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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 05 Dec 2011 14:06:51 -0500

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/2011/Dec/05/t1323112019ehyz6seg5t93n0h.htm/, Retrieved Fri, 03 May 2024 07:37:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151186, Retrieved Fri, 03 May 2024 07:37:04 +0000

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Estimated Impact

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

-       [(Partial) Autocorrelation Function] [] [2011-12-05 19:06:51] [4cf172296f32adf71d8383c359dbb80f] [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	'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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151186&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151186&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151186&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.115841	1.4835	0.069931
2	0.146511	1.8763	0.031198
3	0.106961	1.3698	0.086316
4	0.109361	1.4005	0.081626
5	0.219191	2.807	0.002803
6	0.085356	1.0931	0.13798
7	0.044249	0.5667	0.285857
8	0.106592	1.365	0.087055
9	0.106166	1.3596	0.087913
10	0.089915	1.1515	0.125606
11	0.039052	0.5001	0.308836
12	0.014953	0.1915	0.42419
13	0.07343	0.9404	0.174206
14	-0.02084	-0.2669	0.394948
15	-0.048545	-0.6217	0.267508
16	-0.117895	-1.5098	0.06651
17	-0.153814	-1.9698	0.025274
18	0.023851	0.3054	0.380206
19	-0.02527	-0.3236	0.37332
20	-0.06444	-0.8252	0.205217
21	-0.015378	-0.1969	0.422063
22	-0.161619	-2.0697	0.020023

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.115841 & 1.4835 & 0.069931 \tabularnewline
2 & 0.146511 & 1.8763 & 0.031198 \tabularnewline
3 & 0.106961 & 1.3698 & 0.086316 \tabularnewline
4 & 0.109361 & 1.4005 & 0.081626 \tabularnewline
5 & 0.219191 & 2.807 & 0.002803 \tabularnewline
6 & 0.085356 & 1.0931 & 0.13798 \tabularnewline
7 & 0.044249 & 0.5667 & 0.285857 \tabularnewline
8 & 0.106592 & 1.365 & 0.087055 \tabularnewline
9 & 0.106166 & 1.3596 & 0.087913 \tabularnewline
10 & 0.089915 & 1.1515 & 0.125606 \tabularnewline
11 & 0.039052 & 0.5001 & 0.308836 \tabularnewline
12 & 0.014953 & 0.1915 & 0.42419 \tabularnewline
13 & 0.07343 & 0.9404 & 0.174206 \tabularnewline
14 & -0.02084 & -0.2669 & 0.394948 \tabularnewline
15 & -0.048545 & -0.6217 & 0.267508 \tabularnewline
16 & -0.117895 & -1.5098 & 0.06651 \tabularnewline
17 & -0.153814 & -1.9698 & 0.025274 \tabularnewline
18 & 0.023851 & 0.3054 & 0.380206 \tabularnewline
19 & -0.02527 & -0.3236 & 0.37332 \tabularnewline
20 & -0.06444 & -0.8252 & 0.205217 \tabularnewline
21 & -0.015378 & -0.1969 & 0.422063 \tabularnewline
22 & -0.161619 & -2.0697 & 0.020023 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151186&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]0.115841[/C][C]1.4835[/C][C]0.069931[/C][/ROW]
[ROW][C]2[/C][C]0.146511[/C][C]1.8763[/C][C]0.031198[/C][/ROW]
[ROW][C]3[/C][C]0.106961[/C][C]1.3698[/C][C]0.086316[/C][/ROW]
[ROW][C]4[/C][C]0.109361[/C][C]1.4005[/C][C]0.081626[/C][/ROW]
[ROW][C]5[/C][C]0.219191[/C][C]2.807[/C][C]0.002803[/C][/ROW]
[ROW][C]6[/C][C]0.085356[/C][C]1.0931[/C][C]0.13798[/C][/ROW]
[ROW][C]7[/C][C]0.044249[/C][C]0.5667[/C][C]0.285857[/C][/ROW]
[ROW][C]8[/C][C]0.106592[/C][C]1.365[/C][C]0.087055[/C][/ROW]
[ROW][C]9[/C][C]0.106166[/C][C]1.3596[/C][C]0.087913[/C][/ROW]
[ROW][C]10[/C][C]0.089915[/C][C]1.1515[/C][C]0.125606[/C][/ROW]
[ROW][C]11[/C][C]0.039052[/C][C]0.5001[/C][C]0.308836[/C][/ROW]
[ROW][C]12[/C][C]0.014953[/C][C]0.1915[/C][C]0.42419[/C][/ROW]
[ROW][C]13[/C][C]0.07343[/C][C]0.9404[/C][C]0.174206[/C][/ROW]
[ROW][C]14[/C][C]-0.02084[/C][C]-0.2669[/C][C]0.394948[/C][/ROW]
[ROW][C]15[/C][C]-0.048545[/C][C]-0.6217[/C][C]0.267508[/C][/ROW]
[ROW][C]16[/C][C]-0.117895[/C][C]-1.5098[/C][C]0.06651[/C][/ROW]
[ROW][C]17[/C][C]-0.153814[/C][C]-1.9698[/C][C]0.025274[/C][/ROW]
[ROW][C]18[/C][C]0.023851[/C][C]0.3054[/C][C]0.380206[/C][/ROW]
[ROW][C]19[/C][C]-0.02527[/C][C]-0.3236[/C][C]0.37332[/C][/ROW]
[ROW][C]20[/C][C]-0.06444[/C][C]-0.8252[/C][C]0.205217[/C][/ROW]
[ROW][C]21[/C][C]-0.015378[/C][C]-0.1969[/C][C]0.422063[/C][/ROW]
[ROW][C]22[/C][C]-0.161619[/C][C]-2.0697[/C][C]0.020023[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151186&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151186&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	0.115841	1.4835	0.069931
2	0.146511	1.8763	0.031198
3	0.106961	1.3698	0.086316
4	0.109361	1.4005	0.081626
5	0.219191	2.807	0.002803
6	0.085356	1.0931	0.13798
7	0.044249	0.5667	0.285857
8	0.106592	1.365	0.087055
9	0.106166	1.3596	0.087913
10	0.089915	1.1515	0.125606
11	0.039052	0.5001	0.308836
12	0.014953	0.1915	0.42419
13	0.07343	0.9404	0.174206
14	-0.02084	-0.2669	0.394948
15	-0.048545	-0.6217	0.267508
16	-0.117895	-1.5098	0.06651
17	-0.153814	-1.9698	0.025274
18	0.023851	0.3054	0.380206
19	-0.02527	-0.3236	0.37332
20	-0.06444	-0.8252	0.205217
21	-0.015378	-0.1969	0.422063
22	-0.161619	-2.0697	0.020023

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.115841	1.4835	0.069931
2	0.134902	1.7276	0.042972
3	0.079134	1.0134	0.15618
4	0.074815	0.9581	0.169711
5	0.186176	2.3842	0.009129
6	0.024949	0.3195	0.374878
7	-0.02722	-0.3486	0.363925
8	0.060939	0.7804	0.21814
9	0.058975	0.7552	0.225592
10	0.014701	0.1883	0.425449
11	-0.016338	-0.2092	0.417263
12	-0.022222	-0.2846	0.388163
13	0.029072	0.3723	0.355074
14	-0.075656	-0.9689	0.167018
15	-0.085999	-1.1013	0.136186
16	-0.127414	-1.6317	0.052331
17	-0.152286	-1.9502	0.026428
18	0.049537	0.6344	0.263358
19	0.029646	0.3797	0.352346
20	-0.018128	-0.2322	0.408354
21	0.054885	0.7029	0.241565
22	-0.104757	-1.3415	0.0908

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.115841 & 1.4835 & 0.069931 \tabularnewline
2 & 0.134902 & 1.7276 & 0.042972 \tabularnewline
3 & 0.079134 & 1.0134 & 0.15618 \tabularnewline
4 & 0.074815 & 0.9581 & 0.169711 \tabularnewline
5 & 0.186176 & 2.3842 & 0.009129 \tabularnewline
6 & 0.024949 & 0.3195 & 0.374878 \tabularnewline
7 & -0.02722 & -0.3486 & 0.363925 \tabularnewline
8 & 0.060939 & 0.7804 & 0.21814 \tabularnewline
9 & 0.058975 & 0.7552 & 0.225592 \tabularnewline
10 & 0.014701 & 0.1883 & 0.425449 \tabularnewline
11 & -0.016338 & -0.2092 & 0.417263 \tabularnewline
12 & -0.022222 & -0.2846 & 0.388163 \tabularnewline
13 & 0.029072 & 0.3723 & 0.355074 \tabularnewline
14 & -0.075656 & -0.9689 & 0.167018 \tabularnewline
15 & -0.085999 & -1.1013 & 0.136186 \tabularnewline
16 & -0.127414 & -1.6317 & 0.052331 \tabularnewline
17 & -0.152286 & -1.9502 & 0.026428 \tabularnewline
18 & 0.049537 & 0.6344 & 0.263358 \tabularnewline
19 & 0.029646 & 0.3797 & 0.352346 \tabularnewline
20 & -0.018128 & -0.2322 & 0.408354 \tabularnewline
21 & 0.054885 & 0.7029 & 0.241565 \tabularnewline
22 & -0.104757 & -1.3415 & 0.0908 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151186&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]0.115841[/C][C]1.4835[/C][C]0.069931[/C][/ROW]
[ROW][C]2[/C][C]0.134902[/C][C]1.7276[/C][C]0.042972[/C][/ROW]
[ROW][C]3[/C][C]0.079134[/C][C]1.0134[/C][C]0.15618[/C][/ROW]
[ROW][C]4[/C][C]0.074815[/C][C]0.9581[/C][C]0.169711[/C][/ROW]
[ROW][C]5[/C][C]0.186176[/C][C]2.3842[/C][C]0.009129[/C][/ROW]
[ROW][C]6[/C][C]0.024949[/C][C]0.3195[/C][C]0.374878[/C][/ROW]
[ROW][C]7[/C][C]-0.02722[/C][C]-0.3486[/C][C]0.363925[/C][/ROW]
[ROW][C]8[/C][C]0.060939[/C][C]0.7804[/C][C]0.21814[/C][/ROW]
[ROW][C]9[/C][C]0.058975[/C][C]0.7552[/C][C]0.225592[/C][/ROW]
[ROW][C]10[/C][C]0.014701[/C][C]0.1883[/C][C]0.425449[/C][/ROW]
[ROW][C]11[/C][C]-0.016338[/C][C]-0.2092[/C][C]0.417263[/C][/ROW]
[ROW][C]12[/C][C]-0.022222[/C][C]-0.2846[/C][C]0.388163[/C][/ROW]
[ROW][C]13[/C][C]0.029072[/C][C]0.3723[/C][C]0.355074[/C][/ROW]
[ROW][C]14[/C][C]-0.075656[/C][C]-0.9689[/C][C]0.167018[/C][/ROW]
[ROW][C]15[/C][C]-0.085999[/C][C]-1.1013[/C][C]0.136186[/C][/ROW]
[ROW][C]16[/C][C]-0.127414[/C][C]-1.6317[/C][C]0.052331[/C][/ROW]
[ROW][C]17[/C][C]-0.152286[/C][C]-1.9502[/C][C]0.026428[/C][/ROW]
[ROW][C]18[/C][C]0.049537[/C][C]0.6344[/C][C]0.263358[/C][/ROW]
[ROW][C]19[/C][C]0.029646[/C][C]0.3797[/C][C]0.352346[/C][/ROW]
[ROW][C]20[/C][C]-0.018128[/C][C]-0.2322[/C][C]0.408354[/C][/ROW]
[ROW][C]21[/C][C]0.054885[/C][C]0.7029[/C][C]0.241565[/C][/ROW]
[ROW][C]22[/C][C]-0.104757[/C][C]-1.3415[/C][C]0.0908[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151186&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151186&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	0.115841	1.4835	0.069931
2	0.134902	1.7276	0.042972
3	0.079134	1.0134	0.15618
4	0.074815	0.9581	0.169711
5	0.186176	2.3842	0.009129
6	0.024949	0.3195	0.374878
7	-0.02722	-0.3486	0.363925
8	0.060939	0.7804	0.21814
9	0.058975	0.7552	0.225592
10	0.014701	0.1883	0.425449
11	-0.016338	-0.2092	0.417263
12	-0.022222	-0.2846	0.388163
13	0.029072	0.3723	0.355074
14	-0.075656	-0.9689	0.167018
15	-0.085999	-1.1013	0.136186
16	-0.127414	-1.6317	0.052331
17	-0.152286	-1.9502	0.026428
18	0.049537	0.6344	0.263358
19	0.029646	0.3797	0.352346
20	-0.018128	-0.2322	0.408354
21	0.054885	0.7029	0.241565
22	-0.104757	-1.3415	0.0908

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