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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 21 Dec 2012 10:18:29 -0500

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/2012/Dec/21/t1356103304fxr4e5ki8euh34s.htm/, Retrieved Fri, 26 Apr 2024 21:11:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203790, Retrieved Fri, 26 Apr 2024 21:11:01 +0000

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Estimated Impact

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

-     [Multiple Regression] [HPC Retail Sales] [2008-03-08 13:40:54] [1c0f2c85e8a48e42648374b3bcceca26]
- RMPD  [Multiple Regression] [forecast] [2012-11-24 21:49:17] [0883bf8f4217d775edf6393676d58a73]
- R  D    [Multiple Regression] [] [2012-12-21 11:22:02] [0604709baf8ca89a71bc0fcadc3cdffd]
- RMP         [(Partial) Autocorrelation Function] [] [2012-12-21 15:18:29] [b650a28572edc4a1d205c228043a3295] [Current]
- R             [(Partial) Autocorrelation Function] [] [2012-12-21 16:03:13] [0604709baf8ca89a71bc0fcadc3cdffd] 
- RM            [Variance Reduction Matrix] [] [2012-12-21 16:08:14] [0604709baf8ca89a71bc0fcadc3cdffd] 
- RM            [Standard Deviation-Mean Plot] [] [2012-12-21 16:27:44] [0604709baf8ca89a71bc0fcadc3cdffd] 

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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	3 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203790&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203790&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203790&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.834645	6.5188	0
2	0.688345	5.3761	1e-06
3	0.557903	4.3574	2.6e-05
4	0.356322	2.783	0.00358
5	0.182172	1.4228	0.079942
6	0.030354	0.2371	0.406696
7	-0.170924	-1.335	0.093425
8	-0.271849	-2.1232	0.018901
9	-0.317608	-2.4806	0.007945
10	-0.316843	-2.4746	0.008067
11	-0.313209	-2.4462	0.008667
12	-0.258494	-2.0189	0.023949
13	-0.162062	-1.2657	0.105208
14	-0.067155	-0.5245	0.300916
15	0.0635	0.4959	0.310856
16	0.20942	1.6356	0.053535
17	0.259037	2.0231	0.023723

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.834645 & 6.5188 & 0 \tabularnewline
2 & 0.688345 & 5.3761 & 1e-06 \tabularnewline
3 & 0.557903 & 4.3574 & 2.6e-05 \tabularnewline
4 & 0.356322 & 2.783 & 0.00358 \tabularnewline
5 & 0.182172 & 1.4228 & 0.079942 \tabularnewline
6 & 0.030354 & 0.2371 & 0.406696 \tabularnewline
7 & -0.170924 & -1.335 & 0.093425 \tabularnewline
8 & -0.271849 & -2.1232 & 0.018901 \tabularnewline
9 & -0.317608 & -2.4806 & 0.007945 \tabularnewline
10 & -0.316843 & -2.4746 & 0.008067 \tabularnewline
11 & -0.313209 & -2.4462 & 0.008667 \tabularnewline
12 & -0.258494 & -2.0189 & 0.023949 \tabularnewline
13 & -0.162062 & -1.2657 & 0.105208 \tabularnewline
14 & -0.067155 & -0.5245 & 0.300916 \tabularnewline
15 & 0.0635 & 0.4959 & 0.310856 \tabularnewline
16 & 0.20942 & 1.6356 & 0.053535 \tabularnewline
17 & 0.259037 & 2.0231 & 0.023723 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203790&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]0.834645[/C][C]6.5188[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.688345[/C][C]5.3761[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.557903[/C][C]4.3574[/C][C]2.6e-05[/C][/ROW]
[ROW][C]4[/C][C]0.356322[/C][C]2.783[/C][C]0.00358[/C][/ROW]
[ROW][C]5[/C][C]0.182172[/C][C]1.4228[/C][C]0.079942[/C][/ROW]
[ROW][C]6[/C][C]0.030354[/C][C]0.2371[/C][C]0.406696[/C][/ROW]
[ROW][C]7[/C][C]-0.170924[/C][C]-1.335[/C][C]0.093425[/C][/ROW]
[ROW][C]8[/C][C]-0.271849[/C][C]-2.1232[/C][C]0.018901[/C][/ROW]
[ROW][C]9[/C][C]-0.317608[/C][C]-2.4806[/C][C]0.007945[/C][/ROW]
[ROW][C]10[/C][C]-0.316843[/C][C]-2.4746[/C][C]0.008067[/C][/ROW]
[ROW][C]11[/C][C]-0.313209[/C][C]-2.4462[/C][C]0.008667[/C][/ROW]
[ROW][C]12[/C][C]-0.258494[/C][C]-2.0189[/C][C]0.023949[/C][/ROW]
[ROW][C]13[/C][C]-0.162062[/C][C]-1.2657[/C][C]0.105208[/C][/ROW]
[ROW][C]14[/C][C]-0.067155[/C][C]-0.5245[/C][C]0.300916[/C][/ROW]
[ROW][C]15[/C][C]0.0635[/C][C]0.4959[/C][C]0.310856[/C][/ROW]
[ROW][C]16[/C][C]0.20942[/C][C]1.6356[/C][C]0.053535[/C][/ROW]
[ROW][C]17[/C][C]0.259037[/C][C]2.0231[/C][C]0.023723[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203790&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203790&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	0.834645	6.5188	0
2	0.688345	5.3761	1e-06
3	0.557903	4.3574	2.6e-05
4	0.356322	2.783	0.00358
5	0.182172	1.4228	0.079942
6	0.030354	0.2371	0.406696
7	-0.170924	-1.335	0.093425
8	-0.271849	-2.1232	0.018901
9	-0.317608	-2.4806	0.007945
10	-0.316843	-2.4746	0.008067
11	-0.313209	-2.4462	0.008667
12	-0.258494	-2.0189	0.023949
13	-0.162062	-1.2657	0.105208
14	-0.067155	-0.5245	0.300916
15	0.0635	0.4959	0.310856
16	0.20942	1.6356	0.053535
17	0.259037	2.0231	0.023723

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.834645	6.5188	0
2	-0.02732	-0.2134	0.415872
3	-0.031387	-0.2451	0.403586
4	-0.314009	-2.4525	0.008532
5	-0.075819	-0.5922	0.277965
6	-0.085037	-0.6642	0.254545
7	-0.27214	-2.1255	0.018802
8	0.117504	0.9177	0.181186
9	0.052377	0.4091	0.341957
10	0.185358	1.4477	0.076412
11	-0.161347	-1.2602	0.106205
12	0.083284	0.6505	0.258916
13	0.114094	0.8911	0.188188
14	-0.024239	-0.1893	0.425238
15	0.160278	1.2518	0.107709
16	0.107547	0.84	0.202104
17	-0.086554	-0.676	0.250794

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.834645 & 6.5188 & 0 \tabularnewline
2 & -0.02732 & -0.2134 & 0.415872 \tabularnewline
3 & -0.031387 & -0.2451 & 0.403586 \tabularnewline
4 & -0.314009 & -2.4525 & 0.008532 \tabularnewline
5 & -0.075819 & -0.5922 & 0.277965 \tabularnewline
6 & -0.085037 & -0.6642 & 0.254545 \tabularnewline
7 & -0.27214 & -2.1255 & 0.018802 \tabularnewline
8 & 0.117504 & 0.9177 & 0.181186 \tabularnewline
9 & 0.052377 & 0.4091 & 0.341957 \tabularnewline
10 & 0.185358 & 1.4477 & 0.076412 \tabularnewline
11 & -0.161347 & -1.2602 & 0.106205 \tabularnewline
12 & 0.083284 & 0.6505 & 0.258916 \tabularnewline
13 & 0.114094 & 0.8911 & 0.188188 \tabularnewline
14 & -0.024239 & -0.1893 & 0.425238 \tabularnewline
15 & 0.160278 & 1.2518 & 0.107709 \tabularnewline
16 & 0.107547 & 0.84 & 0.202104 \tabularnewline
17 & -0.086554 & -0.676 & 0.250794 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203790&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]0.834645[/C][C]6.5188[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.02732[/C][C]-0.2134[/C][C]0.415872[/C][/ROW]
[ROW][C]3[/C][C]-0.031387[/C][C]-0.2451[/C][C]0.403586[/C][/ROW]
[ROW][C]4[/C][C]-0.314009[/C][C]-2.4525[/C][C]0.008532[/C][/ROW]
[ROW][C]5[/C][C]-0.075819[/C][C]-0.5922[/C][C]0.277965[/C][/ROW]
[ROW][C]6[/C][C]-0.085037[/C][C]-0.6642[/C][C]0.254545[/C][/ROW]
[ROW][C]7[/C][C]-0.27214[/C][C]-2.1255[/C][C]0.018802[/C][/ROW]
[ROW][C]8[/C][C]0.117504[/C][C]0.9177[/C][C]0.181186[/C][/ROW]
[ROW][C]9[/C][C]0.052377[/C][C]0.4091[/C][C]0.341957[/C][/ROW]
[ROW][C]10[/C][C]0.185358[/C][C]1.4477[/C][C]0.076412[/C][/ROW]
[ROW][C]11[/C][C]-0.161347[/C][C]-1.2602[/C][C]0.106205[/C][/ROW]
[ROW][C]12[/C][C]0.083284[/C][C]0.6505[/C][C]0.258916[/C][/ROW]
[ROW][C]13[/C][C]0.114094[/C][C]0.8911[/C][C]0.188188[/C][/ROW]
[ROW][C]14[/C][C]-0.024239[/C][C]-0.1893[/C][C]0.425238[/C][/ROW]
[ROW][C]15[/C][C]0.160278[/C][C]1.2518[/C][C]0.107709[/C][/ROW]
[ROW][C]16[/C][C]0.107547[/C][C]0.84[/C][C]0.202104[/C][/ROW]
[ROW][C]17[/C][C]-0.086554[/C][C]-0.676[/C][C]0.250794[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203790&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203790&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	0.834645	6.5188	0
2	-0.02732	-0.2134	0.415872
3	-0.031387	-0.2451	0.403586
4	-0.314009	-2.4525	0.008532
5	-0.075819	-0.5922	0.277965
6	-0.085037	-0.6642	0.254545
7	-0.27214	-2.1255	0.018802
8	0.117504	0.9177	0.181186
9	0.052377	0.4091	0.341957
10	0.185358	1.4477	0.076412
11	-0.161347	-1.2602	0.106205
12	0.083284	0.6505	0.258916
13	0.114094	0.8911	0.188188
14	-0.024239	-0.1893	0.425238
15	0.160278	1.2518	0.107709
16	0.107547	0.84	0.202104
17	-0.086554	-0.676	0.250794

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par2 = grey ; par3 = FALSE ; par4 = Unknown ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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