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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 05 Dec 2010 12:59:06 +0000

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/2010/Dec/05/t1291553907nvwd8zyx89419h0.htm/, Retrieved Wed, 01 May 2024 22:46:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105377, Retrieved Wed, 01 May 2024 22:46:50 +0000

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Estimated Impact

124

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-    D      [(Partial) Autocorrelation Function] [] [2010-12-05 12:59:06] [6b67b7c8c7d0a997c30f007387afbdb8] [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	3 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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105377&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105377&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105377&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.721997	7.9091	0
2	0.378118	4.1421	3.2e-05
3	0.00147	0.0161	0.493589
4	-0.427046	-4.6781	4e-06
5	-0.715973	-7.8431	0
6	-0.798206	-8.7439	0
7	-0.71598	-7.8432	0
8	-0.385985	-4.2283	2.3e-05
9	0.029647	0.3248	0.372961
10	0.357428	3.9154	7.5e-05
11	0.678533	7.433	0
12	0.84901	9.3004	0
13	0.657996	7.208	0
14	0.358114	3.9229	7.3e-05
15	-0.009708	-0.1063	0.457743
16	-0.390924	-4.2824	1.9e-05
17	-0.621464	-6.8078	0
18	-0.713787	-7.8191	0
19	-0.634949	-6.9555	0
20	-0.333587	-3.6543	0.000192

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.721997 & 7.9091 & 0 \tabularnewline
2 & 0.378118 & 4.1421 & 3.2e-05 \tabularnewline
3 & 0.00147 & 0.0161 & 0.493589 \tabularnewline
4 & -0.427046 & -4.6781 & 4e-06 \tabularnewline
5 & -0.715973 & -7.8431 & 0 \tabularnewline
6 & -0.798206 & -8.7439 & 0 \tabularnewline
7 & -0.71598 & -7.8432 & 0 \tabularnewline
8 & -0.385985 & -4.2283 & 2.3e-05 \tabularnewline
9 & 0.029647 & 0.3248 & 0.372961 \tabularnewline
10 & 0.357428 & 3.9154 & 7.5e-05 \tabularnewline
11 & 0.678533 & 7.433 & 0 \tabularnewline
12 & 0.84901 & 9.3004 & 0 \tabularnewline
13 & 0.657996 & 7.208 & 0 \tabularnewline
14 & 0.358114 & 3.9229 & 7.3e-05 \tabularnewline
15 & -0.009708 & -0.1063 & 0.457743 \tabularnewline
16 & -0.390924 & -4.2824 & 1.9e-05 \tabularnewline
17 & -0.621464 & -6.8078 & 0 \tabularnewline
18 & -0.713787 & -7.8191 & 0 \tabularnewline
19 & -0.634949 & -6.9555 & 0 \tabularnewline
20 & -0.333587 & -3.6543 & 0.000192 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105377&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]0.721997[/C][C]7.9091[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.378118[/C][C]4.1421[/C][C]3.2e-05[/C][/ROW]
[ROW][C]3[/C][C]0.00147[/C][C]0.0161[/C][C]0.493589[/C][/ROW]
[ROW][C]4[/C][C]-0.427046[/C][C]-4.6781[/C][C]4e-06[/C][/ROW]
[ROW][C]5[/C][C]-0.715973[/C][C]-7.8431[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]-0.798206[/C][C]-8.7439[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.71598[/C][C]-7.8432[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]-0.385985[/C][C]-4.2283[/C][C]2.3e-05[/C][/ROW]
[ROW][C]9[/C][C]0.029647[/C][C]0.3248[/C][C]0.372961[/C][/ROW]
[ROW][C]10[/C][C]0.357428[/C][C]3.9154[/C][C]7.5e-05[/C][/ROW]
[ROW][C]11[/C][C]0.678533[/C][C]7.433[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.84901[/C][C]9.3004[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.657996[/C][C]7.208[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.358114[/C][C]3.9229[/C][C]7.3e-05[/C][/ROW]
[ROW][C]15[/C][C]-0.009708[/C][C]-0.1063[/C][C]0.457743[/C][/ROW]
[ROW][C]16[/C][C]-0.390924[/C][C]-4.2824[/C][C]1.9e-05[/C][/ROW]
[ROW][C]17[/C][C]-0.621464[/C][C]-6.8078[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]-0.713787[/C][C]-7.8191[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]-0.634949[/C][C]-6.9555[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]-0.333587[/C][C]-3.6543[/C][C]0.000192[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105377&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105377&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	0.721997	7.9091	0
2	0.378118	4.1421	3.2e-05
3	0.00147	0.0161	0.493589
4	-0.427046	-4.6781	4e-06
5	-0.715973	-7.8431	0
6	-0.798206	-8.7439	0
7	-0.71598	-7.8432	0
8	-0.385985	-4.2283	2.3e-05
9	0.029647	0.3248	0.372961
10	0.357428	3.9154	7.5e-05
11	0.678533	7.433	0
12	0.84901	9.3004	0
13	0.657996	7.208	0
14	0.358114	3.9229	7.3e-05
15	-0.009708	-0.1063	0.457743
16	-0.390924	-4.2824	1.9e-05
17	-0.621464	-6.8078	0
18	-0.713787	-7.8191	0
19	-0.634949	-6.9555	0
20	-0.333587	-3.6543	0.000192

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.721997	7.9091	0
2	-0.299049	-3.2759	0.000689
3	-0.314878	-3.4493	0.000388
4	-0.508132	-5.5663	0
5	-0.343824	-3.7664	0.000129
6	-0.265166	-2.9047	0.002188
7	-0.330766	-3.6234	0.000214
8	-0.012209	-0.1337	0.446917
9	-0.005084	-0.0557	0.477842
10	-0.191771	-2.1007	0.018879
11	0.161486	1.769	0.039718
12	0.343592	3.7639	0.00013
13	-0.160301	-1.756	0.040819
14	-0.050542	-0.5537	0.290421
15	0.025427	0.2785	0.39054
16	0.102107	1.1185	0.132788
17	0.138645	1.5188	0.065724
18	0.050298	0.551	0.291332
19	0.072732	0.7967	0.213588
20	0.018497	0.2026	0.419885

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.721997 & 7.9091 & 0 \tabularnewline
2 & -0.299049 & -3.2759 & 0.000689 \tabularnewline
3 & -0.314878 & -3.4493 & 0.000388 \tabularnewline
4 & -0.508132 & -5.5663 & 0 \tabularnewline
5 & -0.343824 & -3.7664 & 0.000129 \tabularnewline
6 & -0.265166 & -2.9047 & 0.002188 \tabularnewline
7 & -0.330766 & -3.6234 & 0.000214 \tabularnewline
8 & -0.012209 & -0.1337 & 0.446917 \tabularnewline
9 & -0.005084 & -0.0557 & 0.477842 \tabularnewline
10 & -0.191771 & -2.1007 & 0.018879 \tabularnewline
11 & 0.161486 & 1.769 & 0.039718 \tabularnewline
12 & 0.343592 & 3.7639 & 0.00013 \tabularnewline
13 & -0.160301 & -1.756 & 0.040819 \tabularnewline
14 & -0.050542 & -0.5537 & 0.290421 \tabularnewline
15 & 0.025427 & 0.2785 & 0.39054 \tabularnewline
16 & 0.102107 & 1.1185 & 0.132788 \tabularnewline
17 & 0.138645 & 1.5188 & 0.065724 \tabularnewline
18 & 0.050298 & 0.551 & 0.291332 \tabularnewline
19 & 0.072732 & 0.7967 & 0.213588 \tabularnewline
20 & 0.018497 & 0.2026 & 0.419885 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105377&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]0.721997[/C][C]7.9091[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.299049[/C][C]-3.2759[/C][C]0.000689[/C][/ROW]
[ROW][C]3[/C][C]-0.314878[/C][C]-3.4493[/C][C]0.000388[/C][/ROW]
[ROW][C]4[/C][C]-0.508132[/C][C]-5.5663[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]-0.343824[/C][C]-3.7664[/C][C]0.000129[/C][/ROW]
[ROW][C]6[/C][C]-0.265166[/C][C]-2.9047[/C][C]0.002188[/C][/ROW]
[ROW][C]7[/C][C]-0.330766[/C][C]-3.6234[/C][C]0.000214[/C][/ROW]
[ROW][C]8[/C][C]-0.012209[/C][C]-0.1337[/C][C]0.446917[/C][/ROW]
[ROW][C]9[/C][C]-0.005084[/C][C]-0.0557[/C][C]0.477842[/C][/ROW]
[ROW][C]10[/C][C]-0.191771[/C][C]-2.1007[/C][C]0.018879[/C][/ROW]
[ROW][C]11[/C][C]0.161486[/C][C]1.769[/C][C]0.039718[/C][/ROW]
[ROW][C]12[/C][C]0.343592[/C][C]3.7639[/C][C]0.00013[/C][/ROW]
[ROW][C]13[/C][C]-0.160301[/C][C]-1.756[/C][C]0.040819[/C][/ROW]
[ROW][C]14[/C][C]-0.050542[/C][C]-0.5537[/C][C]0.290421[/C][/ROW]
[ROW][C]15[/C][C]0.025427[/C][C]0.2785[/C][C]0.39054[/C][/ROW]
[ROW][C]16[/C][C]0.102107[/C][C]1.1185[/C][C]0.132788[/C][/ROW]
[ROW][C]17[/C][C]0.138645[/C][C]1.5188[/C][C]0.065724[/C][/ROW]
[ROW][C]18[/C][C]0.050298[/C][C]0.551[/C][C]0.291332[/C][/ROW]
[ROW][C]19[/C][C]0.072732[/C][C]0.7967[/C][C]0.213588[/C][/ROW]
[ROW][C]20[/C][C]0.018497[/C][C]0.2026[/C][C]0.419885[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105377&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105377&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	0.721997	7.9091	0
2	-0.299049	-3.2759	0.000689
3	-0.314878	-3.4493	0.000388
4	-0.508132	-5.5663	0
5	-0.343824	-3.7664	0.000129
6	-0.265166	-2.9047	0.002188
7	-0.330766	-3.6234	0.000214
8	-0.012209	-0.1337	0.446917
9	-0.005084	-0.0557	0.477842
10	-0.191771	-2.1007	0.018879
11	0.161486	1.769	0.039718
12	0.343592	3.7639	0.00013
13	-0.160301	-1.756	0.040819
14	-0.050542	-0.5537	0.290421
15	0.025427	0.2785	0.39054
16	0.102107	1.1185	0.132788
17	0.138645	1.5188	0.065724
18	0.050298	0.551	0.291332
19	0.072732	0.7967	0.213588
20	0.018497	0.2026	0.419885

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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code