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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 19 Dec 2009 09:10:09 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/19/t1261239030thmsokc6i9mneen.htm/, Retrieved Sat, 04 May 2024 03:14:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69660, Retrieved Sat, 04 May 2024 03:14:31 +0000

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Estimated Impact

141

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:16:10] [b98453cac15ba1066b407e146608df68]
- RMPD        [Standard Deviation-Mean Plot] [Paper SMP] [2009-12-19 15:14:41] [85be98bd9ebcfd4d73e77f8552419c9a]
- RMP             [(Partial) Autocorrelation Function] [Paper ACF] [2009-12-19 16:10:09] [5cd0e65b1f56b3935a0672588b930e12] [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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69660&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69660&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69660&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.375641	-3.1652	0.001142
2	-0.301875	-2.5436	0.006574
3	0.34392	2.8979	0.002496
4	-0.191342	-1.6123	0.05567
5	-0.150497	-1.2681	0.104451
6	0.394336	3.3227	0.000706
7	-0.26263	-2.213	0.015058
8	-0.074493	-0.6277	0.26611
9	0.364276	3.0694	0.001518
10	-0.426428	-3.5931	0.000299
11	-0.113187	-0.9537	0.171728
12	0.649521	5.473	0
13	-0.321674	-2.7105	0.004209
14	-0.10374	-0.8741	0.192497
15	0.196635	1.6569	0.050979
16	-0.245604	-2.0695	0.02107
17	0.029761	0.2508	0.401356
18	0.253321	2.1345	0.018127

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.375641 & -3.1652 & 0.001142 \tabularnewline
2 & -0.301875 & -2.5436 & 0.006574 \tabularnewline
3 & 0.34392 & 2.8979 & 0.002496 \tabularnewline
4 & -0.191342 & -1.6123 & 0.05567 \tabularnewline
5 & -0.150497 & -1.2681 & 0.104451 \tabularnewline
6 & 0.394336 & 3.3227 & 0.000706 \tabularnewline
7 & -0.26263 & -2.213 & 0.015058 \tabularnewline
8 & -0.074493 & -0.6277 & 0.26611 \tabularnewline
9 & 0.364276 & 3.0694 & 0.001518 \tabularnewline
10 & -0.426428 & -3.5931 & 0.000299 \tabularnewline
11 & -0.113187 & -0.9537 & 0.171728 \tabularnewline
12 & 0.649521 & 5.473 & 0 \tabularnewline
13 & -0.321674 & -2.7105 & 0.004209 \tabularnewline
14 & -0.10374 & -0.8741 & 0.192497 \tabularnewline
15 & 0.196635 & 1.6569 & 0.050979 \tabularnewline
16 & -0.245604 & -2.0695 & 0.02107 \tabularnewline
17 & 0.029761 & 0.2508 & 0.401356 \tabularnewline
18 & 0.253321 & 2.1345 & 0.018127 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69660&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]-0.375641[/C][C]-3.1652[/C][C]0.001142[/C][/ROW]
[ROW][C]2[/C][C]-0.301875[/C][C]-2.5436[/C][C]0.006574[/C][/ROW]
[ROW][C]3[/C][C]0.34392[/C][C]2.8979[/C][C]0.002496[/C][/ROW]
[ROW][C]4[/C][C]-0.191342[/C][C]-1.6123[/C][C]0.05567[/C][/ROW]
[ROW][C]5[/C][C]-0.150497[/C][C]-1.2681[/C][C]0.104451[/C][/ROW]
[ROW][C]6[/C][C]0.394336[/C][C]3.3227[/C][C]0.000706[/C][/ROW]
[ROW][C]7[/C][C]-0.26263[/C][C]-2.213[/C][C]0.015058[/C][/ROW]
[ROW][C]8[/C][C]-0.074493[/C][C]-0.6277[/C][C]0.26611[/C][/ROW]
[ROW][C]9[/C][C]0.364276[/C][C]3.0694[/C][C]0.001518[/C][/ROW]
[ROW][C]10[/C][C]-0.426428[/C][C]-3.5931[/C][C]0.000299[/C][/ROW]
[ROW][C]11[/C][C]-0.113187[/C][C]-0.9537[/C][C]0.171728[/C][/ROW]
[ROW][C]12[/C][C]0.649521[/C][C]5.473[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.321674[/C][C]-2.7105[/C][C]0.004209[/C][/ROW]
[ROW][C]14[/C][C]-0.10374[/C][C]-0.8741[/C][C]0.192497[/C][/ROW]
[ROW][C]15[/C][C]0.196635[/C][C]1.6569[/C][C]0.050979[/C][/ROW]
[ROW][C]16[/C][C]-0.245604[/C][C]-2.0695[/C][C]0.02107[/C][/ROW]
[ROW][C]17[/C][C]0.029761[/C][C]0.2508[/C][C]0.401356[/C][/ROW]
[ROW][C]18[/C][C]0.253321[/C][C]2.1345[/C][C]0.018127[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69660&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69660&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	-0.375641	-3.1652	0.001142
2	-0.301875	-2.5436	0.006574
3	0.34392	2.8979	0.002496
4	-0.191342	-1.6123	0.05567
5	-0.150497	-1.2681	0.104451
6	0.394336	3.3227	0.000706
7	-0.26263	-2.213	0.015058
8	-0.074493	-0.6277	0.26611
9	0.364276	3.0694	0.001518
10	-0.426428	-3.5931	0.000299
11	-0.113187	-0.9537	0.171728
12	0.649521	5.473	0
13	-0.321674	-2.7105	0.004209
14	-0.10374	-0.8741	0.192497
15	0.196635	1.6569	0.050979
16	-0.245604	-2.0695	0.02107
17	0.029761	0.2508	0.401356
18	0.253321	2.1345	0.018127

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.375641	-3.1652	0.001142
2	-0.515757	-4.3458	2.3e-05
3	-0.034423	-0.29	0.386312
4	-0.260381	-2.194	0.015754
5	-0.318312	-2.6821	0.004546
6	0.06534	0.5506	0.291831
7	-0.192167	-1.6192	0.054916
8	-0.106928	-0.901	0.18532
9	0.146248	1.2323	0.110949
10	-0.31691	-2.6703	0.004694
11	-0.49292	-4.1534	4.5e-05
12	0.140869	1.187	0.119596
13	0.081849	0.6897	0.246325
14	0.187414	1.5792	0.05937
15	-0.064171	-0.5407	0.295199
16	-0.080672	-0.6798	0.249436
17	-0.004866	-0.041	0.483704
18	-0.131469	-1.1078	0.135849

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.375641 & -3.1652 & 0.001142 \tabularnewline
2 & -0.515757 & -4.3458 & 2.3e-05 \tabularnewline
3 & -0.034423 & -0.29 & 0.386312 \tabularnewline
4 & -0.260381 & -2.194 & 0.015754 \tabularnewline
5 & -0.318312 & -2.6821 & 0.004546 \tabularnewline
6 & 0.06534 & 0.5506 & 0.291831 \tabularnewline
7 & -0.192167 & -1.6192 & 0.054916 \tabularnewline
8 & -0.106928 & -0.901 & 0.18532 \tabularnewline
9 & 0.146248 & 1.2323 & 0.110949 \tabularnewline
10 & -0.31691 & -2.6703 & 0.004694 \tabularnewline
11 & -0.49292 & -4.1534 & 4.5e-05 \tabularnewline
12 & 0.140869 & 1.187 & 0.119596 \tabularnewline
13 & 0.081849 & 0.6897 & 0.246325 \tabularnewline
14 & 0.187414 & 1.5792 & 0.05937 \tabularnewline
15 & -0.064171 & -0.5407 & 0.295199 \tabularnewline
16 & -0.080672 & -0.6798 & 0.249436 \tabularnewline
17 & -0.004866 & -0.041 & 0.483704 \tabularnewline
18 & -0.131469 & -1.1078 & 0.135849 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69660&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]-0.375641[/C][C]-3.1652[/C][C]0.001142[/C][/ROW]
[ROW][C]2[/C][C]-0.515757[/C][C]-4.3458[/C][C]2.3e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.034423[/C][C]-0.29[/C][C]0.386312[/C][/ROW]
[ROW][C]4[/C][C]-0.260381[/C][C]-2.194[/C][C]0.015754[/C][/ROW]
[ROW][C]5[/C][C]-0.318312[/C][C]-2.6821[/C][C]0.004546[/C][/ROW]
[ROW][C]6[/C][C]0.06534[/C][C]0.5506[/C][C]0.291831[/C][/ROW]
[ROW][C]7[/C][C]-0.192167[/C][C]-1.6192[/C][C]0.054916[/C][/ROW]
[ROW][C]8[/C][C]-0.106928[/C][C]-0.901[/C][C]0.18532[/C][/ROW]
[ROW][C]9[/C][C]0.146248[/C][C]1.2323[/C][C]0.110949[/C][/ROW]
[ROW][C]10[/C][C]-0.31691[/C][C]-2.6703[/C][C]0.004694[/C][/ROW]
[ROW][C]11[/C][C]-0.49292[/C][C]-4.1534[/C][C]4.5e-05[/C][/ROW]
[ROW][C]12[/C][C]0.140869[/C][C]1.187[/C][C]0.119596[/C][/ROW]
[ROW][C]13[/C][C]0.081849[/C][C]0.6897[/C][C]0.246325[/C][/ROW]
[ROW][C]14[/C][C]0.187414[/C][C]1.5792[/C][C]0.05937[/C][/ROW]
[ROW][C]15[/C][C]-0.064171[/C][C]-0.5407[/C][C]0.295199[/C][/ROW]
[ROW][C]16[/C][C]-0.080672[/C][C]-0.6798[/C][C]0.249436[/C][/ROW]
[ROW][C]17[/C][C]-0.004866[/C][C]-0.041[/C][C]0.483704[/C][/ROW]
[ROW][C]18[/C][C]-0.131469[/C][C]-1.1078[/C][C]0.135849[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69660&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69660&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	-0.375641	-3.1652	0.001142
2	-0.515757	-4.3458	2.3e-05
3	-0.034423	-0.29	0.386312
4	-0.260381	-2.194	0.015754
5	-0.318312	-2.6821	0.004546
6	0.06534	0.5506	0.291831
7	-0.192167	-1.6192	0.054916
8	-0.106928	-0.901	0.18532
9	0.146248	1.2323	0.110949
10	-0.31691	-2.6703	0.004694
11	-0.49292	-4.1534	4.5e-05
12	0.140869	1.187	0.119596
13	0.081849	0.6897	0.246325
14	0.187414	1.5792	0.05937
15	-0.064171	-0.5407	0.295199
16	-0.080672	-0.6798	0.249436
17	-0.004866	-0.041	0.483704
18	-0.131469	-1.1078	0.135849

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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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Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code