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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 28 Nov 2009 01:27:19 -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/Nov/28/t1259396973wra9z463c0fxrcw.htm/, Retrieved Sun, 05 May 2024 16:23:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61371, Retrieved Sun, 05 May 2024 16:23:25 +0000

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Estimated Impact

153

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

-     [Univariate Data Series] [ws8:uda personenw...] [2009-11-28 08:23:08] [bd8e774728cf1f2f4e6868fd314defe3]
- RMP     [(Partial) Autocorrelation Function] [ws8: acf d=D=0, L=1] [2009-11-28 08:27:19] [a315839f8c359622c3a1e6ed387dd5cd] [Current]
-   PD      [(Partial) Autocorrelation Function] [ws8: ACF d=D=0, L=1] [2009-11-28 08:36:07] [bd8e774728cf1f2f4e6868fd314defe3] 
-   PD        [(Partial) Autocorrelation Function] [ws8: ACF D=d=1, L=1] [2009-11-28 08:44:04] [bd8e774728cf1f2f4e6868fd314defe3] 
-   P           [(Partial) Autocorrelation Function] [ws8: ACF d=2, D=1...] [2009-11-28 08:47:07] [bd8e774728cf1f2f4e6868fd314defe3] 

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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	7 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 & 7 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61371&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]7 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=61371&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61371&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	7 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.367952	3.2704	0.000796
2	0.125281	1.1135	0.134431
3	-0.053062	-0.4716	0.319246
4	-0.228325	-2.0294	0.022893
5	-0.293232	-2.6063	0.005468
6	-0.493835	-4.3893	1.7e-05
7	-0.284096	-2.5251	0.006784
8	-0.202336	-1.7984	0.037967
9	-0.101051	-0.8982	0.185914
10	0.059743	0.531	0.298452
11	0.273593	2.4317	0.008645
12	0.771679	6.8588	0
13	0.266813	2.3715	0.010076
14	0.08507	0.7561	0.225912
15	-0.037328	-0.3318	0.370467
16	-0.18559	-1.6496	0.051502
17	-0.252828	-2.2472	0.013709
18	-0.445766	-3.9621	8.1e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.367952 & 3.2704 & 0.000796 \tabularnewline
2 & 0.125281 & 1.1135 & 0.134431 \tabularnewline
3 & -0.053062 & -0.4716 & 0.319246 \tabularnewline
4 & -0.228325 & -2.0294 & 0.022893 \tabularnewline
5 & -0.293232 & -2.6063 & 0.005468 \tabularnewline
6 & -0.493835 & -4.3893 & 1.7e-05 \tabularnewline
7 & -0.284096 & -2.5251 & 0.006784 \tabularnewline
8 & -0.202336 & -1.7984 & 0.037967 \tabularnewline
9 & -0.101051 & -0.8982 & 0.185914 \tabularnewline
10 & 0.059743 & 0.531 & 0.298452 \tabularnewline
11 & 0.273593 & 2.4317 & 0.008645 \tabularnewline
12 & 0.771679 & 6.8588 & 0 \tabularnewline
13 & 0.266813 & 2.3715 & 0.010076 \tabularnewline
14 & 0.08507 & 0.7561 & 0.225912 \tabularnewline
15 & -0.037328 & -0.3318 & 0.370467 \tabularnewline
16 & -0.18559 & -1.6496 & 0.051502 \tabularnewline
17 & -0.252828 & -2.2472 & 0.013709 \tabularnewline
18 & -0.445766 & -3.9621 & 8.1e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61371&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]0.367952[/C][C]3.2704[/C][C]0.000796[/C][/ROW]
[ROW][C]2[/C][C]0.125281[/C][C]1.1135[/C][C]0.134431[/C][/ROW]
[ROW][C]3[/C][C]-0.053062[/C][C]-0.4716[/C][C]0.319246[/C][/ROW]
[ROW][C]4[/C][C]-0.228325[/C][C]-2.0294[/C][C]0.022893[/C][/ROW]
[ROW][C]5[/C][C]-0.293232[/C][C]-2.6063[/C][C]0.005468[/C][/ROW]
[ROW][C]6[/C][C]-0.493835[/C][C]-4.3893[/C][C]1.7e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.284096[/C][C]-2.5251[/C][C]0.006784[/C][/ROW]
[ROW][C]8[/C][C]-0.202336[/C][C]-1.7984[/C][C]0.037967[/C][/ROW]
[ROW][C]9[/C][C]-0.101051[/C][C]-0.8982[/C][C]0.185914[/C][/ROW]
[ROW][C]10[/C][C]0.059743[/C][C]0.531[/C][C]0.298452[/C][/ROW]
[ROW][C]11[/C][C]0.273593[/C][C]2.4317[/C][C]0.008645[/C][/ROW]
[ROW][C]12[/C][C]0.771679[/C][C]6.8588[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.266813[/C][C]2.3715[/C][C]0.010076[/C][/ROW]
[ROW][C]14[/C][C]0.08507[/C][C]0.7561[/C][C]0.225912[/C][/ROW]
[ROW][C]15[/C][C]-0.037328[/C][C]-0.3318[/C][C]0.370467[/C][/ROW]
[ROW][C]16[/C][C]-0.18559[/C][C]-1.6496[/C][C]0.051502[/C][/ROW]
[ROW][C]17[/C][C]-0.252828[/C][C]-2.2472[/C][C]0.013709[/C][/ROW]
[ROW][C]18[/C][C]-0.445766[/C][C]-3.9621[/C][C]8.1e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61371&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61371&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	0.367952	3.2704	0.000796
2	0.125281	1.1135	0.134431
3	-0.053062	-0.4716	0.319246
4	-0.228325	-2.0294	0.022893
5	-0.293232	-2.6063	0.005468
6	-0.493835	-4.3893	1.7e-05
7	-0.284096	-2.5251	0.006784
8	-0.202336	-1.7984	0.037967
9	-0.101051	-0.8982	0.185914
10	0.059743	0.531	0.298452
11	0.273593	2.4317	0.008645
12	0.771679	6.8588	0
13	0.266813	2.3715	0.010076
14	0.08507	0.7561	0.225912
15	-0.037328	-0.3318	0.370467
16	-0.18559	-1.6496	0.051502
17	-0.252828	-2.2472	0.013709
18	-0.445766	-3.9621	8.1e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.367952	3.2704	0.000796
2	-0.011691	-0.1039	0.458752
3	-0.11035	-0.9808	0.164839
4	-0.201084	-1.7873	0.038865
5	-0.16262	-1.4454	0.076151
6	-0.398727	-3.544	0.000333
7	-0.050063	-0.445	0.328781
8	-0.196695	-1.7483	0.042152
9	-0.186542	-1.658	0.050639
10	-0.147732	-1.3131	0.09648
11	0.073973	0.6575	0.256391
12	0.646857	5.7494	0
13	-0.389472	-3.4617	0.000435
14	-0.108758	-0.9667	0.168332
15	-0.021956	-0.1951	0.422889
16	0.084581	0.7518	0.227212
17	-0.091199	-0.8106	0.210018
18	-0.082137	-0.73	0.23376

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.367952 & 3.2704 & 0.000796 \tabularnewline
2 & -0.011691 & -0.1039 & 0.458752 \tabularnewline
3 & -0.11035 & -0.9808 & 0.164839 \tabularnewline
4 & -0.201084 & -1.7873 & 0.038865 \tabularnewline
5 & -0.16262 & -1.4454 & 0.076151 \tabularnewline
6 & -0.398727 & -3.544 & 0.000333 \tabularnewline
7 & -0.050063 & -0.445 & 0.328781 \tabularnewline
8 & -0.196695 & -1.7483 & 0.042152 \tabularnewline
9 & -0.186542 & -1.658 & 0.050639 \tabularnewline
10 & -0.147732 & -1.3131 & 0.09648 \tabularnewline
11 & 0.073973 & 0.6575 & 0.256391 \tabularnewline
12 & 0.646857 & 5.7494 & 0 \tabularnewline
13 & -0.389472 & -3.4617 & 0.000435 \tabularnewline
14 & -0.108758 & -0.9667 & 0.168332 \tabularnewline
15 & -0.021956 & -0.1951 & 0.422889 \tabularnewline
16 & 0.084581 & 0.7518 & 0.227212 \tabularnewline
17 & -0.091199 & -0.8106 & 0.210018 \tabularnewline
18 & -0.082137 & -0.73 & 0.23376 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61371&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]0.367952[/C][C]3.2704[/C][C]0.000796[/C][/ROW]
[ROW][C]2[/C][C]-0.011691[/C][C]-0.1039[/C][C]0.458752[/C][/ROW]
[ROW][C]3[/C][C]-0.11035[/C][C]-0.9808[/C][C]0.164839[/C][/ROW]
[ROW][C]4[/C][C]-0.201084[/C][C]-1.7873[/C][C]0.038865[/C][/ROW]
[ROW][C]5[/C][C]-0.16262[/C][C]-1.4454[/C][C]0.076151[/C][/ROW]
[ROW][C]6[/C][C]-0.398727[/C][C]-3.544[/C][C]0.000333[/C][/ROW]
[ROW][C]7[/C][C]-0.050063[/C][C]-0.445[/C][C]0.328781[/C][/ROW]
[ROW][C]8[/C][C]-0.196695[/C][C]-1.7483[/C][C]0.042152[/C][/ROW]
[ROW][C]9[/C][C]-0.186542[/C][C]-1.658[/C][C]0.050639[/C][/ROW]
[ROW][C]10[/C][C]-0.147732[/C][C]-1.3131[/C][C]0.09648[/C][/ROW]
[ROW][C]11[/C][C]0.073973[/C][C]0.6575[/C][C]0.256391[/C][/ROW]
[ROW][C]12[/C][C]0.646857[/C][C]5.7494[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.389472[/C][C]-3.4617[/C][C]0.000435[/C][/ROW]
[ROW][C]14[/C][C]-0.108758[/C][C]-0.9667[/C][C]0.168332[/C][/ROW]
[ROW][C]15[/C][C]-0.021956[/C][C]-0.1951[/C][C]0.422889[/C][/ROW]
[ROW][C]16[/C][C]0.084581[/C][C]0.7518[/C][C]0.227212[/C][/ROW]
[ROW][C]17[/C][C]-0.091199[/C][C]-0.8106[/C][C]0.210018[/C][/ROW]
[ROW][C]18[/C][C]-0.082137[/C][C]-0.73[/C][C]0.23376[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61371&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61371&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	0.367952	3.2704	0.000796
2	-0.011691	-0.1039	0.458752
3	-0.11035	-0.9808	0.164839
4	-0.201084	-1.7873	0.038865
5	-0.16262	-1.4454	0.076151
6	-0.398727	-3.544	0.000333
7	-0.050063	-0.445	0.328781
8	-0.196695	-1.7483	0.042152
9	-0.186542	-1.658	0.050639
10	-0.147732	-1.3131	0.09648
11	0.073973	0.6575	0.256391
12	0.646857	5.7494	0
13	-0.389472	-3.4617	0.000435
14	-0.108758	-0.9667	0.168332
15	-0.021956	-0.1951	0.422889
16	0.084581	0.7518	0.227212
17	-0.091199	-0.8106	0.210018
18	-0.082137	-0.73	0.23376

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 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code