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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

Tue, 03 Dec 2013 08:08:01 -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/2013/Dec/03/t1386076093o6ttv0phskq33a6.htm/, Retrieved Sat, 20 Apr 2024 11:49:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230271, Retrieved Sat, 20 Apr 2024 11:49:54 +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] [] [2013-12-03 13:08:01] [df6648d3354c48eb8905db6c004499bd] [Current]
- RMP     [Variance Reduction Matrix] [] [2013-12-03 13:15:24] [02abc6ae7a9692fad1b511df4cb1357e] 
- R P     [(Partial) Autocorrelation Function] [] [2013-12-03 13:38:44] [02abc6ae7a9692fad1b511df4cb1357e] 
- RMP       [Spectral Analysis] [] [2013-12-03 13:49:35] [02abc6ae7a9692fad1b511df4cb1357e] 
- RMP       [Standard Deviation-Mean Plot] [] [2013-12-03 13:59:53] [02abc6ae7a9692fad1b511df4cb1357e] 
- RMP       [ARIMA Backward Selection] [] [2013-12-03 14:16:40] [02abc6ae7a9692fad1b511df4cb1357e] 

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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	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230271&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230271&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230271&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	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.565353	-4.8633	3e-06
2	0.086349	0.7428	0.229975
3	0.163876	1.4097	0.081407
4	-0.242834	-2.0889	0.020076
5	0.103045	0.8864	0.189129
6	-0.032838	-0.2825	0.389181
7	0.0589	0.5067	0.306943
8	-0.25188	-2.1668	0.016737
9	0.275178	2.3672	0.01027
10	-0.096092	-0.8266	0.205557
11	-0.295228	-2.5396	0.006598
12	0.625846	5.3837	0
13	-0.435343	-3.745	0.000177
14	0.173677	1.494	0.06971
15	0.086552	0.7446	0.229451
16	-0.206755	-1.7786	0.039708
17	0.063955	0.5502	0.291932
18	0.070278	0.6046	0.273664

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.565353 & -4.8633 & 3e-06 \tabularnewline
2 & 0.086349 & 0.7428 & 0.229975 \tabularnewline
3 & 0.163876 & 1.4097 & 0.081407 \tabularnewline
4 & -0.242834 & -2.0889 & 0.020076 \tabularnewline
5 & 0.103045 & 0.8864 & 0.189129 \tabularnewline
6 & -0.032838 & -0.2825 & 0.389181 \tabularnewline
7 & 0.0589 & 0.5067 & 0.306943 \tabularnewline
8 & -0.25188 & -2.1668 & 0.016737 \tabularnewline
9 & 0.275178 & 2.3672 & 0.01027 \tabularnewline
10 & -0.096092 & -0.8266 & 0.205557 \tabularnewline
11 & -0.295228 & -2.5396 & 0.006598 \tabularnewline
12 & 0.625846 & 5.3837 & 0 \tabularnewline
13 & -0.435343 & -3.745 & 0.000177 \tabularnewline
14 & 0.173677 & 1.494 & 0.06971 \tabularnewline
15 & 0.086552 & 0.7446 & 0.229451 \tabularnewline
16 & -0.206755 & -1.7786 & 0.039708 \tabularnewline
17 & 0.063955 & 0.5502 & 0.291932 \tabularnewline
18 & 0.070278 & 0.6046 & 0.273664 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230271&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]-0.565353[/C][C]-4.8633[/C][C]3e-06[/C][/ROW]
[ROW][C]2[/C][C]0.086349[/C][C]0.7428[/C][C]0.229975[/C][/ROW]
[ROW][C]3[/C][C]0.163876[/C][C]1.4097[/C][C]0.081407[/C][/ROW]
[ROW][C]4[/C][C]-0.242834[/C][C]-2.0889[/C][C]0.020076[/C][/ROW]
[ROW][C]5[/C][C]0.103045[/C][C]0.8864[/C][C]0.189129[/C][/ROW]
[ROW][C]6[/C][C]-0.032838[/C][C]-0.2825[/C][C]0.389181[/C][/ROW]
[ROW][C]7[/C][C]0.0589[/C][C]0.5067[/C][C]0.306943[/C][/ROW]
[ROW][C]8[/C][C]-0.25188[/C][C]-2.1668[/C][C]0.016737[/C][/ROW]
[ROW][C]9[/C][C]0.275178[/C][C]2.3672[/C][C]0.01027[/C][/ROW]
[ROW][C]10[/C][C]-0.096092[/C][C]-0.8266[/C][C]0.205557[/C][/ROW]
[ROW][C]11[/C][C]-0.295228[/C][C]-2.5396[/C][C]0.006598[/C][/ROW]
[ROW][C]12[/C][C]0.625846[/C][C]5.3837[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.435343[/C][C]-3.745[/C][C]0.000177[/C][/ROW]
[ROW][C]14[/C][C]0.173677[/C][C]1.494[/C][C]0.06971[/C][/ROW]
[ROW][C]15[/C][C]0.086552[/C][C]0.7446[/C][C]0.229451[/C][/ROW]
[ROW][C]16[/C][C]-0.206755[/C][C]-1.7786[/C][C]0.039708[/C][/ROW]
[ROW][C]17[/C][C]0.063955[/C][C]0.5502[/C][C]0.291932[/C][/ROW]
[ROW][C]18[/C][C]0.070278[/C][C]0.6046[/C][C]0.273664[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230271&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230271&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	-0.565353	-4.8633	3e-06
2	0.086349	0.7428	0.229975
3	0.163876	1.4097	0.081407
4	-0.242834	-2.0889	0.020076
5	0.103045	0.8864	0.189129
6	-0.032838	-0.2825	0.389181
7	0.0589	0.5067	0.306943
8	-0.25188	-2.1668	0.016737
9	0.275178	2.3672	0.01027
10	-0.096092	-0.8266	0.205557
11	-0.295228	-2.5396	0.006598
12	0.625846	5.3837	0
13	-0.435343	-3.745	0.000177
14	0.173677	1.494	0.06971
15	0.086552	0.7446	0.229451
16	-0.206755	-1.7786	0.039708
17	0.063955	0.5502	0.291932
18	0.070278	0.6046	0.273664

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.565353	-4.8633	3e-06
2	-0.34286	-2.9494	0.00213
3	0.059285	0.51	0.305789
4	-0.104493	-0.8989	0.185816
5	-0.132637	-1.141	0.128777
6	-0.144253	-1.2409	0.10928
7	0.059511	0.5119	0.305112
8	-0.342814	-2.949	0.002132
9	-0.113958	-0.9803	0.165065
10	-0.00473	-0.0407	0.483825
11	-0.492498	-4.2366	3.2e-05
12	0.188888	1.6249	0.054221
13	0.139443	1.1995	0.117074
14	0.105814	0.9103	0.182823
15	0.095627	0.8226	0.206684
16	0.014849	0.1277	0.449352
17	-0.108111	-0.93	0.177697
18	0.081841	0.704	0.241815

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.565353 & -4.8633 & 3e-06 \tabularnewline
2 & -0.34286 & -2.9494 & 0.00213 \tabularnewline
3 & 0.059285 & 0.51 & 0.305789 \tabularnewline
4 & -0.104493 & -0.8989 & 0.185816 \tabularnewline
5 & -0.132637 & -1.141 & 0.128777 \tabularnewline
6 & -0.144253 & -1.2409 & 0.10928 \tabularnewline
7 & 0.059511 & 0.5119 & 0.305112 \tabularnewline
8 & -0.342814 & -2.949 & 0.002132 \tabularnewline
9 & -0.113958 & -0.9803 & 0.165065 \tabularnewline
10 & -0.00473 & -0.0407 & 0.483825 \tabularnewline
11 & -0.492498 & -4.2366 & 3.2e-05 \tabularnewline
12 & 0.188888 & 1.6249 & 0.054221 \tabularnewline
13 & 0.139443 & 1.1995 & 0.117074 \tabularnewline
14 & 0.105814 & 0.9103 & 0.182823 \tabularnewline
15 & 0.095627 & 0.8226 & 0.206684 \tabularnewline
16 & 0.014849 & 0.1277 & 0.449352 \tabularnewline
17 & -0.108111 & -0.93 & 0.177697 \tabularnewline
18 & 0.081841 & 0.704 & 0.241815 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230271&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]-0.565353[/C][C]-4.8633[/C][C]3e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.34286[/C][C]-2.9494[/C][C]0.00213[/C][/ROW]
[ROW][C]3[/C][C]0.059285[/C][C]0.51[/C][C]0.305789[/C][/ROW]
[ROW][C]4[/C][C]-0.104493[/C][C]-0.8989[/C][C]0.185816[/C][/ROW]
[ROW][C]5[/C][C]-0.132637[/C][C]-1.141[/C][C]0.128777[/C][/ROW]
[ROW][C]6[/C][C]-0.144253[/C][C]-1.2409[/C][C]0.10928[/C][/ROW]
[ROW][C]7[/C][C]0.059511[/C][C]0.5119[/C][C]0.305112[/C][/ROW]
[ROW][C]8[/C][C]-0.342814[/C][C]-2.949[/C][C]0.002132[/C][/ROW]
[ROW][C]9[/C][C]-0.113958[/C][C]-0.9803[/C][C]0.165065[/C][/ROW]
[ROW][C]10[/C][C]-0.00473[/C][C]-0.0407[/C][C]0.483825[/C][/ROW]
[ROW][C]11[/C][C]-0.492498[/C][C]-4.2366[/C][C]3.2e-05[/C][/ROW]
[ROW][C]12[/C][C]0.188888[/C][C]1.6249[/C][C]0.054221[/C][/ROW]
[ROW][C]13[/C][C]0.139443[/C][C]1.1995[/C][C]0.117074[/C][/ROW]
[ROW][C]14[/C][C]0.105814[/C][C]0.9103[/C][C]0.182823[/C][/ROW]
[ROW][C]15[/C][C]0.095627[/C][C]0.8226[/C][C]0.206684[/C][/ROW]
[ROW][C]16[/C][C]0.014849[/C][C]0.1277[/C][C]0.449352[/C][/ROW]
[ROW][C]17[/C][C]-0.108111[/C][C]-0.93[/C][C]0.177697[/C][/ROW]
[ROW][C]18[/C][C]0.081841[/C][C]0.704[/C][C]0.241815[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230271&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230271&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	-0.565353	-4.8633	3e-06
2	-0.34286	-2.9494	0.00213
3	0.059285	0.51	0.305789
4	-0.104493	-0.8989	0.185816
5	-0.132637	-1.141	0.128777
6	-0.144253	-1.2409	0.10928
7	0.059511	0.5119	0.305112
8	-0.342814	-2.949	0.002132
9	-0.113958	-0.9803	0.165065
10	-0.00473	-0.0407	0.483825
11	-0.492498	-4.2366	3.2e-05
12	0.188888	1.6249	0.054221
13	0.139443	1.1995	0.117074
14	0.105814	0.9103	0.182823
15	0.095627	0.8226	0.206684
16	0.014849	0.1277	0.449352
17	-0.108111	-0.93	0.177697
18	0.081841	0.704	0.241815

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 <- '2'
par3 <- '2'
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