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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 04 Dec 2010 20:25:47 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/04/t12914942853hqms8kufqtbcx7.htm/, Retrieved Sat, 04 May 2024 22:13:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105266, Retrieved Sat, 04 May 2024 22:13:35 +0000

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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] [W9 - autocorrelat...] [2010-12-04 20:25:47] [6f3869f9d1e39c73f93153f1f7803f84] [Current]
-   P     [(Partial) Autocorrelation Function] [W9 - autocorrelat...] [2010-12-04 20:36:59] [48146708a479232c43a8f6e52fbf83b4] 
-   P       [(Partial) Autocorrelation Function] [W9 - autocorrelat...] [2010-12-04 20:50:26] [48146708a479232c43a8f6e52fbf83b4] 

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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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105266&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105266&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105266&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.848021	6.6233	0
2	0.639835	4.9973	3e-06
3	0.511059	3.9915	8.9e-05
4	0.475359	3.7127	0.000223
5	0.491952	3.8423	0.000146
6	0.48343	3.7757	0.000182
7	0.402047	3.1401	0.001302
8	0.285616	2.2307	0.014693
9	0.21778	1.7009	0.047026
10	0.198225	1.5482	0.063375
11	0.251305	1.9628	0.02712
12	0.244443	1.9092	0.030474
13	0.072604	0.5671	0.286377
14	-0.119946	-0.9368	0.176276
15	-0.227506	-1.7769	0.040287
16	-0.272728	-2.1301	0.018604
17	-0.271369	-2.1195	0.019065

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.848021 & 6.6233 & 0 \tabularnewline
2 & 0.639835 & 4.9973 & 3e-06 \tabularnewline
3 & 0.511059 & 3.9915 & 8.9e-05 \tabularnewline
4 & 0.475359 & 3.7127 & 0.000223 \tabularnewline
5 & 0.491952 & 3.8423 & 0.000146 \tabularnewline
6 & 0.48343 & 3.7757 & 0.000182 \tabularnewline
7 & 0.402047 & 3.1401 & 0.001302 \tabularnewline
8 & 0.285616 & 2.2307 & 0.014693 \tabularnewline
9 & 0.21778 & 1.7009 & 0.047026 \tabularnewline
10 & 0.198225 & 1.5482 & 0.063375 \tabularnewline
11 & 0.251305 & 1.9628 & 0.02712 \tabularnewline
12 & 0.244443 & 1.9092 & 0.030474 \tabularnewline
13 & 0.072604 & 0.5671 & 0.286377 \tabularnewline
14 & -0.119946 & -0.9368 & 0.176276 \tabularnewline
15 & -0.227506 & -1.7769 & 0.040287 \tabularnewline
16 & -0.272728 & -2.1301 & 0.018604 \tabularnewline
17 & -0.271369 & -2.1195 & 0.019065 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105266&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]0.848021[/C][C]6.6233[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.639835[/C][C]4.9973[/C][C]3e-06[/C][/ROW]
[ROW][C]3[/C][C]0.511059[/C][C]3.9915[/C][C]8.9e-05[/C][/ROW]
[ROW][C]4[/C][C]0.475359[/C][C]3.7127[/C][C]0.000223[/C][/ROW]
[ROW][C]5[/C][C]0.491952[/C][C]3.8423[/C][C]0.000146[/C][/ROW]
[ROW][C]6[/C][C]0.48343[/C][C]3.7757[/C][C]0.000182[/C][/ROW]
[ROW][C]7[/C][C]0.402047[/C][C]3.1401[/C][C]0.001302[/C][/ROW]
[ROW][C]8[/C][C]0.285616[/C][C]2.2307[/C][C]0.014693[/C][/ROW]
[ROW][C]9[/C][C]0.21778[/C][C]1.7009[/C][C]0.047026[/C][/ROW]
[ROW][C]10[/C][C]0.198225[/C][C]1.5482[/C][C]0.063375[/C][/ROW]
[ROW][C]11[/C][C]0.251305[/C][C]1.9628[/C][C]0.02712[/C][/ROW]
[ROW][C]12[/C][C]0.244443[/C][C]1.9092[/C][C]0.030474[/C][/ROW]
[ROW][C]13[/C][C]0.072604[/C][C]0.5671[/C][C]0.286377[/C][/ROW]
[ROW][C]14[/C][C]-0.119946[/C][C]-0.9368[/C][C]0.176276[/C][/ROW]
[ROW][C]15[/C][C]-0.227506[/C][C]-1.7769[/C][C]0.040287[/C][/ROW]
[ROW][C]16[/C][C]-0.272728[/C][C]-2.1301[/C][C]0.018604[/C][/ROW]
[ROW][C]17[/C][C]-0.271369[/C][C]-2.1195[/C][C]0.019065[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105266&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105266&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	0.848021	6.6233	0
2	0.639835	4.9973	3e-06
3	0.511059	3.9915	8.9e-05
4	0.475359	3.7127	0.000223
5	0.491952	3.8423	0.000146
6	0.48343	3.7757	0.000182
7	0.402047	3.1401	0.001302
8	0.285616	2.2307	0.014693
9	0.21778	1.7009	0.047026
10	0.198225	1.5482	0.063375
11	0.251305	1.9628	0.02712
12	0.244443	1.9092	0.030474
13	0.072604	0.5671	0.286377
14	-0.119946	-0.9368	0.176276
15	-0.227506	-1.7769	0.040287
16	-0.272728	-2.1301	0.018604
17	-0.271369	-2.1195	0.019065

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.848021	6.6233	0
2	-0.282363	-2.2053	0.015605
3	0.21166	1.6531	0.051723
4	0.151892	1.1863	0.120049
5	0.129758	1.0134	0.157427
6	-0.038333	-0.2994	0.382829
7	-0.137477	-1.0737	0.143587
8	-0.066091	-0.5162	0.303794
9	0.077019	0.6015	0.274855
10	-0.033172	-0.2591	0.398223
11	0.234727	1.8333	0.035821
12	-0.27313	-2.1332	0.018469
13	-0.451376	-3.5254	0.000404
14	0.015088	0.1178	0.45329
15	-0.028047	-0.2191	0.413668
16	-0.224213	-1.7512	0.042473
17	0.019499	0.1523	0.43973

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.848021 & 6.6233 & 0 \tabularnewline
2 & -0.282363 & -2.2053 & 0.015605 \tabularnewline
3 & 0.21166 & 1.6531 & 0.051723 \tabularnewline
4 & 0.151892 & 1.1863 & 0.120049 \tabularnewline
5 & 0.129758 & 1.0134 & 0.157427 \tabularnewline
6 & -0.038333 & -0.2994 & 0.382829 \tabularnewline
7 & -0.137477 & -1.0737 & 0.143587 \tabularnewline
8 & -0.066091 & -0.5162 & 0.303794 \tabularnewline
9 & 0.077019 & 0.6015 & 0.274855 \tabularnewline
10 & -0.033172 & -0.2591 & 0.398223 \tabularnewline
11 & 0.234727 & 1.8333 & 0.035821 \tabularnewline
12 & -0.27313 & -2.1332 & 0.018469 \tabularnewline
13 & -0.451376 & -3.5254 & 0.000404 \tabularnewline
14 & 0.015088 & 0.1178 & 0.45329 \tabularnewline
15 & -0.028047 & -0.2191 & 0.413668 \tabularnewline
16 & -0.224213 & -1.7512 & 0.042473 \tabularnewline
17 & 0.019499 & 0.1523 & 0.43973 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105266&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]0.848021[/C][C]6.6233[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.282363[/C][C]-2.2053[/C][C]0.015605[/C][/ROW]
[ROW][C]3[/C][C]0.21166[/C][C]1.6531[/C][C]0.051723[/C][/ROW]
[ROW][C]4[/C][C]0.151892[/C][C]1.1863[/C][C]0.120049[/C][/ROW]
[ROW][C]5[/C][C]0.129758[/C][C]1.0134[/C][C]0.157427[/C][/ROW]
[ROW][C]6[/C][C]-0.038333[/C][C]-0.2994[/C][C]0.382829[/C][/ROW]
[ROW][C]7[/C][C]-0.137477[/C][C]-1.0737[/C][C]0.143587[/C][/ROW]
[ROW][C]8[/C][C]-0.066091[/C][C]-0.5162[/C][C]0.303794[/C][/ROW]
[ROW][C]9[/C][C]0.077019[/C][C]0.6015[/C][C]0.274855[/C][/ROW]
[ROW][C]10[/C][C]-0.033172[/C][C]-0.2591[/C][C]0.398223[/C][/ROW]
[ROW][C]11[/C][C]0.234727[/C][C]1.8333[/C][C]0.035821[/C][/ROW]
[ROW][C]12[/C][C]-0.27313[/C][C]-2.1332[/C][C]0.018469[/C][/ROW]
[ROW][C]13[/C][C]-0.451376[/C][C]-3.5254[/C][C]0.000404[/C][/ROW]
[ROW][C]14[/C][C]0.015088[/C][C]0.1178[/C][C]0.45329[/C][/ROW]
[ROW][C]15[/C][C]-0.028047[/C][C]-0.2191[/C][C]0.413668[/C][/ROW]
[ROW][C]16[/C][C]-0.224213[/C][C]-1.7512[/C][C]0.042473[/C][/ROW]
[ROW][C]17[/C][C]0.019499[/C][C]0.1523[/C][C]0.43973[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105266&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105266&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	0.848021	6.6233	0
2	-0.282363	-2.2053	0.015605
3	0.21166	1.6531	0.051723
4	0.151892	1.1863	0.120049
5	0.129758	1.0134	0.157427
6	-0.038333	-0.2994	0.382829
7	-0.137477	-1.0737	0.143587
8	-0.066091	-0.5162	0.303794
9	0.077019	0.6015	0.274855
10	-0.033172	-0.2591	0.398223
11	0.234727	1.8333	0.035821
12	-0.27313	-2.1332	0.018469
13	-0.451376	-3.5254	0.000404
14	0.015088	0.1178	0.45329
15	-0.028047	-0.2191	0.413668
16	-0.224213	-1.7512	0.042473
17	0.019499	0.1523	0.43973

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code