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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 21 Dec 2016 10:36:33 +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/Dec/21/t1482316615ss070ph2e2nvxi1.htm/, Retrieved Mon, 06 May 2024 14:22:17 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 06 May 2024 14:22:17 +0200

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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 Maurice George Kendall' @ kendall.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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.454008	-4.6963	4e-06
2	0.084671	0.8758	0.191538
3	-0.05575	-0.5767	0.282684
4	0.004661	0.0482	0.480818
5	0.016907	0.1749	0.430748
6	-0.169181	-1.75	0.041491
7	0.083629	0.8651	0.19447
8	-0.114669	-1.1861	0.119097
9	-0.053075	-0.549	0.292072
10	0.115846	1.1983	0.11672
11	-0.062861	-0.6502	0.258467
12	0.249059	2.5763	0.005675
13	-0.162624	-1.6822	0.047723
14	0.12011	1.2424	0.108397
15	-0.078497	-0.812	0.209303
16	0.051262	0.5303	0.298515
17	0.057758	0.5975	0.275732
18	-0.244773	-2.532	0.006398
19	0.122329	1.2654	0.104241
20	-0.056933	-0.5889	0.278577

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.454008 & -4.6963 & 4e-06 \tabularnewline
2 & 0.084671 & 0.8758 & 0.191538 \tabularnewline
3 & -0.05575 & -0.5767 & 0.282684 \tabularnewline
4 & 0.004661 & 0.0482 & 0.480818 \tabularnewline
5 & 0.016907 & 0.1749 & 0.430748 \tabularnewline
6 & -0.169181 & -1.75 & 0.041491 \tabularnewline
7 & 0.083629 & 0.8651 & 0.19447 \tabularnewline
8 & -0.114669 & -1.1861 & 0.119097 \tabularnewline
9 & -0.053075 & -0.549 & 0.292072 \tabularnewline
10 & 0.115846 & 1.1983 & 0.11672 \tabularnewline
11 & -0.062861 & -0.6502 & 0.258467 \tabularnewline
12 & 0.249059 & 2.5763 & 0.005675 \tabularnewline
13 & -0.162624 & -1.6822 & 0.047723 \tabularnewline
14 & 0.12011 & 1.2424 & 0.108397 \tabularnewline
15 & -0.078497 & -0.812 & 0.209303 \tabularnewline
16 & 0.051262 & 0.5303 & 0.298515 \tabularnewline
17 & 0.057758 & 0.5975 & 0.275732 \tabularnewline
18 & -0.244773 & -2.532 & 0.006398 \tabularnewline
19 & 0.122329 & 1.2654 & 0.104241 \tabularnewline
20 & -0.056933 & -0.5889 & 0.278577 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]-0.454008[/C][C]-4.6963[/C][C]4e-06[/C][/ROW]
[ROW][C]2[/C][C]0.084671[/C][C]0.8758[/C][C]0.191538[/C][/ROW]
[ROW][C]3[/C][C]-0.05575[/C][C]-0.5767[/C][C]0.282684[/C][/ROW]
[ROW][C]4[/C][C]0.004661[/C][C]0.0482[/C][C]0.480818[/C][/ROW]
[ROW][C]5[/C][C]0.016907[/C][C]0.1749[/C][C]0.430748[/C][/ROW]
[ROW][C]6[/C][C]-0.169181[/C][C]-1.75[/C][C]0.041491[/C][/ROW]
[ROW][C]7[/C][C]0.083629[/C][C]0.8651[/C][C]0.19447[/C][/ROW]
[ROW][C]8[/C][C]-0.114669[/C][C]-1.1861[/C][C]0.119097[/C][/ROW]
[ROW][C]9[/C][C]-0.053075[/C][C]-0.549[/C][C]0.292072[/C][/ROW]
[ROW][C]10[/C][C]0.115846[/C][C]1.1983[/C][C]0.11672[/C][/ROW]
[ROW][C]11[/C][C]-0.062861[/C][C]-0.6502[/C][C]0.258467[/C][/ROW]
[ROW][C]12[/C][C]0.249059[/C][C]2.5763[/C][C]0.005675[/C][/ROW]
[ROW][C]13[/C][C]-0.162624[/C][C]-1.6822[/C][C]0.047723[/C][/ROW]
[ROW][C]14[/C][C]0.12011[/C][C]1.2424[/C][C]0.108397[/C][/ROW]
[ROW][C]15[/C][C]-0.078497[/C][C]-0.812[/C][C]0.209303[/C][/ROW]
[ROW][C]16[/C][C]0.051262[/C][C]0.5303[/C][C]0.298515[/C][/ROW]
[ROW][C]17[/C][C]0.057758[/C][C]0.5975[/C][C]0.275732[/C][/ROW]
[ROW][C]18[/C][C]-0.244773[/C][C]-2.532[/C][C]0.006398[/C][/ROW]
[ROW][C]19[/C][C]0.122329[/C][C]1.2654[/C][C]0.104241[/C][/ROW]
[ROW][C]20[/C][C]-0.056933[/C][C]-0.5889[/C][C]0.278577[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	-0.454008	-4.6963	4e-06
2	0.084671	0.8758	0.191538
3	-0.05575	-0.5767	0.282684
4	0.004661	0.0482	0.480818
5	0.016907	0.1749	0.430748
6	-0.169181	-1.75	0.041491
7	0.083629	0.8651	0.19447
8	-0.114669	-1.1861	0.119097
9	-0.053075	-0.549	0.292072
10	0.115846	1.1983	0.11672
11	-0.062861	-0.6502	0.258467
12	0.249059	2.5763	0.005675
13	-0.162624	-1.6822	0.047723
14	0.12011	1.2424	0.108397
15	-0.078497	-0.812	0.209303
16	0.051262	0.5303	0.298515
17	0.057758	0.5975	0.275732
18	-0.244773	-2.532	0.006398
19	0.122329	1.2654	0.104241
20	-0.056933	-0.5889	0.278577

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.454008	-4.6963	4e-06
2	-0.152986	-1.5825	0.058244
3	-0.104326	-1.0792	0.141472
4	-0.071981	-0.7446	0.229081
5	-0.017707	-0.1832	0.427508
6	-0.220532	-2.2812	0.012258
7	-0.138568	-1.4334	0.077335
8	-0.215858	-2.2329	0.01382
9	-0.334413	-3.4592	0.00039
10	-0.18772	-1.9418	0.027396
11	-0.244118	-2.5252	0.006515
12	0.056621	0.5857	0.279657
13	-0.036399	-0.3765	0.353642
14	-0.007387	-0.0764	0.469618
15	-0.099185	-1.026	0.153608
16	-0.050905	-0.5266	0.299792
17	0.097196	1.0054	0.158485
18	-0.124631	-1.2892	0.100055
19	-0.051555	-0.5333	0.29747
20	0.034677	0.3587	0.360264

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.454008 & -4.6963 & 4e-06 \tabularnewline
2 & -0.152986 & -1.5825 & 0.058244 \tabularnewline
3 & -0.104326 & -1.0792 & 0.141472 \tabularnewline
4 & -0.071981 & -0.7446 & 0.229081 \tabularnewline
5 & -0.017707 & -0.1832 & 0.427508 \tabularnewline
6 & -0.220532 & -2.2812 & 0.012258 \tabularnewline
7 & -0.138568 & -1.4334 & 0.077335 \tabularnewline
8 & -0.215858 & -2.2329 & 0.01382 \tabularnewline
9 & -0.334413 & -3.4592 & 0.00039 \tabularnewline
10 & -0.18772 & -1.9418 & 0.027396 \tabularnewline
11 & -0.244118 & -2.5252 & 0.006515 \tabularnewline
12 & 0.056621 & 0.5857 & 0.279657 \tabularnewline
13 & -0.036399 & -0.3765 & 0.353642 \tabularnewline
14 & -0.007387 & -0.0764 & 0.469618 \tabularnewline
15 & -0.099185 & -1.026 & 0.153608 \tabularnewline
16 & -0.050905 & -0.5266 & 0.299792 \tabularnewline
17 & 0.097196 & 1.0054 & 0.158485 \tabularnewline
18 & -0.124631 & -1.2892 & 0.100055 \tabularnewline
19 & -0.051555 & -0.5333 & 0.29747 \tabularnewline
20 & 0.034677 & 0.3587 & 0.360264 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]-0.454008[/C][C]-4.6963[/C][C]4e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.152986[/C][C]-1.5825[/C][C]0.058244[/C][/ROW]
[ROW][C]3[/C][C]-0.104326[/C][C]-1.0792[/C][C]0.141472[/C][/ROW]
[ROW][C]4[/C][C]-0.071981[/C][C]-0.7446[/C][C]0.229081[/C][/ROW]
[ROW][C]5[/C][C]-0.017707[/C][C]-0.1832[/C][C]0.427508[/C][/ROW]
[ROW][C]6[/C][C]-0.220532[/C][C]-2.2812[/C][C]0.012258[/C][/ROW]
[ROW][C]7[/C][C]-0.138568[/C][C]-1.4334[/C][C]0.077335[/C][/ROW]
[ROW][C]8[/C][C]-0.215858[/C][C]-2.2329[/C][C]0.01382[/C][/ROW]
[ROW][C]9[/C][C]-0.334413[/C][C]-3.4592[/C][C]0.00039[/C][/ROW]
[ROW][C]10[/C][C]-0.18772[/C][C]-1.9418[/C][C]0.027396[/C][/ROW]
[ROW][C]11[/C][C]-0.244118[/C][C]-2.5252[/C][C]0.006515[/C][/ROW]
[ROW][C]12[/C][C]0.056621[/C][C]0.5857[/C][C]0.279657[/C][/ROW]
[ROW][C]13[/C][C]-0.036399[/C][C]-0.3765[/C][C]0.353642[/C][/ROW]
[ROW][C]14[/C][C]-0.007387[/C][C]-0.0764[/C][C]0.469618[/C][/ROW]
[ROW][C]15[/C][C]-0.099185[/C][C]-1.026[/C][C]0.153608[/C][/ROW]
[ROW][C]16[/C][C]-0.050905[/C][C]-0.5266[/C][C]0.299792[/C][/ROW]
[ROW][C]17[/C][C]0.097196[/C][C]1.0054[/C][C]0.158485[/C][/ROW]
[ROW][C]18[/C][C]-0.124631[/C][C]-1.2892[/C][C]0.100055[/C][/ROW]
[ROW][C]19[/C][C]-0.051555[/C][C]-0.5333[/C][C]0.29747[/C][/ROW]
[ROW][C]20[/C][C]0.034677[/C][C]0.3587[/C][C]0.360264[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	-0.454008	-4.6963	4e-06
2	-0.152986	-1.5825	0.058244
3	-0.104326	-1.0792	0.141472
4	-0.071981	-0.7446	0.229081
5	-0.017707	-0.1832	0.427508
6	-0.220532	-2.2812	0.012258
7	-0.138568	-1.4334	0.077335
8	-0.215858	-2.2329	0.01382
9	-0.334413	-3.4592	0.00039
10	-0.18772	-1.9418	0.027396
11	-0.244118	-2.5252	0.006515
12	0.056621	0.5857	0.279657
13	-0.036399	-0.3765	0.353642
14	-0.007387	-0.0764	0.469618
15	-0.099185	-1.026	0.153608
16	-0.050905	-0.5266	0.299792
17	0.097196	1.0054	0.158485
18	-0.124631	-1.2892	0.100055
19	-0.051555	-0.5333	0.29747
20	0.034677	0.3587	0.360264

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 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code