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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 15 Dec 2013 07:41:55 -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/2013/Dec/15/t1387111353odbhfs7935bhxbp.htm/, Retrieved Thu, 25 Apr 2024 20:41:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232340, Retrieved Thu, 25 Apr 2024 20:41:48 +0000

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User-defined keywords

Estimated Impact

186

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

-       [(Partial) Autocorrelation Function] [Wine sales - ACF] [2013-12-15 12:41:55] [e87fe8ad852a0fa5d933f43041f410cc] [Current]
- R P     [(Partial) Autocorrelation Function] [Wine sales - ACF] [2013-12-15 12:55:51] [e1b6e5c15a370139a1f66dc7648af660] 
- RMP     [Spectral Analysis] [Wine sales - Spec...] [2013-12-15 13:00:49] [e1b6e5c15a370139a1f66dc7648af660] 
- RMP     [Spectral Analysis] [Wine sales - Spec...] [2013-12-15 13:02:24] [e1b6e5c15a370139a1f66dc7648af660] 
- RMP     [Standard Deviation-Mean Plot] [Wine sales - SMP] [2013-12-15 13:07:07] [e1b6e5c15a370139a1f66dc7648af660] 
- RMP     [ARIMA Backward Selection] [Wine sales - ARIM...] [2013-12-15 13:15:54] [e1b6e5c15a370139a1f66dc7648af660] 

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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	4 seconds
R Server	'Sir Maurice George Kendall' @ kendall.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 & 4 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232340&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232340&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232340&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	4 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.235301	1.8226	0.036671
2	-0.190947	-1.4791	0.072177
3	0.10585	0.8199	0.207755
4	0.194951	1.5101	0.068135
5	-0.14612	-1.1318	0.131103
6	-0.362813	-2.8103	0.003337
7	-0.273234	-2.1165	0.019231
8	0.124475	0.9642	0.169413
9	0.045358	0.3513	0.363281
10	-0.313987	-2.4321	0.009005
11	0.049285	0.3818	0.351995
12	0.610831	4.7315	7e-06
13	0.163024	1.2628	0.105777
14	-0.150729	-1.1675	0.123806
15	-0.021932	-0.1699	0.432836
16	0.07542	0.5842	0.280639
17	-0.096713	-0.7491	0.228351

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.235301 & 1.8226 & 0.036671 \tabularnewline
2 & -0.190947 & -1.4791 & 0.072177 \tabularnewline
3 & 0.10585 & 0.8199 & 0.207755 \tabularnewline
4 & 0.194951 & 1.5101 & 0.068135 \tabularnewline
5 & -0.14612 & -1.1318 & 0.131103 \tabularnewline
6 & -0.362813 & -2.8103 & 0.003337 \tabularnewline
7 & -0.273234 & -2.1165 & 0.019231 \tabularnewline
8 & 0.124475 & 0.9642 & 0.169413 \tabularnewline
9 & 0.045358 & 0.3513 & 0.363281 \tabularnewline
10 & -0.313987 & -2.4321 & 0.009005 \tabularnewline
11 & 0.049285 & 0.3818 & 0.351995 \tabularnewline
12 & 0.610831 & 4.7315 & 7e-06 \tabularnewline
13 & 0.163024 & 1.2628 & 0.105777 \tabularnewline
14 & -0.150729 & -1.1675 & 0.123806 \tabularnewline
15 & -0.021932 & -0.1699 & 0.432836 \tabularnewline
16 & 0.07542 & 0.5842 & 0.280639 \tabularnewline
17 & -0.096713 & -0.7491 & 0.228351 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232340&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]0.235301[/C][C]1.8226[/C][C]0.036671[/C][/ROW]
[ROW][C]2[/C][C]-0.190947[/C][C]-1.4791[/C][C]0.072177[/C][/ROW]
[ROW][C]3[/C][C]0.10585[/C][C]0.8199[/C][C]0.207755[/C][/ROW]
[ROW][C]4[/C][C]0.194951[/C][C]1.5101[/C][C]0.068135[/C][/ROW]
[ROW][C]5[/C][C]-0.14612[/C][C]-1.1318[/C][C]0.131103[/C][/ROW]
[ROW][C]6[/C][C]-0.362813[/C][C]-2.8103[/C][C]0.003337[/C][/ROW]
[ROW][C]7[/C][C]-0.273234[/C][C]-2.1165[/C][C]0.019231[/C][/ROW]
[ROW][C]8[/C][C]0.124475[/C][C]0.9642[/C][C]0.169413[/C][/ROW]
[ROW][C]9[/C][C]0.045358[/C][C]0.3513[/C][C]0.363281[/C][/ROW]
[ROW][C]10[/C][C]-0.313987[/C][C]-2.4321[/C][C]0.009005[/C][/ROW]
[ROW][C]11[/C][C]0.049285[/C][C]0.3818[/C][C]0.351995[/C][/ROW]
[ROW][C]12[/C][C]0.610831[/C][C]4.7315[/C][C]7e-06[/C][/ROW]
[ROW][C]13[/C][C]0.163024[/C][C]1.2628[/C][C]0.105777[/C][/ROW]
[ROW][C]14[/C][C]-0.150729[/C][C]-1.1675[/C][C]0.123806[/C][/ROW]
[ROW][C]15[/C][C]-0.021932[/C][C]-0.1699[/C][C]0.432836[/C][/ROW]
[ROW][C]16[/C][C]0.07542[/C][C]0.5842[/C][C]0.280639[/C][/ROW]
[ROW][C]17[/C][C]-0.096713[/C][C]-0.7491[/C][C]0.228351[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232340&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232340&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	0.235301	1.8226	0.036671
2	-0.190947	-1.4791	0.072177
3	0.10585	0.8199	0.207755
4	0.194951	1.5101	0.068135
5	-0.14612	-1.1318	0.131103
6	-0.362813	-2.8103	0.003337
7	-0.273234	-2.1165	0.019231
8	0.124475	0.9642	0.169413
9	0.045358	0.3513	0.363281
10	-0.313987	-2.4321	0.009005
11	0.049285	0.3818	0.351995
12	0.610831	4.7315	7e-06
13	0.163024	1.2628	0.105777
14	-0.150729	-1.1675	0.123806
15	-0.021932	-0.1699	0.432836
16	0.07542	0.5842	0.280639
17	-0.096713	-0.7491	0.228351

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.235301	1.8226	0.036671
2	-0.26075	-2.0198	0.02394
3	0.254258	1.9695	0.02676
4	0.039482	0.3058	0.380398
5	-0.175403	-1.3587	0.089669
6	-0.268859	-2.0826	0.020781
7	-0.266026	-2.0606	0.021841
8	0.220192	1.7056	0.046627
9	-0.012175	-0.0943	0.46259
10	-0.192581	-1.4917	0.070505
11	0.197493	1.5298	0.065664
12	0.427073	3.3081	0.000796
13	-0.146671	-1.1361	0.130214
14	-0.006831	-0.0529	0.478988
15	-0.219293	-1.6986	0.047284
16	-0.161959	-1.2545	0.107257
17	-0.077308	-0.5988	0.275773

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.235301 & 1.8226 & 0.036671 \tabularnewline
2 & -0.26075 & -2.0198 & 0.02394 \tabularnewline
3 & 0.254258 & 1.9695 & 0.02676 \tabularnewline
4 & 0.039482 & 0.3058 & 0.380398 \tabularnewline
5 & -0.175403 & -1.3587 & 0.089669 \tabularnewline
6 & -0.268859 & -2.0826 & 0.020781 \tabularnewline
7 & -0.266026 & -2.0606 & 0.021841 \tabularnewline
8 & 0.220192 & 1.7056 & 0.046627 \tabularnewline
9 & -0.012175 & -0.0943 & 0.46259 \tabularnewline
10 & -0.192581 & -1.4917 & 0.070505 \tabularnewline
11 & 0.197493 & 1.5298 & 0.065664 \tabularnewline
12 & 0.427073 & 3.3081 & 0.000796 \tabularnewline
13 & -0.146671 & -1.1361 & 0.130214 \tabularnewline
14 & -0.006831 & -0.0529 & 0.478988 \tabularnewline
15 & -0.219293 & -1.6986 & 0.047284 \tabularnewline
16 & -0.161959 & -1.2545 & 0.107257 \tabularnewline
17 & -0.077308 & -0.5988 & 0.275773 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232340&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]0.235301[/C][C]1.8226[/C][C]0.036671[/C][/ROW]
[ROW][C]2[/C][C]-0.26075[/C][C]-2.0198[/C][C]0.02394[/C][/ROW]
[ROW][C]3[/C][C]0.254258[/C][C]1.9695[/C][C]0.02676[/C][/ROW]
[ROW][C]4[/C][C]0.039482[/C][C]0.3058[/C][C]0.380398[/C][/ROW]
[ROW][C]5[/C][C]-0.175403[/C][C]-1.3587[/C][C]0.089669[/C][/ROW]
[ROW][C]6[/C][C]-0.268859[/C][C]-2.0826[/C][C]0.020781[/C][/ROW]
[ROW][C]7[/C][C]-0.266026[/C][C]-2.0606[/C][C]0.021841[/C][/ROW]
[ROW][C]8[/C][C]0.220192[/C][C]1.7056[/C][C]0.046627[/C][/ROW]
[ROW][C]9[/C][C]-0.012175[/C][C]-0.0943[/C][C]0.46259[/C][/ROW]
[ROW][C]10[/C][C]-0.192581[/C][C]-1.4917[/C][C]0.070505[/C][/ROW]
[ROW][C]11[/C][C]0.197493[/C][C]1.5298[/C][C]0.065664[/C][/ROW]
[ROW][C]12[/C][C]0.427073[/C][C]3.3081[/C][C]0.000796[/C][/ROW]
[ROW][C]13[/C][C]-0.146671[/C][C]-1.1361[/C][C]0.130214[/C][/ROW]
[ROW][C]14[/C][C]-0.006831[/C][C]-0.0529[/C][C]0.478988[/C][/ROW]
[ROW][C]15[/C][C]-0.219293[/C][C]-1.6986[/C][C]0.047284[/C][/ROW]
[ROW][C]16[/C][C]-0.161959[/C][C]-1.2545[/C][C]0.107257[/C][/ROW]
[ROW][C]17[/C][C]-0.077308[/C][C]-0.5988[/C][C]0.275773[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232340&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232340&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	0.235301	1.8226	0.036671
2	-0.26075	-2.0198	0.02394
3	0.254258	1.9695	0.02676
4	0.039482	0.3058	0.380398
5	-0.175403	-1.3587	0.089669
6	-0.268859	-2.0826	0.020781
7	-0.266026	-2.0606	0.021841
8	0.220192	1.7056	0.046627
9	-0.012175	-0.0943	0.46259
10	-0.192581	-1.4917	0.070505
11	0.197493	1.5298	0.065664
12	0.427073	3.3081	0.000796
13	-0.146671	-1.1361	0.130214
14	-0.006831	-0.0529	0.478988
15	-0.219293	-1.6986	0.047284
16	-0.161959	-1.2545	0.107257
17	-0.077308	-0.5988	0.275773

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):

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 ; 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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Figures (Output of Computation)

Input Parameters & R Code