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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 19 Dec 2010 14:56:25 +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/19/t1292770509ilyr3740bwfi0xu.htm/, Retrieved Sat, 04 May 2024 21:45:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112460, Retrieved Sat, 04 May 2024 21:45:29 +0000

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User-defined keywords

Estimated Impact

185

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] [ACF 1] [2010-12-06 22:52:14] [b8e188bcc949964bed729335b3416734]
-    D        [(Partial) Autocorrelation Function] [ACF Nieuwbouw] [2010-12-19 14:56:25] [278a0539dc236556c5f30b5bc56ff9eb] [Current]
-   P           [(Partial) Autocorrelation Function] [ACF Nieuwbouw] [2010-12-19 15:50:37] [b8e188bcc949964bed729335b3416734] 
-   P             [(Partial) Autocorrelation Function] [ACF Nieuwbouw 1] [2010-12-19 15:57:46] [b8e188bcc949964bed729335b3416734] 

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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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112460&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112460&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112460&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.464025	3.7982	0.000158
2	0.385198	3.153	0.001209
3	0.4519	3.699	0.000219
4	0.219182	1.7941	0.038656
5	0.155774	1.2751	0.103345
6	0.184602	1.511	0.067741
7	0.201247	1.6473	0.052091
8	0.196596	1.6092	0.056136
9	0.25454	2.0835	0.020512
10	0.221184	1.8105	0.037353
11	0.022918	0.1876	0.425883
12	0.171673	1.4052	0.08229
13	0.040854	0.3344	0.36956
14	-0.030198	-0.2472	0.402763
15	-0.007411	-0.0607	0.475903
16	-0.022898	-0.1874	0.425946
17	-0.010381	-0.085	0.466267
18	0.024563	0.2011	0.420633

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.464025 & 3.7982 & 0.000158 \tabularnewline
2 & 0.385198 & 3.153 & 0.001209 \tabularnewline
3 & 0.4519 & 3.699 & 0.000219 \tabularnewline
4 & 0.219182 & 1.7941 & 0.038656 \tabularnewline
5 & 0.155774 & 1.2751 & 0.103345 \tabularnewline
6 & 0.184602 & 1.511 & 0.067741 \tabularnewline
7 & 0.201247 & 1.6473 & 0.052091 \tabularnewline
8 & 0.196596 & 1.6092 & 0.056136 \tabularnewline
9 & 0.25454 & 2.0835 & 0.020512 \tabularnewline
10 & 0.221184 & 1.8105 & 0.037353 \tabularnewline
11 & 0.022918 & 0.1876 & 0.425883 \tabularnewline
12 & 0.171673 & 1.4052 & 0.08229 \tabularnewline
13 & 0.040854 & 0.3344 & 0.36956 \tabularnewline
14 & -0.030198 & -0.2472 & 0.402763 \tabularnewline
15 & -0.007411 & -0.0607 & 0.475903 \tabularnewline
16 & -0.022898 & -0.1874 & 0.425946 \tabularnewline
17 & -0.010381 & -0.085 & 0.466267 \tabularnewline
18 & 0.024563 & 0.2011 & 0.420633 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112460&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]0.464025[/C][C]3.7982[/C][C]0.000158[/C][/ROW]
[ROW][C]2[/C][C]0.385198[/C][C]3.153[/C][C]0.001209[/C][/ROW]
[ROW][C]3[/C][C]0.4519[/C][C]3.699[/C][C]0.000219[/C][/ROW]
[ROW][C]4[/C][C]0.219182[/C][C]1.7941[/C][C]0.038656[/C][/ROW]
[ROW][C]5[/C][C]0.155774[/C][C]1.2751[/C][C]0.103345[/C][/ROW]
[ROW][C]6[/C][C]0.184602[/C][C]1.511[/C][C]0.067741[/C][/ROW]
[ROW][C]7[/C][C]0.201247[/C][C]1.6473[/C][C]0.052091[/C][/ROW]
[ROW][C]8[/C][C]0.196596[/C][C]1.6092[/C][C]0.056136[/C][/ROW]
[ROW][C]9[/C][C]0.25454[/C][C]2.0835[/C][C]0.020512[/C][/ROW]
[ROW][C]10[/C][C]0.221184[/C][C]1.8105[/C][C]0.037353[/C][/ROW]
[ROW][C]11[/C][C]0.022918[/C][C]0.1876[/C][C]0.425883[/C][/ROW]
[ROW][C]12[/C][C]0.171673[/C][C]1.4052[/C][C]0.08229[/C][/ROW]
[ROW][C]13[/C][C]0.040854[/C][C]0.3344[/C][C]0.36956[/C][/ROW]
[ROW][C]14[/C][C]-0.030198[/C][C]-0.2472[/C][C]0.402763[/C][/ROW]
[ROW][C]15[/C][C]-0.007411[/C][C]-0.0607[/C][C]0.475903[/C][/ROW]
[ROW][C]16[/C][C]-0.022898[/C][C]-0.1874[/C][C]0.425946[/C][/ROW]
[ROW][C]17[/C][C]-0.010381[/C][C]-0.085[/C][C]0.466267[/C][/ROW]
[ROW][C]18[/C][C]0.024563[/C][C]0.2011[/C][C]0.420633[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112460&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112460&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	0.464025	3.7982	0.000158
2	0.385198	3.153	0.001209
3	0.4519	3.699	0.000219
4	0.219182	1.7941	0.038656
5	0.155774	1.2751	0.103345
6	0.184602	1.511	0.067741
7	0.201247	1.6473	0.052091
8	0.196596	1.6092	0.056136
9	0.25454	2.0835	0.020512
10	0.221184	1.8105	0.037353
11	0.022918	0.1876	0.425883
12	0.171673	1.4052	0.08229
13	0.040854	0.3344	0.36956
14	-0.030198	-0.2472	0.402763
15	-0.007411	-0.0607	0.475903
16	-0.022898	-0.1874	0.425946
17	-0.010381	-0.085	0.466267
18	0.024563	0.2011	0.420633

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.464025	3.7982	0.000158
2	0.216494	1.7721	0.040464
3	0.282653	2.3136	0.011883
4	-0.134313	-1.0994	0.137765
5	-0.058184	-0.4763	0.31772
6	0.032724	0.2679	0.394816
7	0.165189	1.3521	0.09044
8	0.091197	0.7465	0.228994
9	0.107277	0.8781	0.191514
10	-0.034426	-0.2818	0.389486
11	-0.277455	-2.2711	0.013181
12	0.144115	1.1796	0.121159
13	-0.073212	-0.5993	0.275507
14	0.052968	0.4336	0.332999
15	-0.138692	-1.1352	0.13016
16	-0.015639	-0.128	0.449262
17	6e-05	5e-04	0.499806
18	0.103539	0.8475	0.199865

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.464025 & 3.7982 & 0.000158 \tabularnewline
2 & 0.216494 & 1.7721 & 0.040464 \tabularnewline
3 & 0.282653 & 2.3136 & 0.011883 \tabularnewline
4 & -0.134313 & -1.0994 & 0.137765 \tabularnewline
5 & -0.058184 & -0.4763 & 0.31772 \tabularnewline
6 & 0.032724 & 0.2679 & 0.394816 \tabularnewline
7 & 0.165189 & 1.3521 & 0.09044 \tabularnewline
8 & 0.091197 & 0.7465 & 0.228994 \tabularnewline
9 & 0.107277 & 0.8781 & 0.191514 \tabularnewline
10 & -0.034426 & -0.2818 & 0.389486 \tabularnewline
11 & -0.277455 & -2.2711 & 0.013181 \tabularnewline
12 & 0.144115 & 1.1796 & 0.121159 \tabularnewline
13 & -0.073212 & -0.5993 & 0.275507 \tabularnewline
14 & 0.052968 & 0.4336 & 0.332999 \tabularnewline
15 & -0.138692 & -1.1352 & 0.13016 \tabularnewline
16 & -0.015639 & -0.128 & 0.449262 \tabularnewline
17 & 6e-05 & 5e-04 & 0.499806 \tabularnewline
18 & 0.103539 & 0.8475 & 0.199865 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112460&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]0.464025[/C][C]3.7982[/C][C]0.000158[/C][/ROW]
[ROW][C]2[/C][C]0.216494[/C][C]1.7721[/C][C]0.040464[/C][/ROW]
[ROW][C]3[/C][C]0.282653[/C][C]2.3136[/C][C]0.011883[/C][/ROW]
[ROW][C]4[/C][C]-0.134313[/C][C]-1.0994[/C][C]0.137765[/C][/ROW]
[ROW][C]5[/C][C]-0.058184[/C][C]-0.4763[/C][C]0.31772[/C][/ROW]
[ROW][C]6[/C][C]0.032724[/C][C]0.2679[/C][C]0.394816[/C][/ROW]
[ROW][C]7[/C][C]0.165189[/C][C]1.3521[/C][C]0.09044[/C][/ROW]
[ROW][C]8[/C][C]0.091197[/C][C]0.7465[/C][C]0.228994[/C][/ROW]
[ROW][C]9[/C][C]0.107277[/C][C]0.8781[/C][C]0.191514[/C][/ROW]
[ROW][C]10[/C][C]-0.034426[/C][C]-0.2818[/C][C]0.389486[/C][/ROW]
[ROW][C]11[/C][C]-0.277455[/C][C]-2.2711[/C][C]0.013181[/C][/ROW]
[ROW][C]12[/C][C]0.144115[/C][C]1.1796[/C][C]0.121159[/C][/ROW]
[ROW][C]13[/C][C]-0.073212[/C][C]-0.5993[/C][C]0.275507[/C][/ROW]
[ROW][C]14[/C][C]0.052968[/C][C]0.4336[/C][C]0.332999[/C][/ROW]
[ROW][C]15[/C][C]-0.138692[/C][C]-1.1352[/C][C]0.13016[/C][/ROW]
[ROW][C]16[/C][C]-0.015639[/C][C]-0.128[/C][C]0.449262[/C][/ROW]
[ROW][C]17[/C][C]6e-05[/C][C]5e-04[/C][C]0.499806[/C][/ROW]
[ROW][C]18[/C][C]0.103539[/C][C]0.8475[/C][C]0.199865[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112460&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112460&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	0.464025	3.7982	0.000158
2	0.216494	1.7721	0.040464
3	0.282653	2.3136	0.011883
4	-0.134313	-1.0994	0.137765
5	-0.058184	-0.4763	0.31772
6	0.032724	0.2679	0.394816
7	0.165189	1.3521	0.09044
8	0.091197	0.7465	0.228994
9	0.107277	0.8781	0.191514
10	-0.034426	-0.2818	0.389486
11	-0.277455	-2.2711	0.013181
12	0.144115	1.1796	0.121159
13	-0.073212	-0.5993	0.275507
14	0.052968	0.4336	0.332999
15	-0.138692	-1.1352	0.13016
16	-0.015639	-0.128	0.449262
17	6e-05	5e-04	0.499806
18	0.103539	0.8475	0.199865

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