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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 04 Dec 2011 16:41:13 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/04/t1323034909dtnlxu02enn9w1m.htm/, Retrieved Sun, 05 May 2024 11:12:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150783, Retrieved Sun, 05 May 2024 11:12:44 +0000

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-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
- R  D      [(Partial) Autocorrelation Function] [] [2011-12-04 21:41:13] [c092f3a3bdd85c7279ddab6c8c6c9261] [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	'George Udny Yule' @ yule.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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150783&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150783&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150783&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	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.87438	6.7729	0
2	0.676129	5.2373	1e-06
3	0.550638	4.2652	3.6e-05
4	0.515713	3.9947	9e-05
5	0.544904	4.2208	4.2e-05
6	0.555605	4.3037	3.1e-05
7	0.490698	3.8009	0.00017
8	0.404905	3.1364	0.001325
9	0.357822	2.7717	0.003708
10	0.387942	3.005	0.001936
11	0.485237	3.7586	0.000195
12	0.525623	4.0715	6.9e-05
13	0.408503	3.1642	0.001221
14	0.225538	1.747	0.042876
15	0.098394	0.7622	0.224476
16	0.055423	0.4293	0.334619
17	0.078885	0.611	0.27174

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.87438 & 6.7729 & 0 \tabularnewline
2 & 0.676129 & 5.2373 & 1e-06 \tabularnewline
3 & 0.550638 & 4.2652 & 3.6e-05 \tabularnewline
4 & 0.515713 & 3.9947 & 9e-05 \tabularnewline
5 & 0.544904 & 4.2208 & 4.2e-05 \tabularnewline
6 & 0.555605 & 4.3037 & 3.1e-05 \tabularnewline
7 & 0.490698 & 3.8009 & 0.00017 \tabularnewline
8 & 0.404905 & 3.1364 & 0.001325 \tabularnewline
9 & 0.357822 & 2.7717 & 0.003708 \tabularnewline
10 & 0.387942 & 3.005 & 0.001936 \tabularnewline
11 & 0.485237 & 3.7586 & 0.000195 \tabularnewline
12 & 0.525623 & 4.0715 & 6.9e-05 \tabularnewline
13 & 0.408503 & 3.1642 & 0.001221 \tabularnewline
14 & 0.225538 & 1.747 & 0.042876 \tabularnewline
15 & 0.098394 & 0.7622 & 0.224476 \tabularnewline
16 & 0.055423 & 0.4293 & 0.334619 \tabularnewline
17 & 0.078885 & 0.611 & 0.27174 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150783&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]0.87438[/C][C]6.7729[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.676129[/C][C]5.2373[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.550638[/C][C]4.2652[/C][C]3.6e-05[/C][/ROW]
[ROW][C]4[/C][C]0.515713[/C][C]3.9947[/C][C]9e-05[/C][/ROW]
[ROW][C]5[/C][C]0.544904[/C][C]4.2208[/C][C]4.2e-05[/C][/ROW]
[ROW][C]6[/C][C]0.555605[/C][C]4.3037[/C][C]3.1e-05[/C][/ROW]
[ROW][C]7[/C][C]0.490698[/C][C]3.8009[/C][C]0.00017[/C][/ROW]
[ROW][C]8[/C][C]0.404905[/C][C]3.1364[/C][C]0.001325[/C][/ROW]
[ROW][C]9[/C][C]0.357822[/C][C]2.7717[/C][C]0.003708[/C][/ROW]
[ROW][C]10[/C][C]0.387942[/C][C]3.005[/C][C]0.001936[/C][/ROW]
[ROW][C]11[/C][C]0.485237[/C][C]3.7586[/C][C]0.000195[/C][/ROW]
[ROW][C]12[/C][C]0.525623[/C][C]4.0715[/C][C]6.9e-05[/C][/ROW]
[ROW][C]13[/C][C]0.408503[/C][C]3.1642[/C][C]0.001221[/C][/ROW]
[ROW][C]14[/C][C]0.225538[/C][C]1.747[/C][C]0.042876[/C][/ROW]
[ROW][C]15[/C][C]0.098394[/C][C]0.7622[/C][C]0.224476[/C][/ROW]
[ROW][C]16[/C][C]0.055423[/C][C]0.4293[/C][C]0.334619[/C][/ROW]
[ROW][C]17[/C][C]0.078885[/C][C]0.611[/C][C]0.27174[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150783&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150783&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	0.87438	6.7729	0
2	0.676129	5.2373	1e-06
3	0.550638	4.2652	3.6e-05
4	0.515713	3.9947	9e-05
5	0.544904	4.2208	4.2e-05
6	0.555605	4.3037	3.1e-05
7	0.490698	3.8009	0.00017
8	0.404905	3.1364	0.001325
9	0.357822	2.7717	0.003708
10	0.387942	3.005	0.001936
11	0.485237	3.7586	0.000195
12	0.525623	4.0715	6.9e-05
13	0.408503	3.1642	0.001221
14	0.225538	1.747	0.042876
15	0.098394	0.7622	0.224476
16	0.055423	0.4293	0.334619
17	0.078885	0.611	0.27174

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.87438	6.7729	0
2	-0.375483	-2.9085	0.002543
3	0.325201	2.519	0.007226
4	0.111671	0.865	0.195242
5	0.212202	1.6437	0.052733
6	-0.095844	-0.7424	0.230369
7	-0.117117	-0.9072	0.18397
8	0.092332	0.7152	0.238629
9	0.042589	0.3299	0.371314
10	0.222525	1.7237	0.044958
11	0.194899	1.5097	0.068187
12	-0.215908	-1.6724	0.049825
13	-0.420634	-3.2582	0.000924
14	-0.067886	-0.5258	0.300468
15	0.007292	0.0565	0.477571
16	-0.101506	-0.7863	0.217404
17	0.010155	0.0787	0.468782

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.87438 & 6.7729 & 0 \tabularnewline
2 & -0.375483 & -2.9085 & 0.002543 \tabularnewline
3 & 0.325201 & 2.519 & 0.007226 \tabularnewline
4 & 0.111671 & 0.865 & 0.195242 \tabularnewline
5 & 0.212202 & 1.6437 & 0.052733 \tabularnewline
6 & -0.095844 & -0.7424 & 0.230369 \tabularnewline
7 & -0.117117 & -0.9072 & 0.18397 \tabularnewline
8 & 0.092332 & 0.7152 & 0.238629 \tabularnewline
9 & 0.042589 & 0.3299 & 0.371314 \tabularnewline
10 & 0.222525 & 1.7237 & 0.044958 \tabularnewline
11 & 0.194899 & 1.5097 & 0.068187 \tabularnewline
12 & -0.215908 & -1.6724 & 0.049825 \tabularnewline
13 & -0.420634 & -3.2582 & 0.000924 \tabularnewline
14 & -0.067886 & -0.5258 & 0.300468 \tabularnewline
15 & 0.007292 & 0.0565 & 0.477571 \tabularnewline
16 & -0.101506 & -0.7863 & 0.217404 \tabularnewline
17 & 0.010155 & 0.0787 & 0.468782 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150783&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]0.87438[/C][C]6.7729[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.375483[/C][C]-2.9085[/C][C]0.002543[/C][/ROW]
[ROW][C]3[/C][C]0.325201[/C][C]2.519[/C][C]0.007226[/C][/ROW]
[ROW][C]4[/C][C]0.111671[/C][C]0.865[/C][C]0.195242[/C][/ROW]
[ROW][C]5[/C][C]0.212202[/C][C]1.6437[/C][C]0.052733[/C][/ROW]
[ROW][C]6[/C][C]-0.095844[/C][C]-0.7424[/C][C]0.230369[/C][/ROW]
[ROW][C]7[/C][C]-0.117117[/C][C]-0.9072[/C][C]0.18397[/C][/ROW]
[ROW][C]8[/C][C]0.092332[/C][C]0.7152[/C][C]0.238629[/C][/ROW]
[ROW][C]9[/C][C]0.042589[/C][C]0.3299[/C][C]0.371314[/C][/ROW]
[ROW][C]10[/C][C]0.222525[/C][C]1.7237[/C][C]0.044958[/C][/ROW]
[ROW][C]11[/C][C]0.194899[/C][C]1.5097[/C][C]0.068187[/C][/ROW]
[ROW][C]12[/C][C]-0.215908[/C][C]-1.6724[/C][C]0.049825[/C][/ROW]
[ROW][C]13[/C][C]-0.420634[/C][C]-3.2582[/C][C]0.000924[/C][/ROW]
[ROW][C]14[/C][C]-0.067886[/C][C]-0.5258[/C][C]0.300468[/C][/ROW]
[ROW][C]15[/C][C]0.007292[/C][C]0.0565[/C][C]0.477571[/C][/ROW]
[ROW][C]16[/C][C]-0.101506[/C][C]-0.7863[/C][C]0.217404[/C][/ROW]
[ROW][C]17[/C][C]0.010155[/C][C]0.0787[/C][C]0.468782[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150783&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150783&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	0.87438	6.7729	0
2	-0.375483	-2.9085	0.002543
3	0.325201	2.519	0.007226
4	0.111671	0.865	0.195242
5	0.212202	1.6437	0.052733
6	-0.095844	-0.7424	0.230369
7	-0.117117	-0.9072	0.18397
8	0.092332	0.7152	0.238629
9	0.042589	0.3299	0.371314
10	0.222525	1.7237	0.044958
11	0.194899	1.5097	0.068187
12	-0.215908	-1.6724	0.049825
13	-0.420634	-3.2582	0.000924
14	-0.067886	-0.5258	0.300468
15	0.007292	0.0565	0.477571
16	-0.101506	-0.7863	0.217404
17	0.010155	0.0787	0.468782

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 ; 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 (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