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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 14 Dec 2010 16:01:09 +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/14/t1292342350l158ghwctcl6ui4.htm/, Retrieved Fri, 03 May 2024 03:25:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=109790, Retrieved Fri, 03 May 2024 03:25:32 +0000

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102

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-       [(Partial) Autocorrelation Function] [] [2010-12-14 16:01:09] [4afc4ea409ad669ec2851bc39795365d] [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	6 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 6 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109790&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109790&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109790&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	6 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.846734	6.5588	0
2	0.622569	4.8224	5e-06
3	0.48752	3.7763	0.000184
4	0.454735	3.5224	0.000412
5	0.48381	3.7476	0.000202
6	0.479801	3.7165	0.000223
7	0.393532	3.0483	0.00171
8	0.242284	1.8767	0.03271
9	0.128905	0.9985	0.161026
10	0.103322	0.8003	0.213339
11	0.180246	1.3962	0.083903
12	0.209127	1.6199	0.055251
13	0.045434	0.3519	0.363062
14	-0.156331	-1.2109	0.115335
15	-0.268809	-2.0822	0.020799
16	-0.299792	-2.3222	0.011817
17	-0.280766	-2.1748	0.016799

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.846734 & 6.5588 & 0 \tabularnewline
2 & 0.622569 & 4.8224 & 5e-06 \tabularnewline
3 & 0.48752 & 3.7763 & 0.000184 \tabularnewline
4 & 0.454735 & 3.5224 & 0.000412 \tabularnewline
5 & 0.48381 & 3.7476 & 0.000202 \tabularnewline
6 & 0.479801 & 3.7165 & 0.000223 \tabularnewline
7 & 0.393532 & 3.0483 & 0.00171 \tabularnewline
8 & 0.242284 & 1.8767 & 0.03271 \tabularnewline
9 & 0.128905 & 0.9985 & 0.161026 \tabularnewline
10 & 0.103322 & 0.8003 & 0.213339 \tabularnewline
11 & 0.180246 & 1.3962 & 0.083903 \tabularnewline
12 & 0.209127 & 1.6199 & 0.055251 \tabularnewline
13 & 0.045434 & 0.3519 & 0.363062 \tabularnewline
14 & -0.156331 & -1.2109 & 0.115335 \tabularnewline
15 & -0.268809 & -2.0822 & 0.020799 \tabularnewline
16 & -0.299792 & -2.3222 & 0.011817 \tabularnewline
17 & -0.280766 & -2.1748 & 0.016799 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109790&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]0.846734[/C][C]6.5588[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.622569[/C][C]4.8224[/C][C]5e-06[/C][/ROW]
[ROW][C]3[/C][C]0.48752[/C][C]3.7763[/C][C]0.000184[/C][/ROW]
[ROW][C]4[/C][C]0.454735[/C][C]3.5224[/C][C]0.000412[/C][/ROW]
[ROW][C]5[/C][C]0.48381[/C][C]3.7476[/C][C]0.000202[/C][/ROW]
[ROW][C]6[/C][C]0.479801[/C][C]3.7165[/C][C]0.000223[/C][/ROW]
[ROW][C]7[/C][C]0.393532[/C][C]3.0483[/C][C]0.00171[/C][/ROW]
[ROW][C]8[/C][C]0.242284[/C][C]1.8767[/C][C]0.03271[/C][/ROW]
[ROW][C]9[/C][C]0.128905[/C][C]0.9985[/C][C]0.161026[/C][/ROW]
[ROW][C]10[/C][C]0.103322[/C][C]0.8003[/C][C]0.213339[/C][/ROW]
[ROW][C]11[/C][C]0.180246[/C][C]1.3962[/C][C]0.083903[/C][/ROW]
[ROW][C]12[/C][C]0.209127[/C][C]1.6199[/C][C]0.055251[/C][/ROW]
[ROW][C]13[/C][C]0.045434[/C][C]0.3519[/C][C]0.363062[/C][/ROW]
[ROW][C]14[/C][C]-0.156331[/C][C]-1.2109[/C][C]0.115335[/C][/ROW]
[ROW][C]15[/C][C]-0.268809[/C][C]-2.0822[/C][C]0.020799[/C][/ROW]
[ROW][C]16[/C][C]-0.299792[/C][C]-2.3222[/C][C]0.011817[/C][/ROW]
[ROW][C]17[/C][C]-0.280766[/C][C]-2.1748[/C][C]0.016799[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109790&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109790&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	0.846734	6.5588	0
2	0.622569	4.8224	5e-06
3	0.48752	3.7763	0.000184
4	0.454735	3.5224	0.000412
5	0.48381	3.7476	0.000202
6	0.479801	3.7165	0.000223
7	0.393532	3.0483	0.00171
8	0.242284	1.8767	0.03271
9	0.128905	0.9985	0.161026
10	0.103322	0.8003	0.213339
11	0.180246	1.3962	0.083903
12	0.209127	1.6199	0.055251
13	0.045434	0.3519	0.363062
14	-0.156331	-1.2109	0.115335
15	-0.268809	-2.0822	0.020799
16	-0.299792	-2.3222	0.011817
17	-0.280766	-2.1748	0.016799

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.846734	6.5588	0
2	-0.33348	-2.5831	0.006123
3	0.266114	2.0613	0.021807
4	0.129888	1.0061	0.159203
5	0.163072	1.2632	0.10571
6	-0.084393	-0.6537	0.257899
7	-0.122544	-0.9492	0.173159
8	-0.188036	-1.4565	0.075231
9	0.057226	0.4433	0.329582
10	0.022039	0.1707	0.432511
11	0.268996	2.0836	0.020731
12	-0.279328	-2.1637	0.017241
13	-0.491877	-3.8101	0.000165
14	0.098466	0.7627	0.22431
15	0.061926	0.4797	0.316601
16	-0.194966	-1.5102	0.06812
17	-0.085107	-0.6592	0.256133

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.846734 & 6.5588 & 0 \tabularnewline
2 & -0.33348 & -2.5831 & 0.006123 \tabularnewline
3 & 0.266114 & 2.0613 & 0.021807 \tabularnewline
4 & 0.129888 & 1.0061 & 0.159203 \tabularnewline
5 & 0.163072 & 1.2632 & 0.10571 \tabularnewline
6 & -0.084393 & -0.6537 & 0.257899 \tabularnewline
7 & -0.122544 & -0.9492 & 0.173159 \tabularnewline
8 & -0.188036 & -1.4565 & 0.075231 \tabularnewline
9 & 0.057226 & 0.4433 & 0.329582 \tabularnewline
10 & 0.022039 & 0.1707 & 0.432511 \tabularnewline
11 & 0.268996 & 2.0836 & 0.020731 \tabularnewline
12 & -0.279328 & -2.1637 & 0.017241 \tabularnewline
13 & -0.491877 & -3.8101 & 0.000165 \tabularnewline
14 & 0.098466 & 0.7627 & 0.22431 \tabularnewline
15 & 0.061926 & 0.4797 & 0.316601 \tabularnewline
16 & -0.194966 & -1.5102 & 0.06812 \tabularnewline
17 & -0.085107 & -0.6592 & 0.256133 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109790&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]0.846734[/C][C]6.5588[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.33348[/C][C]-2.5831[/C][C]0.006123[/C][/ROW]
[ROW][C]3[/C][C]0.266114[/C][C]2.0613[/C][C]0.021807[/C][/ROW]
[ROW][C]4[/C][C]0.129888[/C][C]1.0061[/C][C]0.159203[/C][/ROW]
[ROW][C]5[/C][C]0.163072[/C][C]1.2632[/C][C]0.10571[/C][/ROW]
[ROW][C]6[/C][C]-0.084393[/C][C]-0.6537[/C][C]0.257899[/C][/ROW]
[ROW][C]7[/C][C]-0.122544[/C][C]-0.9492[/C][C]0.173159[/C][/ROW]
[ROW][C]8[/C][C]-0.188036[/C][C]-1.4565[/C][C]0.075231[/C][/ROW]
[ROW][C]9[/C][C]0.057226[/C][C]0.4433[/C][C]0.329582[/C][/ROW]
[ROW][C]10[/C][C]0.022039[/C][C]0.1707[/C][C]0.432511[/C][/ROW]
[ROW][C]11[/C][C]0.268996[/C][C]2.0836[/C][C]0.020731[/C][/ROW]
[ROW][C]12[/C][C]-0.279328[/C][C]-2.1637[/C][C]0.017241[/C][/ROW]
[ROW][C]13[/C][C]-0.491877[/C][C]-3.8101[/C][C]0.000165[/C][/ROW]
[ROW][C]14[/C][C]0.098466[/C][C]0.7627[/C][C]0.22431[/C][/ROW]
[ROW][C]15[/C][C]0.061926[/C][C]0.4797[/C][C]0.316601[/C][/ROW]
[ROW][C]16[/C][C]-0.194966[/C][C]-1.5102[/C][C]0.06812[/C][/ROW]
[ROW][C]17[/C][C]-0.085107[/C][C]-0.6592[/C][C]0.256133[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109790&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109790&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	0.846734	6.5588	0
2	-0.33348	-2.5831	0.006123
3	0.266114	2.0613	0.021807
4	0.129888	1.0061	0.159203
5	0.163072	1.2632	0.10571
6	-0.084393	-0.6537	0.257899
7	-0.122544	-0.9492	0.173159
8	-0.188036	-1.4565	0.075231
9	0.057226	0.4433	0.329582
10	0.022039	0.1707	0.432511
11	0.268996	2.0836	0.020731
12	-0.279328	-2.1637	0.017241
13	-0.491877	-3.8101	0.000165
14	0.098466	0.7627	0.22431
15	0.061926	0.4797	0.316601
16	-0.194966	-1.5102	0.06812
17	-0.085107	-0.6592	0.256133

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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Input Parameters & R Code