW]
[ROW][C]11[/C][C]0.167938[/C][C]1.1635[/C][C]0.125187[/C][/ROW]
[ROW][C]12[/C][C]-0.019071[/C][C]-0.1321[/C][C]0.447717[/C][/ROW]
[ROW][C]13[/C][C]-0.024675[/C][C]-0.171[/C][C]0.43249[/C][/ROW]
[ROW][C]14[/C][C]-0.031159[/C][C]-0.2159[/C][C]0.415[/C][/ROW]
[ROW][C]15[/C][C]0.056314[/C][C]0.3902[/C][C]0.349074[/C][/ROW]
[ROW][C]16[/C][C]-0.261906[/C][C]-1.8145[/C][C]0.037923[/C][/ROW]
[ROW][C]17[/C][C]-0.010366[/C][C]-0.0718[/C][C]0.471522[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61235&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61235&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	0.541656	3.7527	0.000236
2	0.482273	3.3413	0.000811
3	0.460879	3.1931	0.001243
4	-0.239235	-1.6575	0.051974
5	-0.319394	-2.2128	0.015849
6	-0.073901	-0.512	0.305498
7	-0.073118	-0.5066	0.307385
8	0.087943	0.6093	0.272604
9	-0.106209	-0.7358	0.232704
10	0.069572	0.482	0.315995
11	0.167938	1.1635	0.125187
12	-0.019071	-0.1321	0.447717
13	-0.024675	-0.171	0.43249
14	-0.031159	-0.2159	0.415
15	0.056314	0.3902	0.349074
16	-0.261906	-1.8145	0.037923
17	-0.010366	-0.0718	0.471522

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 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; 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