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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 05 Mar 2015 17:57:41 +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/2015/Mar/05/t14255783282pf64gynxpzh6fs.htm/, Retrieved Fri, 17 May 2024 04:10:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=277979, Retrieved Fri, 17 May 2024 04:10:19 +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)

-       [(Partial) Autocorrelation Function] [] [2015-03-05 17:57:41] [3b0947f879d0db9a6034293524e1b6d0] [Current]

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Dataseries X:

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Histogram

Boxplots

6
6.7
-0.6
5.8
16.4
1.5
5.1
14.7
4.3
1.5
9.1
4.3
5.7
13
14.5
9.7
-4.7
7.3
5.2
-2.5
11.5
4.9
-2.4
-0.3
4.4
7.9
-9.7
-4.1
16.4
-4.9
3.5
3.8
-0.2
3.1
0.7
-2.8
5.9
-5.3
-2.9
6.6
-8.1
1.3
6.9
-7.2
-1.9
4
-5.7
3.9
-7.6
-0.9
7.3
-3.7
-2.5
9.3
1.3
9.5
11.3
-1.7
8
-4.8
1.6
1.9
-0.9
5.5
1.7
-5.4
1.9
0.2
-13.3
-8.2
0.2
5.7
-1.2
-2.8
5.5
-17.3
1.4
-2.2
-8.6
-5
4.1
0.7
-4.2
-2.3
-3.4
-4.2
-14.2
1.6
-4.9
-1.8
-0.5
-2.3
-5.3
-0.2
5.1
-1.5

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	'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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277979&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277979&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277979&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.496675	-4.841	2e-06
2	-0.226152	-2.2043	0.014961
3	0.428352	4.1751	3.3e-05
4	-0.231625	-2.2576	0.01313
5	-0.022766	-0.2219	0.412436
6	0.061356	0.598	0.275624
7	-0.068546	-0.6681	0.252843
8	0.186765	1.8204	0.035926
9	-0.20611	-2.0089	0.023692
10	-0.029313	-0.2857	0.38786
11	0.437269	4.262	2.4e-05
12	-0.541447	-5.2774	0
13	0.128038	1.248	0.107557
14	0.288215	2.8092	0.003015
15	-0.343903	-3.352	0.000577
16	0.095602	0.9318	0.176898
17	0.114361	1.1147	0.133906
18	-0.053629	-0.5227	0.301196
19	-0.004192	-0.0409	0.483746

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.496675 & -4.841 & 2e-06 \tabularnewline
2 & -0.226152 & -2.2043 & 0.014961 \tabularnewline
3 & 0.428352 & 4.1751 & 3.3e-05 \tabularnewline
4 & -0.231625 & -2.2576 & 0.01313 \tabularnewline
5 & -0.022766 & -0.2219 & 0.412436 \tabularnewline
6 & 0.061356 & 0.598 & 0.275624 \tabularnewline
7 & -0.068546 & -0.6681 & 0.252843 \tabularnewline
8 & 0.186765 & 1.8204 & 0.035926 \tabularnewline
9 & -0.20611 & -2.0089 & 0.023692 \tabularnewline
10 & -0.029313 & -0.2857 & 0.38786 \tabularnewline
11 & 0.437269 & 4.262 & 2.4e-05 \tabularnewline
12 & -0.541447 & -5.2774 & 0 \tabularnewline
13 & 0.128038 & 1.248 & 0.107557 \tabularnewline
14 & 0.288215 & 2.8092 & 0.003015 \tabularnewline
15 & -0.343903 & -3.352 & 0.000577 \tabularnewline
16 & 0.095602 & 0.9318 & 0.176898 \tabularnewline
17 & 0.114361 & 1.1147 & 0.133906 \tabularnewline
18 & -0.053629 & -0.5227 & 0.301196 \tabularnewline
19 & -0.004192 & -0.0409 & 0.483746 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277979&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]-0.496675[/C][C]-4.841[/C][C]2e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.226152[/C][C]-2.2043[/C][C]0.014961[/C][/ROW]
[ROW][C]3[/C][C]0.428352[/C][C]4.1751[/C][C]3.3e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.231625[/C][C]-2.2576[/C][C]0.01313[/C][/ROW]
[ROW][C]5[/C][C]-0.022766[/C][C]-0.2219[/C][C]0.412436[/C][/ROW]
[ROW][C]6[/C][C]0.061356[/C][C]0.598[/C][C]0.275624[/C][/ROW]
[ROW][C]7[/C][C]-0.068546[/C][C]-0.6681[/C][C]0.252843[/C][/ROW]
[ROW][C]8[/C][C]0.186765[/C][C]1.8204[/C][C]0.035926[/C][/ROW]
[ROW][C]9[/C][C]-0.20611[/C][C]-2.0089[/C][C]0.023692[/C][/ROW]
[ROW][C]10[/C][C]-0.029313[/C][C]-0.2857[/C][C]0.38786[/C][/ROW]
[ROW][C]11[/C][C]0.437269[/C][C]4.262[/C][C]2.4e-05[/C][/ROW]
[ROW][C]12[/C][C]-0.541447[/C][C]-5.2774[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.128038[/C][C]1.248[/C][C]0.107557[/C][/ROW]
[ROW][C]14[/C][C]0.288215[/C][C]2.8092[/C][C]0.003015[/C][/ROW]
[ROW][C]15[/C][C]-0.343903[/C][C]-3.352[/C][C]0.000577[/C][/ROW]
[ROW][C]16[/C][C]0.095602[/C][C]0.9318[/C][C]0.176898[/C][/ROW]
[ROW][C]17[/C][C]0.114361[/C][C]1.1147[/C][C]0.133906[/C][/ROW]
[ROW][C]18[/C][C]-0.053629[/C][C]-0.5227[/C][C]0.301196[/C][/ROW]
[ROW][C]19[/C][C]-0.004192[/C][C]-0.0409[/C][C]0.483746[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277979&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277979&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	-0.496675	-4.841	2e-06
2	-0.226152	-2.2043	0.014961
3	0.428352	4.1751	3.3e-05
4	-0.231625	-2.2576	0.01313
5	-0.022766	-0.2219	0.412436
6	0.061356	0.598	0.275624
7	-0.068546	-0.6681	0.252843
8	0.186765	1.8204	0.035926
9	-0.20611	-2.0089	0.023692
10	-0.029313	-0.2857	0.38786
11	0.437269	4.262	2.4e-05
12	-0.541447	-5.2774	0
13	0.128038	1.248	0.107557
14	0.288215	2.8092	0.003015
15	-0.343903	-3.352	0.000577
16	0.095602	0.9318	0.176898
17	0.114361	1.1147	0.133906
18	-0.053629	-0.5227	0.301196
19	-0.004192	-0.0409	0.483746

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.496675	-4.841	2e-06
2	-0.627676	-6.1178	0
3	-0.145065	-1.4139	0.080328
4	-0.194337	-1.8942	0.030623
5	-0.059026	-0.5753	0.283219
6	-0.225457	-2.1975	0.015208
7	-0.286497	-2.7924	0.003163
8	0.031099	0.3031	0.381231
9	-0.083921	-0.818	0.207713
10	-0.229009	-2.2321	0.013979
11	0.356777	3.4774	0.000383
12	-0.053576	-0.5222	0.301376
13	-0.013645	-0.133	0.447241
14	-0.087167	-0.8496	0.198842
15	-0.05774	-0.5628	0.287455
16	-0.134789	-1.3138	0.096045
17	-0.121202	-1.1813	0.12021
18	0.064873	0.6323	0.264353
19	-0.006611	-0.0644	0.47438

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.496675 & -4.841 & 2e-06 \tabularnewline
2 & -0.627676 & -6.1178 & 0 \tabularnewline
3 & -0.145065 & -1.4139 & 0.080328 \tabularnewline
4 & -0.194337 & -1.8942 & 0.030623 \tabularnewline
5 & -0.059026 & -0.5753 & 0.283219 \tabularnewline
6 & -0.225457 & -2.1975 & 0.015208 \tabularnewline
7 & -0.286497 & -2.7924 & 0.003163 \tabularnewline
8 & 0.031099 & 0.3031 & 0.381231 \tabularnewline
9 & -0.083921 & -0.818 & 0.207713 \tabularnewline
10 & -0.229009 & -2.2321 & 0.013979 \tabularnewline
11 & 0.356777 & 3.4774 & 0.000383 \tabularnewline
12 & -0.053576 & -0.5222 & 0.301376 \tabularnewline
13 & -0.013645 & -0.133 & 0.447241 \tabularnewline
14 & -0.087167 & -0.8496 & 0.198842 \tabularnewline
15 & -0.05774 & -0.5628 & 0.287455 \tabularnewline
16 & -0.134789 & -1.3138 & 0.096045 \tabularnewline
17 & -0.121202 & -1.1813 & 0.12021 \tabularnewline
18 & 0.064873 & 0.6323 & 0.264353 \tabularnewline
19 & -0.006611 & -0.0644 & 0.47438 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277979&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]-0.496675[/C][C]-4.841[/C][C]2e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.627676[/C][C]-6.1178[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.145065[/C][C]-1.4139[/C][C]0.080328[/C][/ROW]
[ROW][C]4[/C][C]-0.194337[/C][C]-1.8942[/C][C]0.030623[/C][/ROW]
[ROW][C]5[/C][C]-0.059026[/C][C]-0.5753[/C][C]0.283219[/C][/ROW]
[ROW][C]6[/C][C]-0.225457[/C][C]-2.1975[/C][C]0.015208[/C][/ROW]
[ROW][C]7[/C][C]-0.286497[/C][C]-2.7924[/C][C]0.003163[/C][/ROW]
[ROW][C]8[/C][C]0.031099[/C][C]0.3031[/C][C]0.381231[/C][/ROW]
[ROW][C]9[/C][C]-0.083921[/C][C]-0.818[/C][C]0.207713[/C][/ROW]
[ROW][C]10[/C][C]-0.229009[/C][C]-2.2321[/C][C]0.013979[/C][/ROW]
[ROW][C]11[/C][C]0.356777[/C][C]3.4774[/C][C]0.000383[/C][/ROW]
[ROW][C]12[/C][C]-0.053576[/C][C]-0.5222[/C][C]0.301376[/C][/ROW]
[ROW][C]13[/C][C]-0.013645[/C][C]-0.133[/C][C]0.447241[/C][/ROW]
[ROW][C]14[/C][C]-0.087167[/C][C]-0.8496[/C][C]0.198842[/C][/ROW]
[ROW][C]15[/C][C]-0.05774[/C][C]-0.5628[/C][C]0.287455[/C][/ROW]
[ROW][C]16[/C][C]-0.134789[/C][C]-1.3138[/C][C]0.096045[/C][/ROW]
[ROW][C]17[/C][C]-0.121202[/C][C]-1.1813[/C][C]0.12021[/C][/ROW]
[ROW][C]18[/C][C]0.064873[/C][C]0.6323[/C][C]0.264353[/C][/ROW]
[ROW][C]19[/C][C]-0.006611[/C][C]-0.0644[/C][C]0.47438[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277979&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277979&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	-0.496675	-4.841	2e-06
2	-0.627676	-6.1178	0
3	-0.145065	-1.4139	0.080328
4	-0.194337	-1.8942	0.030623
5	-0.059026	-0.5753	0.283219
6	-0.225457	-2.1975	0.015208
7	-0.286497	-2.7924	0.003163
8	0.031099	0.3031	0.381231
9	-0.083921	-0.818	0.207713
10	-0.229009	-2.2321	0.013979
11	0.356777	3.4774	0.000383
12	-0.053576	-0.5222	0.301376
13	-0.013645	-0.133	0.447241
14	-0.087167	-0.8496	0.198842
15	-0.05774	-0.5628	0.287455
16	-0.134789	-1.3138	0.096045
17	-0.121202	-1.1813	0.12021
18	0.064873	0.6323	0.264353
19	-0.006611	-0.0644	0.47438

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '1'
par2 <- '1'
par1 <- 'Default'
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