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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 15 Dec 2009 13:38:12 -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/15/t1260909872lg9xx5mm8loswja.htm/, Retrieved Wed, 08 May 2024 21:47:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=68135, Retrieved Wed, 08 May 2024 21:47:05 +0000

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

-     [(Partial) Autocorrelation Function] [] [2009-11-26 17:18:03] [69bbb86d5181c362d5647cae31af3dc7]
-    D    [(Partial) Autocorrelation Function] [] [2009-12-15 20:38:12] [8cd69d0f4298074aa572ca2f9b39b6ae] [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=68135&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=68135&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68135&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	0.890527	6.898	0
2	0.727437	5.6347	0
3	0.618678	4.7923	6e-06
4	0.575508	4.4579	1.8e-05
5	0.576149	4.4628	1.8e-05
6	0.56402	4.3689	2.5e-05
7	0.508262	3.937	0.000109
8	0.433857	3.3606	0.000678
9	0.377091	2.9209	0.002456
10	0.374052	2.8974	0.002623
11	0.418909	3.2449	0.000962
12	0.4227	3.2742	0.000881
13	0.28349	2.1959	0.015988
14	0.113765	0.8812	0.190859
15	-0.003497	-0.0271	0.489238
16	-0.060835	-0.4712	0.319595
17	-0.073933	-0.5727	0.284499

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.890527 & 6.898 & 0 \tabularnewline
2 & 0.727437 & 5.6347 & 0 \tabularnewline
3 & 0.618678 & 4.7923 & 6e-06 \tabularnewline
4 & 0.575508 & 4.4579 & 1.8e-05 \tabularnewline
5 & 0.576149 & 4.4628 & 1.8e-05 \tabularnewline
6 & 0.56402 & 4.3689 & 2.5e-05 \tabularnewline
7 & 0.508262 & 3.937 & 0.000109 \tabularnewline
8 & 0.433857 & 3.3606 & 0.000678 \tabularnewline
9 & 0.377091 & 2.9209 & 0.002456 \tabularnewline
10 & 0.374052 & 2.8974 & 0.002623 \tabularnewline
11 & 0.418909 & 3.2449 & 0.000962 \tabularnewline
12 & 0.4227 & 3.2742 & 0.000881 \tabularnewline
13 & 0.28349 & 2.1959 & 0.015988 \tabularnewline
14 & 0.113765 & 0.8812 & 0.190859 \tabularnewline
15 & -0.003497 & -0.0271 & 0.489238 \tabularnewline
16 & -0.060835 & -0.4712 & 0.319595 \tabularnewline
17 & -0.073933 & -0.5727 & 0.284499 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68135&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]0.890527[/C][C]6.898[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.727437[/C][C]5.6347[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.618678[/C][C]4.7923[/C][C]6e-06[/C][/ROW]
[ROW][C]4[/C][C]0.575508[/C][C]4.4579[/C][C]1.8e-05[/C][/ROW]
[ROW][C]5[/C][C]0.576149[/C][C]4.4628[/C][C]1.8e-05[/C][/ROW]
[ROW][C]6[/C][C]0.56402[/C][C]4.3689[/C][C]2.5e-05[/C][/ROW]
[ROW][C]7[/C][C]0.508262[/C][C]3.937[/C][C]0.000109[/C][/ROW]
[ROW][C]8[/C][C]0.433857[/C][C]3.3606[/C][C]0.000678[/C][/ROW]
[ROW][C]9[/C][C]0.377091[/C][C]2.9209[/C][C]0.002456[/C][/ROW]
[ROW][C]10[/C][C]0.374052[/C][C]2.8974[/C][C]0.002623[/C][/ROW]
[ROW][C]11[/C][C]0.418909[/C][C]3.2449[/C][C]0.000962[/C][/ROW]
[ROW][C]12[/C][C]0.4227[/C][C]3.2742[/C][C]0.000881[/C][/ROW]
[ROW][C]13[/C][C]0.28349[/C][C]2.1959[/C][C]0.015988[/C][/ROW]
[ROW][C]14[/C][C]0.113765[/C][C]0.8812[/C][C]0.190859[/C][/ROW]
[ROW][C]15[/C][C]-0.003497[/C][C]-0.0271[/C][C]0.489238[/C][/ROW]
[ROW][C]16[/C][C]-0.060835[/C][C]-0.4712[/C][C]0.319595[/C][/ROW]
[ROW][C]17[/C][C]-0.073933[/C][C]-0.5727[/C][C]0.284499[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68135&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68135&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	0.890527	6.898	0
2	0.727437	5.6347	0
3	0.618678	4.7923	6e-06
4	0.575508	4.4579	1.8e-05
5	0.576149	4.4628	1.8e-05
6	0.56402	4.3689	2.5e-05
7	0.508262	3.937	0.000109
8	0.433857	3.3606	0.000678
9	0.377091	2.9209	0.002456
10	0.374052	2.8974	0.002623
11	0.418909	3.2449	0.000962
12	0.4227	3.2742	0.000881
13	0.28349	2.1959	0.015988
14	0.113765	0.8812	0.190859
15	-0.003497	-0.0271	0.489238
16	-0.060835	-0.4712	0.319595
17	-0.073933	-0.5727	0.284499

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.890527	6.898	0
2	-0.316971	-2.4553	0.008497
3	0.256825	1.9894	0.025613
4	0.118088	0.9147	0.182005
5	0.144873	1.1222	0.133128
6	-0.062562	-0.4846	0.314862
7	-0.078977	-0.6118	0.271506
8	-0.006678	-0.0517	0.479458
9	0.022728	0.1761	0.430424
10	0.158719	1.2294	0.111854
11	0.132375	1.0254	0.154652
12	-0.203496	-1.5763	0.06011
13	-0.58464	-4.5286	1.4e-05
14	0.10732	0.8313	0.204552
15	-0.069475	-0.5381	0.296233
16	-0.095359	-0.7387	0.2315
17	-0.062921	-0.4874	0.313882

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.890527 & 6.898 & 0 \tabularnewline
2 & -0.316971 & -2.4553 & 0.008497 \tabularnewline
3 & 0.256825 & 1.9894 & 0.025613 \tabularnewline
4 & 0.118088 & 0.9147 & 0.182005 \tabularnewline
5 & 0.144873 & 1.1222 & 0.133128 \tabularnewline
6 & -0.062562 & -0.4846 & 0.314862 \tabularnewline
7 & -0.078977 & -0.6118 & 0.271506 \tabularnewline
8 & -0.006678 & -0.0517 & 0.479458 \tabularnewline
9 & 0.022728 & 0.1761 & 0.430424 \tabularnewline
10 & 0.158719 & 1.2294 & 0.111854 \tabularnewline
11 & 0.132375 & 1.0254 & 0.154652 \tabularnewline
12 & -0.203496 & -1.5763 & 0.06011 \tabularnewline
13 & -0.58464 & -4.5286 & 1.4e-05 \tabularnewline
14 & 0.10732 & 0.8313 & 0.204552 \tabularnewline
15 & -0.069475 & -0.5381 & 0.296233 \tabularnewline
16 & -0.095359 & -0.7387 & 0.2315 \tabularnewline
17 & -0.062921 & -0.4874 & 0.313882 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68135&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]0.890527[/C][C]6.898[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.316971[/C][C]-2.4553[/C][C]0.008497[/C][/ROW]
[ROW][C]3[/C][C]0.256825[/C][C]1.9894[/C][C]0.025613[/C][/ROW]
[ROW][C]4[/C][C]0.118088[/C][C]0.9147[/C][C]0.182005[/C][/ROW]
[ROW][C]5[/C][C]0.144873[/C][C]1.1222[/C][C]0.133128[/C][/ROW]
[ROW][C]6[/C][C]-0.062562[/C][C]-0.4846[/C][C]0.314862[/C][/ROW]
[ROW][C]7[/C][C]-0.078977[/C][C]-0.6118[/C][C]0.271506[/C][/ROW]
[ROW][C]8[/C][C]-0.006678[/C][C]-0.0517[/C][C]0.479458[/C][/ROW]
[ROW][C]9[/C][C]0.022728[/C][C]0.1761[/C][C]0.430424[/C][/ROW]
[ROW][C]10[/C][C]0.158719[/C][C]1.2294[/C][C]0.111854[/C][/ROW]
[ROW][C]11[/C][C]0.132375[/C][C]1.0254[/C][C]0.154652[/C][/ROW]
[ROW][C]12[/C][C]-0.203496[/C][C]-1.5763[/C][C]0.06011[/C][/ROW]
[ROW][C]13[/C][C]-0.58464[/C][C]-4.5286[/C][C]1.4e-05[/C][/ROW]
[ROW][C]14[/C][C]0.10732[/C][C]0.8313[/C][C]0.204552[/C][/ROW]
[ROW][C]15[/C][C]-0.069475[/C][C]-0.5381[/C][C]0.296233[/C][/ROW]
[ROW][C]16[/C][C]-0.095359[/C][C]-0.7387[/C][C]0.2315[/C][/ROW]
[ROW][C]17[/C][C]-0.062921[/C][C]-0.4874[/C][C]0.313882[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68135&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68135&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	0.890527	6.898	0
2	-0.316971	-2.4553	0.008497
3	0.256825	1.9894	0.025613
4	0.118088	0.9147	0.182005
5	0.144873	1.1222	0.133128
6	-0.062562	-0.4846	0.314862
7	-0.078977	-0.6118	0.271506
8	-0.006678	-0.0517	0.479458
9	0.022728	0.1761	0.430424
10	0.158719	1.2294	0.111854
11	0.132375	1.0254	0.154652
12	-0.203496	-1.5763	0.06011
13	-0.58464	-4.5286	1.4e-05
14	0.10732	0.8313	0.204552
15	-0.069475	-0.5381	0.296233
16	-0.095359	-0.7387	0.2315
17	-0.062921	-0.4874	0.313882

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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code