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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 04 Dec 2009 13:46:30 -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/04/t1259959633ru79mnbizj7uj20.htm/, Retrieved Sat, 27 Apr 2024 22:37:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64148, Retrieved Sat, 27 Apr 2024 22:37:27 +0000

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User-defined keywords

Estimated Impact

137

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] [] [2009-11-27 14:46:03] [b98453cac15ba1066b407e146608df68]
- R PD    [(Partial) Autocorrelation Function] [ws9-3] [2009-12-04 20:43:56] [74be16979710d4c4e7c6647856088456]
-   P         [(Partial) Autocorrelation Function] [ws9-4] [2009-12-04 20:46:30] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-   PD          [(Partial) Autocorrelation Function] [] [2009-12-04 21:40:54] [badc6a9acdc45286bea7f74742e15a21] 
-   P           [(Partial) Autocorrelation Function] [WS9 acf] [2009-12-09 18:50:44] [626f1d98f4a7f05bcb9f17666b672c60] 

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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	'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64148&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64148&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64148&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.531855	-4.3208	2.7e-05
2	-0.005718	-0.0465	0.481544
3	0.171228	1.3911	0.084439
4	-0.062148	-0.5049	0.307659
5	-0.072195	-0.5865	0.279766
6	0.00901	0.0732	0.470935
7	-0.048134	-0.391	0.348511
8	0.022401	0.182	0.428075
9	0.073318	0.5956	0.276727
10	-0.073604	-0.598	0.275957
11	-0.04353	-0.3536	0.362368
12	0.185146	1.5041	0.068659
13	-0.163781	-1.3306	0.093956
14	0.037801	0.3071	0.379868
15	0.091942	0.7469	0.228875
16	-0.15447	-1.2549	0.106967
17	0.149797	1.217	0.113977
18	-0.124189	-1.0089	0.15835

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.531855 & -4.3208 & 2.7e-05 \tabularnewline
2 & -0.005718 & -0.0465 & 0.481544 \tabularnewline
3 & 0.171228 & 1.3911 & 0.084439 \tabularnewline
4 & -0.062148 & -0.5049 & 0.307659 \tabularnewline
5 & -0.072195 & -0.5865 & 0.279766 \tabularnewline
6 & 0.00901 & 0.0732 & 0.470935 \tabularnewline
7 & -0.048134 & -0.391 & 0.348511 \tabularnewline
8 & 0.022401 & 0.182 & 0.428075 \tabularnewline
9 & 0.073318 & 0.5956 & 0.276727 \tabularnewline
10 & -0.073604 & -0.598 & 0.275957 \tabularnewline
11 & -0.04353 & -0.3536 & 0.362368 \tabularnewline
12 & 0.185146 & 1.5041 & 0.068659 \tabularnewline
13 & -0.163781 & -1.3306 & 0.093956 \tabularnewline
14 & 0.037801 & 0.3071 & 0.379868 \tabularnewline
15 & 0.091942 & 0.7469 & 0.228875 \tabularnewline
16 & -0.15447 & -1.2549 & 0.106967 \tabularnewline
17 & 0.149797 & 1.217 & 0.113977 \tabularnewline
18 & -0.124189 & -1.0089 & 0.15835 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64148&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]-0.531855[/C][C]-4.3208[/C][C]2.7e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.005718[/C][C]-0.0465[/C][C]0.481544[/C][/ROW]
[ROW][C]3[/C][C]0.171228[/C][C]1.3911[/C][C]0.084439[/C][/ROW]
[ROW][C]4[/C][C]-0.062148[/C][C]-0.5049[/C][C]0.307659[/C][/ROW]
[ROW][C]5[/C][C]-0.072195[/C][C]-0.5865[/C][C]0.279766[/C][/ROW]
[ROW][C]6[/C][C]0.00901[/C][C]0.0732[/C][C]0.470935[/C][/ROW]
[ROW][C]7[/C][C]-0.048134[/C][C]-0.391[/C][C]0.348511[/C][/ROW]
[ROW][C]8[/C][C]0.022401[/C][C]0.182[/C][C]0.428075[/C][/ROW]
[ROW][C]9[/C][C]0.073318[/C][C]0.5956[/C][C]0.276727[/C][/ROW]
[ROW][C]10[/C][C]-0.073604[/C][C]-0.598[/C][C]0.275957[/C][/ROW]
[ROW][C]11[/C][C]-0.04353[/C][C]-0.3536[/C][C]0.362368[/C][/ROW]
[ROW][C]12[/C][C]0.185146[/C][C]1.5041[/C][C]0.068659[/C][/ROW]
[ROW][C]13[/C][C]-0.163781[/C][C]-1.3306[/C][C]0.093956[/C][/ROW]
[ROW][C]14[/C][C]0.037801[/C][C]0.3071[/C][C]0.379868[/C][/ROW]
[ROW][C]15[/C][C]0.091942[/C][C]0.7469[/C][C]0.228875[/C][/ROW]
[ROW][C]16[/C][C]-0.15447[/C][C]-1.2549[/C][C]0.106967[/C][/ROW]
[ROW][C]17[/C][C]0.149797[/C][C]1.217[/C][C]0.113977[/C][/ROW]
[ROW][C]18[/C][C]-0.124189[/C][C]-1.0089[/C][C]0.15835[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64148&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64148&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	-0.531855	-4.3208	2.7e-05
2	-0.005718	-0.0465	0.481544
3	0.171228	1.3911	0.084439
4	-0.062148	-0.5049	0.307659
5	-0.072195	-0.5865	0.279766
6	0.00901	0.0732	0.470935
7	-0.048134	-0.391	0.348511
8	0.022401	0.182	0.428075
9	0.073318	0.5956	0.276727
10	-0.073604	-0.598	0.275957
11	-0.04353	-0.3536	0.362368
12	0.185146	1.5041	0.068659
13	-0.163781	-1.3306	0.093956
14	0.037801	0.3071	0.379868
15	0.091942	0.7469	0.228875
16	-0.15447	-1.2549	0.106967
17	0.149797	1.217	0.113977
18	-0.124189	-1.0089	0.15835

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.531855	-4.3208	2.7e-05
2	-0.40242	-3.2693	0.000857
3	-0.078313	-0.6362	0.263418
4	0.044665	0.3629	0.358934
5	-0.035902	-0.2917	0.385728
6	-0.139466	-1.133	0.130651
7	-0.247358	-2.0095	0.024286
8	-0.204638	-1.6625	0.050579
9	0.015038	0.1222	0.451569
10	0.05059	0.411	0.341204
11	-0.125825	-1.0222	0.155207
12	0.008095	0.0658	0.473881
13	-0.081934	-0.6656	0.253982
14	-0.04508	-0.3662	0.357682
15	0.088449	0.7186	0.237472
16	-0.059534	-0.4837	0.315115
17	0.066427	0.5397	0.295624
18	-0.092654	-0.7527	0.227145

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.531855 & -4.3208 & 2.7e-05 \tabularnewline
2 & -0.40242 & -3.2693 & 0.000857 \tabularnewline
3 & -0.078313 & -0.6362 & 0.263418 \tabularnewline
4 & 0.044665 & 0.3629 & 0.358934 \tabularnewline
5 & -0.035902 & -0.2917 & 0.385728 \tabularnewline
6 & -0.139466 & -1.133 & 0.130651 \tabularnewline
7 & -0.247358 & -2.0095 & 0.024286 \tabularnewline
8 & -0.204638 & -1.6625 & 0.050579 \tabularnewline
9 & 0.015038 & 0.1222 & 0.451569 \tabularnewline
10 & 0.05059 & 0.411 & 0.341204 \tabularnewline
11 & -0.125825 & -1.0222 & 0.155207 \tabularnewline
12 & 0.008095 & 0.0658 & 0.473881 \tabularnewline
13 & -0.081934 & -0.6656 & 0.253982 \tabularnewline
14 & -0.04508 & -0.3662 & 0.357682 \tabularnewline
15 & 0.088449 & 0.7186 & 0.237472 \tabularnewline
16 & -0.059534 & -0.4837 & 0.315115 \tabularnewline
17 & 0.066427 & 0.5397 & 0.295624 \tabularnewline
18 & -0.092654 & -0.7527 & 0.227145 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64148&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]-0.531855[/C][C]-4.3208[/C][C]2.7e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.40242[/C][C]-3.2693[/C][C]0.000857[/C][/ROW]
[ROW][C]3[/C][C]-0.078313[/C][C]-0.6362[/C][C]0.263418[/C][/ROW]
[ROW][C]4[/C][C]0.044665[/C][C]0.3629[/C][C]0.358934[/C][/ROW]
[ROW][C]5[/C][C]-0.035902[/C][C]-0.2917[/C][C]0.385728[/C][/ROW]
[ROW][C]6[/C][C]-0.139466[/C][C]-1.133[/C][C]0.130651[/C][/ROW]
[ROW][C]7[/C][C]-0.247358[/C][C]-2.0095[/C][C]0.024286[/C][/ROW]
[ROW][C]8[/C][C]-0.204638[/C][C]-1.6625[/C][C]0.050579[/C][/ROW]
[ROW][C]9[/C][C]0.015038[/C][C]0.1222[/C][C]0.451569[/C][/ROW]
[ROW][C]10[/C][C]0.05059[/C][C]0.411[/C][C]0.341204[/C][/ROW]
[ROW][C]11[/C][C]-0.125825[/C][C]-1.0222[/C][C]0.155207[/C][/ROW]
[ROW][C]12[/C][C]0.008095[/C][C]0.0658[/C][C]0.473881[/C][/ROW]
[ROW][C]13[/C][C]-0.081934[/C][C]-0.6656[/C][C]0.253982[/C][/ROW]
[ROW][C]14[/C][C]-0.04508[/C][C]-0.3662[/C][C]0.357682[/C][/ROW]
[ROW][C]15[/C][C]0.088449[/C][C]0.7186[/C][C]0.237472[/C][/ROW]
[ROW][C]16[/C][C]-0.059534[/C][C]-0.4837[/C][C]0.315115[/C][/ROW]
[ROW][C]17[/C][C]0.066427[/C][C]0.5397[/C][C]0.295624[/C][/ROW]
[ROW][C]18[/C][C]-0.092654[/C][C]-0.7527[/C][C]0.227145[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64148&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64148&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	-0.531855	-4.3208	2.7e-05
2	-0.40242	-3.2693	0.000857
3	-0.078313	-0.6362	0.263418
4	0.044665	0.3629	0.358934
5	-0.035902	-0.2917	0.385728
6	-0.139466	-1.133	0.130651
7	-0.247358	-2.0095	0.024286
8	-0.204638	-1.6625	0.050579
9	0.015038	0.1222	0.451569
10	0.05059	0.411	0.341204
11	-0.125825	-1.0222	0.155207
12	0.008095	0.0658	0.473881
13	-0.081934	-0.6656	0.253982
14	-0.04508	-0.3662	0.357682
15	0.088449	0.7186	0.237472
16	-0.059534	-0.4837	0.315115
17	0.066427	0.5397	0.295624
18	-0.092654	-0.7527	0.227145

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.5 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 0.5 ; par3 = 1 ; 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