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Author's title

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

Thu, 08 Nov 2012 19:14:05 -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/2012/Nov/08/t13524201420431gsk5qntaquc.htm/, Retrieved Mon, 29 Apr 2024 08:31:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=187001, Retrieved Mon, 29 Apr 2024 08:31:29 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-     [Classical Decomposition] [HPC Retail Sales] [2008-03-02 16:19:32] [74be16979710d4c4e7c6647856088456]
- RMPD    [(Partial) Autocorrelation Function] [autocorrelatie ] [2012-11-09 00:14:05] [18a55f974a2e8651a7d8da0218fcbdb6] [Current]

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Dataseries X:

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Histogram

Boxplots

14
14
15
13
8
7
3
3
4
4
0
-4
-14
-18
-8
-1
1
2
0
1
0
-1
-3
-3
-3
-4
-8
-9
-13
-18
-11
-9
-10
-13
-11
-5
-15
-6
-6
-3
-1
-3
-4
-6
0
-4
-2
-2
-6
-7
-6
-6
-3
-2
-5
-11
-11
-11
-10
-14
-8
-9
-5
-1
-2
-5
-4
-6
-2
-2
-2
-2
2
1
-8
-1
1
-1
2
2
1
-1
-2
-2
-1
-8
-4
-6
-3
-3
-7
-9
-11
-13
-11
-9
-17
-22
-25
-20
-24
-24
-22
-19
-18
-17
-11
-11
-12
-10
-15
-15
-15
-13
-8
-13
-9
-7
-4
-4
-2
0
-2
-3
1
-2
-1
1
-3
-4
-9
-9
-7
-14
-12
-16
-20
-12
-12
-10
-10
-13
-16

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187001&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]3 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=187001&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187001&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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.854329	10.2163	0
2	0.735018	8.7895	0
3	0.625246	7.4769	0
4	0.518413	6.1993	0
5	0.450879	5.3917	0
6	0.377483	4.514	7e-06
7	0.310815	3.7168	0.000144
8	0.219345	2.623	0.004831
9	0.13162	1.5739	0.058855
10	0.061121	0.7309	0.233018
11	0.011468	0.1371	0.445555
12	-0.017587	-0.2103	0.416864
13	-0.008135	-0.0973	0.461319
14	0.011565	0.1383	0.445098
15	0.0188	0.2248	0.411221
16	0.002666	0.0319	0.487308
17	-0.041293	-0.4938	0.311107
18	-0.072968	-0.8726	0.192179
19	-0.093894	-1.1228	0.131701
20	-0.126766	-1.5159	0.065875
21	-0.160141	-1.915	0.028744

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.854329 & 10.2163 & 0 \tabularnewline
2 & 0.735018 & 8.7895 & 0 \tabularnewline
3 & 0.625246 & 7.4769 & 0 \tabularnewline
4 & 0.518413 & 6.1993 & 0 \tabularnewline
5 & 0.450879 & 5.3917 & 0 \tabularnewline
6 & 0.377483 & 4.514 & 7e-06 \tabularnewline
7 & 0.310815 & 3.7168 & 0.000144 \tabularnewline
8 & 0.219345 & 2.623 & 0.004831 \tabularnewline
9 & 0.13162 & 1.5739 & 0.058855 \tabularnewline
10 & 0.061121 & 0.7309 & 0.233018 \tabularnewline
11 & 0.011468 & 0.1371 & 0.445555 \tabularnewline
12 & -0.017587 & -0.2103 & 0.416864 \tabularnewline
13 & -0.008135 & -0.0973 & 0.461319 \tabularnewline
14 & 0.011565 & 0.1383 & 0.445098 \tabularnewline
15 & 0.0188 & 0.2248 & 0.411221 \tabularnewline
16 & 0.002666 & 0.0319 & 0.487308 \tabularnewline
17 & -0.041293 & -0.4938 & 0.311107 \tabularnewline
18 & -0.072968 & -0.8726 & 0.192179 \tabularnewline
19 & -0.093894 & -1.1228 & 0.131701 \tabularnewline
20 & -0.126766 & -1.5159 & 0.065875 \tabularnewline
21 & -0.160141 & -1.915 & 0.028744 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187001&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]0.854329[/C][C]10.2163[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.735018[/C][C]8.7895[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.625246[/C][C]7.4769[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.518413[/C][C]6.1993[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.450879[/C][C]5.3917[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.377483[/C][C]4.514[/C][C]7e-06[/C][/ROW]
[ROW][C]7[/C][C]0.310815[/C][C]3.7168[/C][C]0.000144[/C][/ROW]
[ROW][C]8[/C][C]0.219345[/C][C]2.623[/C][C]0.004831[/C][/ROW]
[ROW][C]9[/C][C]0.13162[/C][C]1.5739[/C][C]0.058855[/C][/ROW]
[ROW][C]10[/C][C]0.061121[/C][C]0.7309[/C][C]0.233018[/C][/ROW]
[ROW][C]11[/C][C]0.011468[/C][C]0.1371[/C][C]0.445555[/C][/ROW]
[ROW][C]12[/C][C]-0.017587[/C][C]-0.2103[/C][C]0.416864[/C][/ROW]
[ROW][C]13[/C][C]-0.008135[/C][C]-0.0973[/C][C]0.461319[/C][/ROW]
[ROW][C]14[/C][C]0.011565[/C][C]0.1383[/C][C]0.445098[/C][/ROW]
[ROW][C]15[/C][C]0.0188[/C][C]0.2248[/C][C]0.411221[/C][/ROW]
[ROW][C]16[/C][C]0.002666[/C][C]0.0319[/C][C]0.487308[/C][/ROW]
[ROW][C]17[/C][C]-0.041293[/C][C]-0.4938[/C][C]0.311107[/C][/ROW]
[ROW][C]18[/C][C]-0.072968[/C][C]-0.8726[/C][C]0.192179[/C][/ROW]
[ROW][C]19[/C][C]-0.093894[/C][C]-1.1228[/C][C]0.131701[/C][/ROW]
[ROW][C]20[/C][C]-0.126766[/C][C]-1.5159[/C][C]0.065875[/C][/ROW]
[ROW][C]21[/C][C]-0.160141[/C][C]-1.915[/C][C]0.028744[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187001&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187001&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	0.854329	10.2163	0
2	0.735018	8.7895	0
3	0.625246	7.4769	0
4	0.518413	6.1993	0
5	0.450879	5.3917	0
6	0.377483	4.514	7e-06
7	0.310815	3.7168	0.000144
8	0.219345	2.623	0.004831
9	0.13162	1.5739	0.058855
10	0.061121	0.7309	0.233018
11	0.011468	0.1371	0.445555
12	-0.017587	-0.2103	0.416864
13	-0.008135	-0.0973	0.461319
14	0.011565	0.1383	0.445098
15	0.0188	0.2248	0.411221
16	0.002666	0.0319	0.487308
17	-0.041293	-0.4938	0.311107
18	-0.072968	-0.8726	0.192179
19	-0.093894	-1.1228	0.131701
20	-0.126766	-1.5159	0.065875
21	-0.160141	-1.915	0.028744

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.854329	10.2163	0
2	0.019031	0.2276	0.41015
3	-0.025958	-0.3104	0.378349
4	-0.050762	-0.607	0.2724
5	0.078781	0.9421	0.173869
6	-0.049135	-0.5876	0.278874
7	-0.023059	-0.2757	0.391571
8	-0.140428	-1.6793	0.047641
9	-0.053173	-0.6359	0.262941
10	-0.016089	-0.1924	0.423853
11	0.025125	0.3005	0.382135
12	0.012869	0.1539	0.438959
13	0.121641	1.4546	0.073984
14	0.057818	0.6914	0.245216
15	-0.011424	-0.1366	0.445766
16	-0.090988	-1.0881	0.1392
17	-0.126184	-1.5089	0.06676
18	-0.028089	-0.3359	0.36872
19	-0.01389	-0.1661	0.434156
20	-0.111491	-1.3332	0.092286
21	-0.077922	-0.9318	0.176503

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.854329 & 10.2163 & 0 \tabularnewline
2 & 0.019031 & 0.2276 & 0.41015 \tabularnewline
3 & -0.025958 & -0.3104 & 0.378349 \tabularnewline
4 & -0.050762 & -0.607 & 0.2724 \tabularnewline
5 & 0.078781 & 0.9421 & 0.173869 \tabularnewline
6 & -0.049135 & -0.5876 & 0.278874 \tabularnewline
7 & -0.023059 & -0.2757 & 0.391571 \tabularnewline
8 & -0.140428 & -1.6793 & 0.047641 \tabularnewline
9 & -0.053173 & -0.6359 & 0.262941 \tabularnewline
10 & -0.016089 & -0.1924 & 0.423853 \tabularnewline
11 & 0.025125 & 0.3005 & 0.382135 \tabularnewline
12 & 0.012869 & 0.1539 & 0.438959 \tabularnewline
13 & 0.121641 & 1.4546 & 0.073984 \tabularnewline
14 & 0.057818 & 0.6914 & 0.245216 \tabularnewline
15 & -0.011424 & -0.1366 & 0.445766 \tabularnewline
16 & -0.090988 & -1.0881 & 0.1392 \tabularnewline
17 & -0.126184 & -1.5089 & 0.06676 \tabularnewline
18 & -0.028089 & -0.3359 & 0.36872 \tabularnewline
19 & -0.01389 & -0.1661 & 0.434156 \tabularnewline
20 & -0.111491 & -1.3332 & 0.092286 \tabularnewline
21 & -0.077922 & -0.9318 & 0.176503 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187001&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]0.854329[/C][C]10.2163[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.019031[/C][C]0.2276[/C][C]0.41015[/C][/ROW]
[ROW][C]3[/C][C]-0.025958[/C][C]-0.3104[/C][C]0.378349[/C][/ROW]
[ROW][C]4[/C][C]-0.050762[/C][C]-0.607[/C][C]0.2724[/C][/ROW]
[ROW][C]5[/C][C]0.078781[/C][C]0.9421[/C][C]0.173869[/C][/ROW]
[ROW][C]6[/C][C]-0.049135[/C][C]-0.5876[/C][C]0.278874[/C][/ROW]
[ROW][C]7[/C][C]-0.023059[/C][C]-0.2757[/C][C]0.391571[/C][/ROW]
[ROW][C]8[/C][C]-0.140428[/C][C]-1.6793[/C][C]0.047641[/C][/ROW]
[ROW][C]9[/C][C]-0.053173[/C][C]-0.6359[/C][C]0.262941[/C][/ROW]
[ROW][C]10[/C][C]-0.016089[/C][C]-0.1924[/C][C]0.423853[/C][/ROW]
[ROW][C]11[/C][C]0.025125[/C][C]0.3005[/C][C]0.382135[/C][/ROW]
[ROW][C]12[/C][C]0.012869[/C][C]0.1539[/C][C]0.438959[/C][/ROW]
[ROW][C]13[/C][C]0.121641[/C][C]1.4546[/C][C]0.073984[/C][/ROW]
[ROW][C]14[/C][C]0.057818[/C][C]0.6914[/C][C]0.245216[/C][/ROW]
[ROW][C]15[/C][C]-0.011424[/C][C]-0.1366[/C][C]0.445766[/C][/ROW]
[ROW][C]16[/C][C]-0.090988[/C][C]-1.0881[/C][C]0.1392[/C][/ROW]
[ROW][C]17[/C][C]-0.126184[/C][C]-1.5089[/C][C]0.06676[/C][/ROW]
[ROW][C]18[/C][C]-0.028089[/C][C]-0.3359[/C][C]0.36872[/C][/ROW]
[ROW][C]19[/C][C]-0.01389[/C][C]-0.1661[/C][C]0.434156[/C][/ROW]
[ROW][C]20[/C][C]-0.111491[/C][C]-1.3332[/C][C]0.092286[/C][/ROW]
[ROW][C]21[/C][C]-0.077922[/C][C]-0.9318[/C][C]0.176503[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187001&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187001&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	0.854329	10.2163	0
2	0.019031	0.2276	0.41015
3	-0.025958	-0.3104	0.378349
4	-0.050762	-0.607	0.2724
5	0.078781	0.9421	0.173869
6	-0.049135	-0.5876	0.278874
7	-0.023059	-0.2757	0.391571
8	-0.140428	-1.6793	0.047641
9	-0.053173	-0.6359	0.262941
10	-0.016089	-0.1924	0.423853
11	0.025125	0.3005	0.382135
12	0.012869	0.1539	0.438959
13	0.121641	1.4546	0.073984
14	0.057818	0.6914	0.245216
15	-0.011424	-0.1366	0.445766
16	-0.090988	-1.0881	0.1392
17	-0.126184	-1.5089	0.06676
18	-0.028089	-0.3359	0.36872
19	-0.01389	-0.1661	0.434156
20	-0.111491	-1.3332	0.092286
21	-0.077922	-0.9318	0.176503

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