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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 15 Dec 2009 03:10:04 -0700

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/2009/Dec/15/t12608718700ioy1giotlhjgxv.htm/, Retrieved Wed, 08 May 2024 03:42:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67811, Retrieved Wed, 08 May 2024 03:42:40 +0000

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-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2009-12-15 10:10:04] [6df9bd2792d60592b4a24994398a86db] [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=67811&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=67811&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67811&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	0.861382	9.8965	0
2	0.803519	9.2317	0
3	0.840711	9.659	0
4	0.772174	8.8716	0
5	0.747093	8.5834	0
6	0.773841	8.8908	0
7	0.680963	7.8237	0
8	0.655529	7.5315	0
9	0.657621	7.5555	0
10	0.572448	6.5769	0
11	0.602229	6.9191	0
12	0.653155	7.5042	0
13	0.53002	6.0895	0
14	0.473679	5.4422	0
15	0.493425	5.669	0
16	0.435876	5.0078	1e-06
17	0.423834	4.8695	2e-06
18	0.438926	5.0429	1e-06
19	0.36835	4.232	2.2e-05
20	0.347903	3.9971	5.3e-05
21	0.342425	3.9342	6.7e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.861382 & 9.8965 & 0 \tabularnewline
2 & 0.803519 & 9.2317 & 0 \tabularnewline
3 & 0.840711 & 9.659 & 0 \tabularnewline
4 & 0.772174 & 8.8716 & 0 \tabularnewline
5 & 0.747093 & 8.5834 & 0 \tabularnewline
6 & 0.773841 & 8.8908 & 0 \tabularnewline
7 & 0.680963 & 7.8237 & 0 \tabularnewline
8 & 0.655529 & 7.5315 & 0 \tabularnewline
9 & 0.657621 & 7.5555 & 0 \tabularnewline
10 & 0.572448 & 6.5769 & 0 \tabularnewline
11 & 0.602229 & 6.9191 & 0 \tabularnewline
12 & 0.653155 & 7.5042 & 0 \tabularnewline
13 & 0.53002 & 6.0895 & 0 \tabularnewline
14 & 0.473679 & 5.4422 & 0 \tabularnewline
15 & 0.493425 & 5.669 & 0 \tabularnewline
16 & 0.435876 & 5.0078 & 1e-06 \tabularnewline
17 & 0.423834 & 4.8695 & 2e-06 \tabularnewline
18 & 0.438926 & 5.0429 & 1e-06 \tabularnewline
19 & 0.36835 & 4.232 & 2.2e-05 \tabularnewline
20 & 0.347903 & 3.9971 & 5.3e-05 \tabularnewline
21 & 0.342425 & 3.9342 & 6.7e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67811&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]0.861382[/C][C]9.8965[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.803519[/C][C]9.2317[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.840711[/C][C]9.659[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.772174[/C][C]8.8716[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.747093[/C][C]8.5834[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.773841[/C][C]8.8908[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.680963[/C][C]7.8237[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.655529[/C][C]7.5315[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.657621[/C][C]7.5555[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.572448[/C][C]6.5769[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.602229[/C][C]6.9191[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.653155[/C][C]7.5042[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.53002[/C][C]6.0895[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.473679[/C][C]5.4422[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.493425[/C][C]5.669[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.435876[/C][C]5.0078[/C][C]1e-06[/C][/ROW]
[ROW][C]17[/C][C]0.423834[/C][C]4.8695[/C][C]2e-06[/C][/ROW]
[ROW][C]18[/C][C]0.438926[/C][C]5.0429[/C][C]1e-06[/C][/ROW]
[ROW][C]19[/C][C]0.36835[/C][C]4.232[/C][C]2.2e-05[/C][/ROW]
[ROW][C]20[/C][C]0.347903[/C][C]3.9971[/C][C]5.3e-05[/C][/ROW]
[ROW][C]21[/C][C]0.342425[/C][C]3.9342[/C][C]6.7e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67811&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67811&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	0.861382	9.8965	0
2	0.803519	9.2317	0
3	0.840711	9.659	0
4	0.772174	8.8716	0
5	0.747093	8.5834	0
6	0.773841	8.8908	0
7	0.680963	7.8237	0
8	0.655529	7.5315	0
9	0.657621	7.5555	0
10	0.572448	6.5769	0
11	0.602229	6.9191	0
12	0.653155	7.5042	0
13	0.53002	6.0895	0
14	0.473679	5.4422	0
15	0.493425	5.669	0
16	0.435876	5.0078	1e-06
17	0.423834	4.8695	2e-06
18	0.438926	5.0429	1e-06
19	0.36835	4.232	2.2e-05
20	0.347903	3.9971	5.3e-05
21	0.342425	3.9342	6.7e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.861382	9.8965	0
2	0.238507	2.7402	0.003495
3	0.444673	5.1089	1e-06
4	-0.155848	-1.7906	0.037828
5	0.150814	1.7327	0.042741
6	0.105216	1.2088	0.114443
7	-0.278798	-3.2032	0.000852
8	0.101656	1.1679	0.122469
9	-0.125183	-1.4382	0.076366
10	-0.100174	-1.1509	0.125925
11	0.349154	4.0115	5e-05
12	0.159156	1.8286	0.034862
13	-0.352573	-4.0508	4.3e-05
14	-0.267374	-3.0719	0.001292
15	0.005869	0.0674	0.473171
16	0.154814	1.7787	0.038797
17	0.037869	0.4351	0.332108
18	0.040917	0.4701	0.31953
19	0.016896	0.1941	0.42319
20	-0.045713	-0.5252	0.300162
21	-0.028617	-0.3288	0.371422

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.861382 & 9.8965 & 0 \tabularnewline
2 & 0.238507 & 2.7402 & 0.003495 \tabularnewline
3 & 0.444673 & 5.1089 & 1e-06 \tabularnewline
4 & -0.155848 & -1.7906 & 0.037828 \tabularnewline
5 & 0.150814 & 1.7327 & 0.042741 \tabularnewline
6 & 0.105216 & 1.2088 & 0.114443 \tabularnewline
7 & -0.278798 & -3.2032 & 0.000852 \tabularnewline
8 & 0.101656 & 1.1679 & 0.122469 \tabularnewline
9 & -0.125183 & -1.4382 & 0.076366 \tabularnewline
10 & -0.100174 & -1.1509 & 0.125925 \tabularnewline
11 & 0.349154 & 4.0115 & 5e-05 \tabularnewline
12 & 0.159156 & 1.8286 & 0.034862 \tabularnewline
13 & -0.352573 & -4.0508 & 4.3e-05 \tabularnewline
14 & -0.267374 & -3.0719 & 0.001292 \tabularnewline
15 & 0.005869 & 0.0674 & 0.473171 \tabularnewline
16 & 0.154814 & 1.7787 & 0.038797 \tabularnewline
17 & 0.037869 & 0.4351 & 0.332108 \tabularnewline
18 & 0.040917 & 0.4701 & 0.31953 \tabularnewline
19 & 0.016896 & 0.1941 & 0.42319 \tabularnewline
20 & -0.045713 & -0.5252 & 0.300162 \tabularnewline
21 & -0.028617 & -0.3288 & 0.371422 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67811&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]0.861382[/C][C]9.8965[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.238507[/C][C]2.7402[/C][C]0.003495[/C][/ROW]
[ROW][C]3[/C][C]0.444673[/C][C]5.1089[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]-0.155848[/C][C]-1.7906[/C][C]0.037828[/C][/ROW]
[ROW][C]5[/C][C]0.150814[/C][C]1.7327[/C][C]0.042741[/C][/ROW]
[ROW][C]6[/C][C]0.105216[/C][C]1.2088[/C][C]0.114443[/C][/ROW]
[ROW][C]7[/C][C]-0.278798[/C][C]-3.2032[/C][C]0.000852[/C][/ROW]
[ROW][C]8[/C][C]0.101656[/C][C]1.1679[/C][C]0.122469[/C][/ROW]
[ROW][C]9[/C][C]-0.125183[/C][C]-1.4382[/C][C]0.076366[/C][/ROW]
[ROW][C]10[/C][C]-0.100174[/C][C]-1.1509[/C][C]0.125925[/C][/ROW]
[ROW][C]11[/C][C]0.349154[/C][C]4.0115[/C][C]5e-05[/C][/ROW]
[ROW][C]12[/C][C]0.159156[/C][C]1.8286[/C][C]0.034862[/C][/ROW]
[ROW][C]13[/C][C]-0.352573[/C][C]-4.0508[/C][C]4.3e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.267374[/C][C]-3.0719[/C][C]0.001292[/C][/ROW]
[ROW][C]15[/C][C]0.005869[/C][C]0.0674[/C][C]0.473171[/C][/ROW]
[ROW][C]16[/C][C]0.154814[/C][C]1.7787[/C][C]0.038797[/C][/ROW]
[ROW][C]17[/C][C]0.037869[/C][C]0.4351[/C][C]0.332108[/C][/ROW]
[ROW][C]18[/C][C]0.040917[/C][C]0.4701[/C][C]0.31953[/C][/ROW]
[ROW][C]19[/C][C]0.016896[/C][C]0.1941[/C][C]0.42319[/C][/ROW]
[ROW][C]20[/C][C]-0.045713[/C][C]-0.5252[/C][C]0.300162[/C][/ROW]
[ROW][C]21[/C][C]-0.028617[/C][C]-0.3288[/C][C]0.371422[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67811&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67811&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	0.861382	9.8965	0
2	0.238507	2.7402	0.003495
3	0.444673	5.1089	1e-06
4	-0.155848	-1.7906	0.037828
5	0.150814	1.7327	0.042741
6	0.105216	1.2088	0.114443
7	-0.278798	-3.2032	0.000852
8	0.101656	1.1679	0.122469
9	-0.125183	-1.4382	0.076366
10	-0.100174	-1.1509	0.125925
11	0.349154	4.0115	5e-05
12	0.159156	1.8286	0.034862
13	-0.352573	-4.0508	4.3e-05
14	-0.267374	-3.0719	0.001292
15	0.005869	0.0674	0.473171
16	0.154814	1.7787	0.038797
17	0.037869	0.4351	0.332108
18	0.040917	0.4701	0.31953
19	0.016896	0.1941	0.42319
20	-0.045713	-0.5252	0.300162
21	-0.028617	-0.3288	0.371422

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.0 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; 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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code