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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 08 Mar 2016 13:51:00 +0000

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/2016/Mar/08/t1457445121ag6o11tbh5wchxk.htm/, Retrieved Sun, 28 Apr 2024 20:47:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293675, Retrieved Sun, 28 Apr 2024 20:47:19 +0000

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Estimated Impact

118

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-       [(Partial) Autocorrelation Function] [] [2016-03-08 13:51:00] [1af9caed13b550360754d0d82088541b] [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	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293675&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293675&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293675&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' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.963804	8.1782	0
2	0.929559	7.8876	0
3	0.887415	7.53	0
4	0.843194	7.1547	0
5	0.808878	6.8636	0
6	0.759033	6.4406	0
7	0.704715	5.9797	0
8	0.646895	5.4891	0
9	0.592174	5.0248	2e-06
10	0.537867	4.564	1e-05
11	0.491605	4.1714	4.2e-05
12	0.436498	3.7038	0.000207
13	0.380866	3.2318	0.000928
14	0.32106	2.7243	0.004041
15	0.257097	2.1815	0.016205
16	0.196243	1.6652	0.050112
17	0.137255	1.1646	0.124003
18	0.08423	0.7147	0.238547

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.963804 & 8.1782 & 0 \tabularnewline
2 & 0.929559 & 7.8876 & 0 \tabularnewline
3 & 0.887415 & 7.53 & 0 \tabularnewline
4 & 0.843194 & 7.1547 & 0 \tabularnewline
5 & 0.808878 & 6.8636 & 0 \tabularnewline
6 & 0.759033 & 6.4406 & 0 \tabularnewline
7 & 0.704715 & 5.9797 & 0 \tabularnewline
8 & 0.646895 & 5.4891 & 0 \tabularnewline
9 & 0.592174 & 5.0248 & 2e-06 \tabularnewline
10 & 0.537867 & 4.564 & 1e-05 \tabularnewline
11 & 0.491605 & 4.1714 & 4.2e-05 \tabularnewline
12 & 0.436498 & 3.7038 & 0.000207 \tabularnewline
13 & 0.380866 & 3.2318 & 0.000928 \tabularnewline
14 & 0.32106 & 2.7243 & 0.004041 \tabularnewline
15 & 0.257097 & 2.1815 & 0.016205 \tabularnewline
16 & 0.196243 & 1.6652 & 0.050112 \tabularnewline
17 & 0.137255 & 1.1646 & 0.124003 \tabularnewline
18 & 0.08423 & 0.7147 & 0.238547 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293675&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]0.963804[/C][C]8.1782[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.929559[/C][C]7.8876[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.887415[/C][C]7.53[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.843194[/C][C]7.1547[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.808878[/C][C]6.8636[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.759033[/C][C]6.4406[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.704715[/C][C]5.9797[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.646895[/C][C]5.4891[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.592174[/C][C]5.0248[/C][C]2e-06[/C][/ROW]
[ROW][C]10[/C][C]0.537867[/C][C]4.564[/C][C]1e-05[/C][/ROW]
[ROW][C]11[/C][C]0.491605[/C][C]4.1714[/C][C]4.2e-05[/C][/ROW]
[ROW][C]12[/C][C]0.436498[/C][C]3.7038[/C][C]0.000207[/C][/ROW]
[ROW][C]13[/C][C]0.380866[/C][C]3.2318[/C][C]0.000928[/C][/ROW]
[ROW][C]14[/C][C]0.32106[/C][C]2.7243[/C][C]0.004041[/C][/ROW]
[ROW][C]15[/C][C]0.257097[/C][C]2.1815[/C][C]0.016205[/C][/ROW]
[ROW][C]16[/C][C]0.196243[/C][C]1.6652[/C][C]0.050112[/C][/ROW]
[ROW][C]17[/C][C]0.137255[/C][C]1.1646[/C][C]0.124003[/C][/ROW]
[ROW][C]18[/C][C]0.08423[/C][C]0.7147[/C][C]0.238547[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293675&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293675&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	0.963804	8.1782	0
2	0.929559	7.8876	0
3	0.887415	7.53	0
4	0.843194	7.1547	0
5	0.808878	6.8636	0
6	0.759033	6.4406	0
7	0.704715	5.9797	0
8	0.646895	5.4891	0
9	0.592174	5.0248	2e-06
10	0.537867	4.564	1e-05
11	0.491605	4.1714	4.2e-05
12	0.436498	3.7038	0.000207
13	0.380866	3.2318	0.000928
14	0.32106	2.7243	0.004041
15	0.257097	2.1815	0.016205
16	0.196243	1.6652	0.050112
17	0.137255	1.1646	0.124003
18	0.08423	0.7147	0.238547

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.963804	8.1782	0
2	0.009004	0.0764	0.469654
3	-0.128156	-1.0874	0.140235
4	-0.058064	-0.4927	0.311867
5	0.127949	1.0857	0.14062
6	-0.230501	-1.9559	0.027181
7	-0.138186	-1.1726	0.122421
8	-0.044188	-0.3749	0.354402
9	0.063075	0.5352	0.297076
10	-0.083846	-0.7115	0.239551
11	0.091265	0.7744	0.220613
12	-0.135531	-1.15	0.126972
13	-0.036819	-0.3124	0.377813
14	-0.117261	-0.995	0.161536
15	-0.067367	-0.5716	0.284676
16	-0.091769	-0.7787	0.219358
17	0.032612	0.2767	0.391395
18	0.029562	0.2508	0.401325

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.963804 & 8.1782 & 0 \tabularnewline
2 & 0.009004 & 0.0764 & 0.469654 \tabularnewline
3 & -0.128156 & -1.0874 & 0.140235 \tabularnewline
4 & -0.058064 & -0.4927 & 0.311867 \tabularnewline
5 & 0.127949 & 1.0857 & 0.14062 \tabularnewline
6 & -0.230501 & -1.9559 & 0.027181 \tabularnewline
7 & -0.138186 & -1.1726 & 0.122421 \tabularnewline
8 & -0.044188 & -0.3749 & 0.354402 \tabularnewline
9 & 0.063075 & 0.5352 & 0.297076 \tabularnewline
10 & -0.083846 & -0.7115 & 0.239551 \tabularnewline
11 & 0.091265 & 0.7744 & 0.220613 \tabularnewline
12 & -0.135531 & -1.15 & 0.126972 \tabularnewline
13 & -0.036819 & -0.3124 & 0.377813 \tabularnewline
14 & -0.117261 & -0.995 & 0.161536 \tabularnewline
15 & -0.067367 & -0.5716 & 0.284676 \tabularnewline
16 & -0.091769 & -0.7787 & 0.219358 \tabularnewline
17 & 0.032612 & 0.2767 & 0.391395 \tabularnewline
18 & 0.029562 & 0.2508 & 0.401325 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293675&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]0.963804[/C][C]8.1782[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.009004[/C][C]0.0764[/C][C]0.469654[/C][/ROW]
[ROW][C]3[/C][C]-0.128156[/C][C]-1.0874[/C][C]0.140235[/C][/ROW]
[ROW][C]4[/C][C]-0.058064[/C][C]-0.4927[/C][C]0.311867[/C][/ROW]
[ROW][C]5[/C][C]0.127949[/C][C]1.0857[/C][C]0.14062[/C][/ROW]
[ROW][C]6[/C][C]-0.230501[/C][C]-1.9559[/C][C]0.027181[/C][/ROW]
[ROW][C]7[/C][C]-0.138186[/C][C]-1.1726[/C][C]0.122421[/C][/ROW]
[ROW][C]8[/C][C]-0.044188[/C][C]-0.3749[/C][C]0.354402[/C][/ROW]
[ROW][C]9[/C][C]0.063075[/C][C]0.5352[/C][C]0.297076[/C][/ROW]
[ROW][C]10[/C][C]-0.083846[/C][C]-0.7115[/C][C]0.239551[/C][/ROW]
[ROW][C]11[/C][C]0.091265[/C][C]0.7744[/C][C]0.220613[/C][/ROW]
[ROW][C]12[/C][C]-0.135531[/C][C]-1.15[/C][C]0.126972[/C][/ROW]
[ROW][C]13[/C][C]-0.036819[/C][C]-0.3124[/C][C]0.377813[/C][/ROW]
[ROW][C]14[/C][C]-0.117261[/C][C]-0.995[/C][C]0.161536[/C][/ROW]
[ROW][C]15[/C][C]-0.067367[/C][C]-0.5716[/C][C]0.284676[/C][/ROW]
[ROW][C]16[/C][C]-0.091769[/C][C]-0.7787[/C][C]0.219358[/C][/ROW]
[ROW][C]17[/C][C]0.032612[/C][C]0.2767[/C][C]0.391395[/C][/ROW]
[ROW][C]18[/C][C]0.029562[/C][C]0.2508[/C][C]0.401325[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293675&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293675&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	0.963804	8.1782	0
2	0.009004	0.0764	0.469654
3	-0.128156	-1.0874	0.140235
4	-0.058064	-0.4927	0.311867
5	0.127949	1.0857	0.14062
6	-0.230501	-1.9559	0.027181
7	-0.138186	-1.1726	0.122421
8	-0.044188	-0.3749	0.354402
9	0.063075	0.5352	0.297076
10	-0.083846	-0.7115	0.239551
11	0.091265	0.7744	0.220613
12	-0.135531	-1.15	0.126972
13	-0.036819	-0.3124	0.377813
14	-0.117261	-0.995	0.161536
15	-0.067367	-0.5716	0.284676
16	-0.091769	-0.7787	0.219358
17	0.032612	0.2767	0.391395
18	0.029562	0.2508	0.401325

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)
x <- na.omit(x)
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')

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Input Parameters & R Code