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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 21 May 2015 21:01:05 +0100

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/2015/May/21/t14322384761itytcj4ip0ncwi.htm/, Retrieved Sat, 04 May 2024 19:00:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279206, Retrieved Sat, 04 May 2024 19:00:53 +0000

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Estimated Impact

131

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

-       [(Partial) Autocorrelation Function] [] [2015-05-21 20:01:05] [d87d05de12b09f00f3ae4d3dfdb2afe6] [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	'Sir Ronald Aylmer Fisher' @ fisher.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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279206&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279206&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279206&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.341185	3.127	0.001213
2	0.30172	2.7653	0.003495
3	-0.052857	-0.4844	0.314665
4	-0.084356	-0.7731	0.220806
5	-0.246467	-2.2589	0.01324
6	-0.099065	-0.9079	0.183252
7	-0.228716	-2.0962	0.019536
8	-0.088168	-0.8081	0.210666
9	-0.012813	-0.1174	0.4534
10	0.173154	1.587	0.058137
11	0.305125	2.7965	0.003201
12	0.436789	4.0032	6.7e-05
13	0.162709	1.4913	0.06982
14	0.225764	2.0692	0.020803
15	0.048039	0.4403	0.330432
16	-0.059297	-0.5435	0.294124
17	-0.173867	-1.5935	0.057401
18	-0.178202	-1.6332	0.05308
19	-0.246032	-2.2549	0.01337

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.341185 & 3.127 & 0.001213 \tabularnewline
2 & 0.30172 & 2.7653 & 0.003495 \tabularnewline
3 & -0.052857 & -0.4844 & 0.314665 \tabularnewline
4 & -0.084356 & -0.7731 & 0.220806 \tabularnewline
5 & -0.246467 & -2.2589 & 0.01324 \tabularnewline
6 & -0.099065 & -0.9079 & 0.183252 \tabularnewline
7 & -0.228716 & -2.0962 & 0.019536 \tabularnewline
8 & -0.088168 & -0.8081 & 0.210666 \tabularnewline
9 & -0.012813 & -0.1174 & 0.4534 \tabularnewline
10 & 0.173154 & 1.587 & 0.058137 \tabularnewline
11 & 0.305125 & 2.7965 & 0.003201 \tabularnewline
12 & 0.436789 & 4.0032 & 6.7e-05 \tabularnewline
13 & 0.162709 & 1.4913 & 0.06982 \tabularnewline
14 & 0.225764 & 2.0692 & 0.020803 \tabularnewline
15 & 0.048039 & 0.4403 & 0.330432 \tabularnewline
16 & -0.059297 & -0.5435 & 0.294124 \tabularnewline
17 & -0.173867 & -1.5935 & 0.057401 \tabularnewline
18 & -0.178202 & -1.6332 & 0.05308 \tabularnewline
19 & -0.246032 & -2.2549 & 0.01337 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279206&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]0.341185[/C][C]3.127[/C][C]0.001213[/C][/ROW]
[ROW][C]2[/C][C]0.30172[/C][C]2.7653[/C][C]0.003495[/C][/ROW]
[ROW][C]3[/C][C]-0.052857[/C][C]-0.4844[/C][C]0.314665[/C][/ROW]
[ROW][C]4[/C][C]-0.084356[/C][C]-0.7731[/C][C]0.220806[/C][/ROW]
[ROW][C]5[/C][C]-0.246467[/C][C]-2.2589[/C][C]0.01324[/C][/ROW]
[ROW][C]6[/C][C]-0.099065[/C][C]-0.9079[/C][C]0.183252[/C][/ROW]
[ROW][C]7[/C][C]-0.228716[/C][C]-2.0962[/C][C]0.019536[/C][/ROW]
[ROW][C]8[/C][C]-0.088168[/C][C]-0.8081[/C][C]0.210666[/C][/ROW]
[ROW][C]9[/C][C]-0.012813[/C][C]-0.1174[/C][C]0.4534[/C][/ROW]
[ROW][C]10[/C][C]0.173154[/C][C]1.587[/C][C]0.058137[/C][/ROW]
[ROW][C]11[/C][C]0.305125[/C][C]2.7965[/C][C]0.003201[/C][/ROW]
[ROW][C]12[/C][C]0.436789[/C][C]4.0032[/C][C]6.7e-05[/C][/ROW]
[ROW][C]13[/C][C]0.162709[/C][C]1.4913[/C][C]0.06982[/C][/ROW]
[ROW][C]14[/C][C]0.225764[/C][C]2.0692[/C][C]0.020803[/C][/ROW]
[ROW][C]15[/C][C]0.048039[/C][C]0.4403[/C][C]0.330432[/C][/ROW]
[ROW][C]16[/C][C]-0.059297[/C][C]-0.5435[/C][C]0.294124[/C][/ROW]
[ROW][C]17[/C][C]-0.173867[/C][C]-1.5935[/C][C]0.057401[/C][/ROW]
[ROW][C]18[/C][C]-0.178202[/C][C]-1.6332[/C][C]0.05308[/C][/ROW]
[ROW][C]19[/C][C]-0.246032[/C][C]-2.2549[/C][C]0.01337[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279206&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279206&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	0.341185	3.127	0.001213
2	0.30172	2.7653	0.003495
3	-0.052857	-0.4844	0.314665
4	-0.084356	-0.7731	0.220806
5	-0.246467	-2.2589	0.01324
6	-0.099065	-0.9079	0.183252
7	-0.228716	-2.0962	0.019536
8	-0.088168	-0.8081	0.210666
9	-0.012813	-0.1174	0.4534
10	0.173154	1.587	0.058137
11	0.305125	2.7965	0.003201
12	0.436789	4.0032	6.7e-05
13	0.162709	1.4913	0.06982
14	0.225764	2.0692	0.020803
15	0.048039	0.4403	0.330432
16	-0.059297	-0.5435	0.294124
17	-0.173867	-1.5935	0.057401
18	-0.178202	-1.6332	0.05308
19	-0.246032	-2.2549	0.01337

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.341185	3.127	0.001213
2	0.209726	1.9222	0.028987
3	-0.243588	-2.2325	0.014121
4	-0.08481	-0.7773	0.219585
5	-0.14088	-1.2912	0.10009
6	0.05983	0.5484	0.292452
7	-0.158628	-1.4538	0.074857
8	-0.037085	-0.3399	0.367393
9	0.112698	1.0329	0.152309
10	0.14482	1.3273	0.094003
11	0.222252	2.037	0.022401
12	0.226898	2.0796	0.020308
13	-0.157379	-1.4424	0.076454
14	0.150189	1.3765	0.086162
15	0.119536	1.0956	0.1382
16	-0.105309	-0.9652	0.168614
17	-0.062656	-0.5743	0.283666
18	-0.045419	-0.4163	0.339135
19	-0.012562	-0.1151	0.454307

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.341185 & 3.127 & 0.001213 \tabularnewline
2 & 0.209726 & 1.9222 & 0.028987 \tabularnewline
3 & -0.243588 & -2.2325 & 0.014121 \tabularnewline
4 & -0.08481 & -0.7773 & 0.219585 \tabularnewline
5 & -0.14088 & -1.2912 & 0.10009 \tabularnewline
6 & 0.05983 & 0.5484 & 0.292452 \tabularnewline
7 & -0.158628 & -1.4538 & 0.074857 \tabularnewline
8 & -0.037085 & -0.3399 & 0.367393 \tabularnewline
9 & 0.112698 & 1.0329 & 0.152309 \tabularnewline
10 & 0.14482 & 1.3273 & 0.094003 \tabularnewline
11 & 0.222252 & 2.037 & 0.022401 \tabularnewline
12 & 0.226898 & 2.0796 & 0.020308 \tabularnewline
13 & -0.157379 & -1.4424 & 0.076454 \tabularnewline
14 & 0.150189 & 1.3765 & 0.086162 \tabularnewline
15 & 0.119536 & 1.0956 & 0.1382 \tabularnewline
16 & -0.105309 & -0.9652 & 0.168614 \tabularnewline
17 & -0.062656 & -0.5743 & 0.283666 \tabularnewline
18 & -0.045419 & -0.4163 & 0.339135 \tabularnewline
19 & -0.012562 & -0.1151 & 0.454307 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279206&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]0.341185[/C][C]3.127[/C][C]0.001213[/C][/ROW]
[ROW][C]2[/C][C]0.209726[/C][C]1.9222[/C][C]0.028987[/C][/ROW]
[ROW][C]3[/C][C]-0.243588[/C][C]-2.2325[/C][C]0.014121[/C][/ROW]
[ROW][C]4[/C][C]-0.08481[/C][C]-0.7773[/C][C]0.219585[/C][/ROW]
[ROW][C]5[/C][C]-0.14088[/C][C]-1.2912[/C][C]0.10009[/C][/ROW]
[ROW][C]6[/C][C]0.05983[/C][C]0.5484[/C][C]0.292452[/C][/ROW]
[ROW][C]7[/C][C]-0.158628[/C][C]-1.4538[/C][C]0.074857[/C][/ROW]
[ROW][C]8[/C][C]-0.037085[/C][C]-0.3399[/C][C]0.367393[/C][/ROW]
[ROW][C]9[/C][C]0.112698[/C][C]1.0329[/C][C]0.152309[/C][/ROW]
[ROW][C]10[/C][C]0.14482[/C][C]1.3273[/C][C]0.094003[/C][/ROW]
[ROW][C]11[/C][C]0.222252[/C][C]2.037[/C][C]0.022401[/C][/ROW]
[ROW][C]12[/C][C]0.226898[/C][C]2.0796[/C][C]0.020308[/C][/ROW]
[ROW][C]13[/C][C]-0.157379[/C][C]-1.4424[/C][C]0.076454[/C][/ROW]
[ROW][C]14[/C][C]0.150189[/C][C]1.3765[/C][C]0.086162[/C][/ROW]
[ROW][C]15[/C][C]0.119536[/C][C]1.0956[/C][C]0.1382[/C][/ROW]
[ROW][C]16[/C][C]-0.105309[/C][C]-0.9652[/C][C]0.168614[/C][/ROW]
[ROW][C]17[/C][C]-0.062656[/C][C]-0.5743[/C][C]0.283666[/C][/ROW]
[ROW][C]18[/C][C]-0.045419[/C][C]-0.4163[/C][C]0.339135[/C][/ROW]
[ROW][C]19[/C][C]-0.012562[/C][C]-0.1151[/C][C]0.454307[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279206&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279206&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	0.341185	3.127	0.001213
2	0.209726	1.9222	0.028987
3	-0.243588	-2.2325	0.014121
4	-0.08481	-0.7773	0.219585
5	-0.14088	-1.2912	0.10009
6	0.05983	0.5484	0.292452
7	-0.158628	-1.4538	0.074857
8	-0.037085	-0.3399	0.367393
9	0.112698	1.0329	0.152309
10	0.14482	1.3273	0.094003
11	0.222252	2.037	0.022401
12	0.226898	2.0796	0.020308
13	-0.157379	-1.4424	0.076454
14	0.150189	1.3765	0.086162
15	0.119536	1.0956	0.1382
16	-0.105309	-0.9652	0.168614
17	-0.062656	-0.5743	0.283666
18	-0.045419	-0.4163	0.339135
19	-0.012562	-0.1151	0.454307

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code