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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 04 Dec 2011 08:51:42 -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/2011/Dec/04/t1323006716camuh8dfcg5fuc9.htm/, Retrieved Sun, 05 May 2024 12:54:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150629, Retrieved Sun, 05 May 2024 12:54:51 +0000

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User-defined keywords

Estimated Impact

110

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       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [(Partial) Autocorrelation Function] [Births] [2010-11-29 09:36:27] [b98453cac15ba1066b407e146608df68]
- R PD          [(Partial) Autocorrelation Function] [WS9] [2011-12-02 13:40:33] [91ce4971c808115c699d50336245df56]
- R P               [(Partial) Autocorrelation Function] [] [2011-12-04 13:51:42] [858ef1d716a843f745df26a736207017] [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	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150629&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150629&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150629&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.529698	-4.0341	8.1e-05
2	-0.217835	-1.659	0.051259
3	0.459146	3.4968	0.000455
4	-0.221162	-1.6843	0.048747
5	-0.079261	-0.6036	0.27422
6	0.143325	1.0915	0.139776
7	-0.093452	-0.7117	0.239749
8	0.151098	1.1507	0.127284
9	-0.273088	-2.0798	0.020988
10	0.21908	1.6685	0.050307
11	0.127453	0.9707	0.167876
12	-0.404447	-3.0802	0.00158
13	0.22843	1.7397	0.043611
14	0.129118	0.9833	0.164765
15	-0.23345	-1.7779	0.040331
16	0.055544	0.423	0.336926
17	0.145684	1.1095	0.135898
18	-0.123463	-0.9403	0.17549
19	-0.051995	-0.396	0.346785

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.529698 & -4.0341 & 8.1e-05 \tabularnewline
2 & -0.217835 & -1.659 & 0.051259 \tabularnewline
3 & 0.459146 & 3.4968 & 0.000455 \tabularnewline
4 & -0.221162 & -1.6843 & 0.048747 \tabularnewline
5 & -0.079261 & -0.6036 & 0.27422 \tabularnewline
6 & 0.143325 & 1.0915 & 0.139776 \tabularnewline
7 & -0.093452 & -0.7117 & 0.239749 \tabularnewline
8 & 0.151098 & 1.1507 & 0.127284 \tabularnewline
9 & -0.273088 & -2.0798 & 0.020988 \tabularnewline
10 & 0.21908 & 1.6685 & 0.050307 \tabularnewline
11 & 0.127453 & 0.9707 & 0.167876 \tabularnewline
12 & -0.404447 & -3.0802 & 0.00158 \tabularnewline
13 & 0.22843 & 1.7397 & 0.043611 \tabularnewline
14 & 0.129118 & 0.9833 & 0.164765 \tabularnewline
15 & -0.23345 & -1.7779 & 0.040331 \tabularnewline
16 & 0.055544 & 0.423 & 0.336926 \tabularnewline
17 & 0.145684 & 1.1095 & 0.135898 \tabularnewline
18 & -0.123463 & -0.9403 & 0.17549 \tabularnewline
19 & -0.051995 & -0.396 & 0.346785 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150629&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]-0.529698[/C][C]-4.0341[/C][C]8.1e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.217835[/C][C]-1.659[/C][C]0.051259[/C][/ROW]
[ROW][C]3[/C][C]0.459146[/C][C]3.4968[/C][C]0.000455[/C][/ROW]
[ROW][C]4[/C][C]-0.221162[/C][C]-1.6843[/C][C]0.048747[/C][/ROW]
[ROW][C]5[/C][C]-0.079261[/C][C]-0.6036[/C][C]0.27422[/C][/ROW]
[ROW][C]6[/C][C]0.143325[/C][C]1.0915[/C][C]0.139776[/C][/ROW]
[ROW][C]7[/C][C]-0.093452[/C][C]-0.7117[/C][C]0.239749[/C][/ROW]
[ROW][C]8[/C][C]0.151098[/C][C]1.1507[/C][C]0.127284[/C][/ROW]
[ROW][C]9[/C][C]-0.273088[/C][C]-2.0798[/C][C]0.020988[/C][/ROW]
[ROW][C]10[/C][C]0.21908[/C][C]1.6685[/C][C]0.050307[/C][/ROW]
[ROW][C]11[/C][C]0.127453[/C][C]0.9707[/C][C]0.167876[/C][/ROW]
[ROW][C]12[/C][C]-0.404447[/C][C]-3.0802[/C][C]0.00158[/C][/ROW]
[ROW][C]13[/C][C]0.22843[/C][C]1.7397[/C][C]0.043611[/C][/ROW]
[ROW][C]14[/C][C]0.129118[/C][C]0.9833[/C][C]0.164765[/C][/ROW]
[ROW][C]15[/C][C]-0.23345[/C][C]-1.7779[/C][C]0.040331[/C][/ROW]
[ROW][C]16[/C][C]0.055544[/C][C]0.423[/C][C]0.336926[/C][/ROW]
[ROW][C]17[/C][C]0.145684[/C][C]1.1095[/C][C]0.135898[/C][/ROW]
[ROW][C]18[/C][C]-0.123463[/C][C]-0.9403[/C][C]0.17549[/C][/ROW]
[ROW][C]19[/C][C]-0.051995[/C][C]-0.396[/C][C]0.346785[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150629&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150629&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	-0.529698	-4.0341	8.1e-05
2	-0.217835	-1.659	0.051259
3	0.459146	3.4968	0.000455
4	-0.221162	-1.6843	0.048747
5	-0.079261	-0.6036	0.27422
6	0.143325	1.0915	0.139776
7	-0.093452	-0.7117	0.239749
8	0.151098	1.1507	0.127284
9	-0.273088	-2.0798	0.020988
10	0.21908	1.6685	0.050307
11	0.127453	0.9707	0.167876
12	-0.404447	-3.0802	0.00158
13	0.22843	1.7397	0.043611
14	0.129118	0.9833	0.164765
15	-0.23345	-1.7779	0.040331
16	0.055544	0.423	0.336926
17	0.145684	1.1095	0.135898
18	-0.123463	-0.9403	0.17549
19	-0.051995	-0.396	0.346785

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.529698	-4.0341	8.1e-05
2	-0.692801	-5.2762	1e-06
3	-0.275733	-2.0999	0.020048
4	-0.209961	-1.599	0.057626
5	-0.095061	-0.724	0.235999
6	-0.152448	-1.161	0.125198
7	-0.278145	-2.1183	0.019223
8	0.117043	0.8914	0.188205
9	-0.274572	-2.0911	0.020456
10	-0.070549	-0.5373	0.296563
11	0.193816	1.4761	0.072669
12	0.087349	0.6652	0.254269
13	-0.074327	-0.5661	0.28677
14	-0.213796	-1.6282	0.054449
15	0.019941	0.1519	0.439909
16	-0.134982	-1.028	0.154111
17	0.08998	0.6853	0.247952
18	0.020737	0.1579	0.437531
19	-0.045773	-0.3486	0.364326

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.529698 & -4.0341 & 8.1e-05 \tabularnewline
2 & -0.692801 & -5.2762 & 1e-06 \tabularnewline
3 & -0.275733 & -2.0999 & 0.020048 \tabularnewline
4 & -0.209961 & -1.599 & 0.057626 \tabularnewline
5 & -0.095061 & -0.724 & 0.235999 \tabularnewline
6 & -0.152448 & -1.161 & 0.125198 \tabularnewline
7 & -0.278145 & -2.1183 & 0.019223 \tabularnewline
8 & 0.117043 & 0.8914 & 0.188205 \tabularnewline
9 & -0.274572 & -2.0911 & 0.020456 \tabularnewline
10 & -0.070549 & -0.5373 & 0.296563 \tabularnewline
11 & 0.193816 & 1.4761 & 0.072669 \tabularnewline
12 & 0.087349 & 0.6652 & 0.254269 \tabularnewline
13 & -0.074327 & -0.5661 & 0.28677 \tabularnewline
14 & -0.213796 & -1.6282 & 0.054449 \tabularnewline
15 & 0.019941 & 0.1519 & 0.439909 \tabularnewline
16 & -0.134982 & -1.028 & 0.154111 \tabularnewline
17 & 0.08998 & 0.6853 & 0.247952 \tabularnewline
18 & 0.020737 & 0.1579 & 0.437531 \tabularnewline
19 & -0.045773 & -0.3486 & 0.364326 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150629&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]-0.529698[/C][C]-4.0341[/C][C]8.1e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.692801[/C][C]-5.2762[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]-0.275733[/C][C]-2.0999[/C][C]0.020048[/C][/ROW]
[ROW][C]4[/C][C]-0.209961[/C][C]-1.599[/C][C]0.057626[/C][/ROW]
[ROW][C]5[/C][C]-0.095061[/C][C]-0.724[/C][C]0.235999[/C][/ROW]
[ROW][C]6[/C][C]-0.152448[/C][C]-1.161[/C][C]0.125198[/C][/ROW]
[ROW][C]7[/C][C]-0.278145[/C][C]-2.1183[/C][C]0.019223[/C][/ROW]
[ROW][C]8[/C][C]0.117043[/C][C]0.8914[/C][C]0.188205[/C][/ROW]
[ROW][C]9[/C][C]-0.274572[/C][C]-2.0911[/C][C]0.020456[/C][/ROW]
[ROW][C]10[/C][C]-0.070549[/C][C]-0.5373[/C][C]0.296563[/C][/ROW]
[ROW][C]11[/C][C]0.193816[/C][C]1.4761[/C][C]0.072669[/C][/ROW]
[ROW][C]12[/C][C]0.087349[/C][C]0.6652[/C][C]0.254269[/C][/ROW]
[ROW][C]13[/C][C]-0.074327[/C][C]-0.5661[/C][C]0.28677[/C][/ROW]
[ROW][C]14[/C][C]-0.213796[/C][C]-1.6282[/C][C]0.054449[/C][/ROW]
[ROW][C]15[/C][C]0.019941[/C][C]0.1519[/C][C]0.439909[/C][/ROW]
[ROW][C]16[/C][C]-0.134982[/C][C]-1.028[/C][C]0.154111[/C][/ROW]
[ROW][C]17[/C][C]0.08998[/C][C]0.6853[/C][C]0.247952[/C][/ROW]
[ROW][C]18[/C][C]0.020737[/C][C]0.1579[/C][C]0.437531[/C][/ROW]
[ROW][C]19[/C][C]-0.045773[/C][C]-0.3486[/C][C]0.364326[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150629&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150629&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	-0.529698	-4.0341	8.1e-05
2	-0.692801	-5.2762	1e-06
3	-0.275733	-2.0999	0.020048
4	-0.209961	-1.599	0.057626
5	-0.095061	-0.724	0.235999
6	-0.152448	-1.161	0.125198
7	-0.278145	-2.1183	0.019223
8	0.117043	0.8914	0.188205
9	-0.274572	-2.0911	0.020456
10	-0.070549	-0.5373	0.296563
11	0.193816	1.4761	0.072669
12	0.087349	0.6652	0.254269
13	-0.074327	-0.5661	0.28677
14	-0.213796	-1.6282	0.054449
15	0.019941	0.1519	0.439909
16	-0.134982	-1.028	0.154111
17	0.08998	0.6853	0.247952
18	0.020737	0.1579	0.437531
19	-0.045773	-0.3486	0.364326

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 = 2 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 2 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code