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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 04 Apr 2012 09:33:22 -0400

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/2012/Apr/04/t1333546466vz6q7ivfn5i7xx9.htm/, Retrieved Mon, 29 Apr 2024 03:57:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=164297, Retrieved Mon, 29 Apr 2024 03:57:42 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W12

Estimated Impact

153

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

-       [(Partial) Autocorrelation Function] [] [2012-04-04 13:33:22] [580dcee726213d1997fefc515b1ea0db] [Current]
- R P     [(Partial) Autocorrelation Function] [] [2012-05-28 21:42:59] [e95d449c9105dcfabcb63314f6f5dc88] 
- R P     [(Partial) Autocorrelation Function] [] [2012-05-28 21:44:33] [e95d449c9105dcfabcb63314f6f5dc88] 
- RMPD    [Bootstrap Plot - Central Tendency] [] [2012-05-28 21:47:38] [0112d3169e5bff4e2f0b3452278280c8] 
- RMP     [Bootstrap Plot - Central Tendency] [] [2012-05-28 22:06:53] [0112d3169e5bff4e2f0b3452278280c8] 

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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=164297&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=164297&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164297&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	0.613744	5.5237	0
2	0.469	4.221	3.2e-05
3	0.457093	4.1138	4.6e-05
4	0.246531	2.2188	0.01465
5	0.147209	1.3249	0.094469
6	0.156189	1.4057	0.081819
7	0.179413	1.6147	0.05513
8	0.203536	1.8318	0.035327
9	0.255986	2.3039	0.011896
10	0.239898	2.1591	0.016901
11	0.121408	1.0927	0.138888
12	0.151777	1.366	0.087861
13	0.046252	0.4163	0.339156
14	0.039937	0.3594	0.360103
15	0.086701	0.7803	0.218741
16	0.092759	0.8348	0.203135
17	0.13439	1.2095	0.114992
18	0.184578	1.6612	0.05027
19	0.164789	1.4831	0.070964

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.613744 & 5.5237 & 0 \tabularnewline
2 & 0.469 & 4.221 & 3.2e-05 \tabularnewline
3 & 0.457093 & 4.1138 & 4.6e-05 \tabularnewline
4 & 0.246531 & 2.2188 & 0.01465 \tabularnewline
5 & 0.147209 & 1.3249 & 0.094469 \tabularnewline
6 & 0.156189 & 1.4057 & 0.081819 \tabularnewline
7 & 0.179413 & 1.6147 & 0.05513 \tabularnewline
8 & 0.203536 & 1.8318 & 0.035327 \tabularnewline
9 & 0.255986 & 2.3039 & 0.011896 \tabularnewline
10 & 0.239898 & 2.1591 & 0.016901 \tabularnewline
11 & 0.121408 & 1.0927 & 0.138888 \tabularnewline
12 & 0.151777 & 1.366 & 0.087861 \tabularnewline
13 & 0.046252 & 0.4163 & 0.339156 \tabularnewline
14 & 0.039937 & 0.3594 & 0.360103 \tabularnewline
15 & 0.086701 & 0.7803 & 0.218741 \tabularnewline
16 & 0.092759 & 0.8348 & 0.203135 \tabularnewline
17 & 0.13439 & 1.2095 & 0.114992 \tabularnewline
18 & 0.184578 & 1.6612 & 0.05027 \tabularnewline
19 & 0.164789 & 1.4831 & 0.070964 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164297&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]0.613744[/C][C]5.5237[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.469[/C][C]4.221[/C][C]3.2e-05[/C][/ROW]
[ROW][C]3[/C][C]0.457093[/C][C]4.1138[/C][C]4.6e-05[/C][/ROW]
[ROW][C]4[/C][C]0.246531[/C][C]2.2188[/C][C]0.01465[/C][/ROW]
[ROW][C]5[/C][C]0.147209[/C][C]1.3249[/C][C]0.094469[/C][/ROW]
[ROW][C]6[/C][C]0.156189[/C][C]1.4057[/C][C]0.081819[/C][/ROW]
[ROW][C]7[/C][C]0.179413[/C][C]1.6147[/C][C]0.05513[/C][/ROW]
[ROW][C]8[/C][C]0.203536[/C][C]1.8318[/C][C]0.035327[/C][/ROW]
[ROW][C]9[/C][C]0.255986[/C][C]2.3039[/C][C]0.011896[/C][/ROW]
[ROW][C]10[/C][C]0.239898[/C][C]2.1591[/C][C]0.016901[/C][/ROW]
[ROW][C]11[/C][C]0.121408[/C][C]1.0927[/C][C]0.138888[/C][/ROW]
[ROW][C]12[/C][C]0.151777[/C][C]1.366[/C][C]0.087861[/C][/ROW]
[ROW][C]13[/C][C]0.046252[/C][C]0.4163[/C][C]0.339156[/C][/ROW]
[ROW][C]14[/C][C]0.039937[/C][C]0.3594[/C][C]0.360103[/C][/ROW]
[ROW][C]15[/C][C]0.086701[/C][C]0.7803[/C][C]0.218741[/C][/ROW]
[ROW][C]16[/C][C]0.092759[/C][C]0.8348[/C][C]0.203135[/C][/ROW]
[ROW][C]17[/C][C]0.13439[/C][C]1.2095[/C][C]0.114992[/C][/ROW]
[ROW][C]18[/C][C]0.184578[/C][C]1.6612[/C][C]0.05027[/C][/ROW]
[ROW][C]19[/C][C]0.164789[/C][C]1.4831[/C][C]0.070964[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164297&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164297&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	0.613744	5.5237	0
2	0.469	4.221	3.2e-05
3	0.457093	4.1138	4.6e-05
4	0.246531	2.2188	0.01465
5	0.147209	1.3249	0.094469
6	0.156189	1.4057	0.081819
7	0.179413	1.6147	0.05513
8	0.203536	1.8318	0.035327
9	0.255986	2.3039	0.011896
10	0.239898	2.1591	0.016901
11	0.121408	1.0927	0.138888
12	0.151777	1.366	0.087861
13	0.046252	0.4163	0.339156
14	0.039937	0.3594	0.360103
15	0.086701	0.7803	0.218741
16	0.092759	0.8348	0.203135
17	0.13439	1.2095	0.114992
18	0.184578	1.6612	0.05027
19	0.164789	1.4831	0.070964

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.613744	5.5237	0
2	0.148109	1.333	0.093138
3	0.198442	1.786	0.038923
4	-0.207666	-1.869	0.032619
5	-0.040619	-0.3656	0.357818
6	0.064534	0.5808	0.281493
7	0.175488	1.5794	0.059072
8	0.101634	0.9147	0.18153
9	0.084432	0.7599	0.224763
10	-0.058265	-0.5244	0.30072
11	-0.193107	-1.738	0.043009
12	0.094969	0.8547	0.197613
13	-0.10125	-0.9112	0.182434
14	0.173985	1.5659	0.06064
15	0.016902	0.1521	0.439734
16	0.052848	0.4756	0.317809
17	-0.02086	-0.1877	0.425776
18	0.049707	0.4474	0.327905
19	-0.029135	-0.2622	0.39691

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.613744 & 5.5237 & 0 \tabularnewline
2 & 0.148109 & 1.333 & 0.093138 \tabularnewline
3 & 0.198442 & 1.786 & 0.038923 \tabularnewline
4 & -0.207666 & -1.869 & 0.032619 \tabularnewline
5 & -0.040619 & -0.3656 & 0.357818 \tabularnewline
6 & 0.064534 & 0.5808 & 0.281493 \tabularnewline
7 & 0.175488 & 1.5794 & 0.059072 \tabularnewline
8 & 0.101634 & 0.9147 & 0.18153 \tabularnewline
9 & 0.084432 & 0.7599 & 0.224763 \tabularnewline
10 & -0.058265 & -0.5244 & 0.30072 \tabularnewline
11 & -0.193107 & -1.738 & 0.043009 \tabularnewline
12 & 0.094969 & 0.8547 & 0.197613 \tabularnewline
13 & -0.10125 & -0.9112 & 0.182434 \tabularnewline
14 & 0.173985 & 1.5659 & 0.06064 \tabularnewline
15 & 0.016902 & 0.1521 & 0.439734 \tabularnewline
16 & 0.052848 & 0.4756 & 0.317809 \tabularnewline
17 & -0.02086 & -0.1877 & 0.425776 \tabularnewline
18 & 0.049707 & 0.4474 & 0.327905 \tabularnewline
19 & -0.029135 & -0.2622 & 0.39691 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164297&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]0.613744[/C][C]5.5237[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.148109[/C][C]1.333[/C][C]0.093138[/C][/ROW]
[ROW][C]3[/C][C]0.198442[/C][C]1.786[/C][C]0.038923[/C][/ROW]
[ROW][C]4[/C][C]-0.207666[/C][C]-1.869[/C][C]0.032619[/C][/ROW]
[ROW][C]5[/C][C]-0.040619[/C][C]-0.3656[/C][C]0.357818[/C][/ROW]
[ROW][C]6[/C][C]0.064534[/C][C]0.5808[/C][C]0.281493[/C][/ROW]
[ROW][C]7[/C][C]0.175488[/C][C]1.5794[/C][C]0.059072[/C][/ROW]
[ROW][C]8[/C][C]0.101634[/C][C]0.9147[/C][C]0.18153[/C][/ROW]
[ROW][C]9[/C][C]0.084432[/C][C]0.7599[/C][C]0.224763[/C][/ROW]
[ROW][C]10[/C][C]-0.058265[/C][C]-0.5244[/C][C]0.30072[/C][/ROW]
[ROW][C]11[/C][C]-0.193107[/C][C]-1.738[/C][C]0.043009[/C][/ROW]
[ROW][C]12[/C][C]0.094969[/C][C]0.8547[/C][C]0.197613[/C][/ROW]
[ROW][C]13[/C][C]-0.10125[/C][C]-0.9112[/C][C]0.182434[/C][/ROW]
[ROW][C]14[/C][C]0.173985[/C][C]1.5659[/C][C]0.06064[/C][/ROW]
[ROW][C]15[/C][C]0.016902[/C][C]0.1521[/C][C]0.439734[/C][/ROW]
[ROW][C]16[/C][C]0.052848[/C][C]0.4756[/C][C]0.317809[/C][/ROW]
[ROW][C]17[/C][C]-0.02086[/C][C]-0.1877[/C][C]0.425776[/C][/ROW]
[ROW][C]18[/C][C]0.049707[/C][C]0.4474[/C][C]0.327905[/C][/ROW]
[ROW][C]19[/C][C]-0.029135[/C][C]-0.2622[/C][C]0.39691[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164297&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164297&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	0.613744	5.5237	0
2	0.148109	1.333	0.093138
3	0.198442	1.786	0.038923
4	-0.207666	-1.869	0.032619
5	-0.040619	-0.3656	0.357818
6	0.064534	0.5808	0.281493
7	0.175488	1.5794	0.059072
8	0.101634	0.9147	0.18153
9	0.084432	0.7599	0.224763
10	-0.058265	-0.5244	0.30072
11	-0.193107	-1.738	0.043009
12	0.094969	0.8547	0.197613
13	-0.10125	-0.9112	0.182434
14	0.173985	1.5659	0.06064
15	0.016902	0.1521	0.439734
16	0.052848	0.4756	0.317809
17	-0.02086	-0.1877	0.425776
18	0.049707	0.4474	0.327905
19	-0.029135	-0.2622	0.39691

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 = 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 (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