Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

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

Sun, 18 Dec 2016 16:46:49 +0100

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/18/t1482076090h7vzyurc1v82n9h.htm/, Retrieved Wed, 08 May 2024 22:13:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301149, Retrieved Wed, 08 May 2024 22:13:32 +0000

QR Codes:

Paste this QR Code to cite your computation.

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] [plot en describe ...] [2016-12-18 15:46:49] [84a79156fb687334cf7dc390d7b82d5a] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301149&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301149&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301149&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.632604	-4.0997	9.3e-05
2	0.263919	1.7104	0.047286
3	-0.423925	-2.7473	0.004406
4	0.581702	3.7699	0.000252
5	-0.355809	-2.3059	0.013061
6	0.111991	0.7258	0.235998
7	-0.175876	-1.1398	0.130413
8	0.310865	2.0146	0.025187
9	-0.197468	-1.2797	0.10383
10	0.044319	0.2872	0.387677
11	-0.138788	-0.8994	0.186771
12	0.246702	1.5988	0.05868
13	-0.140932	-0.9133	0.183138
14	0.028208	0.1828	0.427915
15	-0.057982	-0.3758	0.354491
16	0.063145	0.4092	0.342226

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.632604 & -4.0997 & 9.3e-05 \tabularnewline
2 & 0.263919 & 1.7104 & 0.047286 \tabularnewline
3 & -0.423925 & -2.7473 & 0.004406 \tabularnewline
4 & 0.581702 & 3.7699 & 0.000252 \tabularnewline
5 & -0.355809 & -2.3059 & 0.013061 \tabularnewline
6 & 0.111991 & 0.7258 & 0.235998 \tabularnewline
7 & -0.175876 & -1.1398 & 0.130413 \tabularnewline
8 & 0.310865 & 2.0146 & 0.025187 \tabularnewline
9 & -0.197468 & -1.2797 & 0.10383 \tabularnewline
10 & 0.044319 & 0.2872 & 0.387677 \tabularnewline
11 & -0.138788 & -0.8994 & 0.186771 \tabularnewline
12 & 0.246702 & 1.5988 & 0.05868 \tabularnewline
13 & -0.140932 & -0.9133 & 0.183138 \tabularnewline
14 & 0.028208 & 0.1828 & 0.427915 \tabularnewline
15 & -0.057982 & -0.3758 & 0.354491 \tabularnewline
16 & 0.063145 & 0.4092 & 0.342226 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301149&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]-0.632604[/C][C]-4.0997[/C][C]9.3e-05[/C][/ROW]
[ROW][C]2[/C][C]0.263919[/C][C]1.7104[/C][C]0.047286[/C][/ROW]
[ROW][C]3[/C][C]-0.423925[/C][C]-2.7473[/C][C]0.004406[/C][/ROW]
[ROW][C]4[/C][C]0.581702[/C][C]3.7699[/C][C]0.000252[/C][/ROW]
[ROW][C]5[/C][C]-0.355809[/C][C]-2.3059[/C][C]0.013061[/C][/ROW]
[ROW][C]6[/C][C]0.111991[/C][C]0.7258[/C][C]0.235998[/C][/ROW]
[ROW][C]7[/C][C]-0.175876[/C][C]-1.1398[/C][C]0.130413[/C][/ROW]
[ROW][C]8[/C][C]0.310865[/C][C]2.0146[/C][C]0.025187[/C][/ROW]
[ROW][C]9[/C][C]-0.197468[/C][C]-1.2797[/C][C]0.10383[/C][/ROW]
[ROW][C]10[/C][C]0.044319[/C][C]0.2872[/C][C]0.387677[/C][/ROW]
[ROW][C]11[/C][C]-0.138788[/C][C]-0.8994[/C][C]0.186771[/C][/ROW]
[ROW][C]12[/C][C]0.246702[/C][C]1.5988[/C][C]0.05868[/C][/ROW]
[ROW][C]13[/C][C]-0.140932[/C][C]-0.9133[/C][C]0.183138[/C][/ROW]
[ROW][C]14[/C][C]0.028208[/C][C]0.1828[/C][C]0.427915[/C][/ROW]
[ROW][C]15[/C][C]-0.057982[/C][C]-0.3758[/C][C]0.354491[/C][/ROW]
[ROW][C]16[/C][C]0.063145[/C][C]0.4092[/C][C]0.342226[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301149&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301149&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	-0.632604	-4.0997	9.3e-05
2	0.263919	1.7104	0.047286
3	-0.423925	-2.7473	0.004406
4	0.581702	3.7699	0.000252
5	-0.355809	-2.3059	0.013061
6	0.111991	0.7258	0.235998
7	-0.175876	-1.1398	0.130413
8	0.310865	2.0146	0.025187
9	-0.197468	-1.2797	0.10383
10	0.044319	0.2872	0.387677
11	-0.138788	-0.8994	0.186771
12	0.246702	1.5988	0.05868
13	-0.140932	-0.9133	0.183138
14	0.028208	0.1828	0.427915
15	-0.057982	-0.3758	0.354491
16	0.063145	0.4092	0.342226

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.632604	-4.0997	9.3e-05
2	-0.227186	-1.4723	0.074193
3	-0.637699	-4.1328	8.4e-05
4	-0.064035	-0.415	0.34013
5	0.063617	0.4123	0.341114
6	-0.123162	-0.7982	0.214628
7	-0.020022	-0.1298	0.448688
8	0.068939	0.4468	0.328666
9	0.065512	0.4246	0.336659
10	0.096016	0.6223	0.268569
11	-0.09911	-0.6423	0.262083
12	-0.047213	-0.306	0.380567
13	6e-06	0	0.499985
14	-0.039206	-0.2541	0.400335
15	0.105357	0.6828	0.249244
16	-0.121189	-0.7854	0.218315

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.632604 & -4.0997 & 9.3e-05 \tabularnewline
2 & -0.227186 & -1.4723 & 0.074193 \tabularnewline
3 & -0.637699 & -4.1328 & 8.4e-05 \tabularnewline
4 & -0.064035 & -0.415 & 0.34013 \tabularnewline
5 & 0.063617 & 0.4123 & 0.341114 \tabularnewline
6 & -0.123162 & -0.7982 & 0.214628 \tabularnewline
7 & -0.020022 & -0.1298 & 0.448688 \tabularnewline
8 & 0.068939 & 0.4468 & 0.328666 \tabularnewline
9 & 0.065512 & 0.4246 & 0.336659 \tabularnewline
10 & 0.096016 & 0.6223 & 0.268569 \tabularnewline
11 & -0.09911 & -0.6423 & 0.262083 \tabularnewline
12 & -0.047213 & -0.306 & 0.380567 \tabularnewline
13 & 6e-06 & 0 & 0.499985 \tabularnewline
14 & -0.039206 & -0.2541 & 0.400335 \tabularnewline
15 & 0.105357 & 0.6828 & 0.249244 \tabularnewline
16 & -0.121189 & -0.7854 & 0.218315 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301149&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]-0.632604[/C][C]-4.0997[/C][C]9.3e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.227186[/C][C]-1.4723[/C][C]0.074193[/C][/ROW]
[ROW][C]3[/C][C]-0.637699[/C][C]-4.1328[/C][C]8.4e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.064035[/C][C]-0.415[/C][C]0.34013[/C][/ROW]
[ROW][C]5[/C][C]0.063617[/C][C]0.4123[/C][C]0.341114[/C][/ROW]
[ROW][C]6[/C][C]-0.123162[/C][C]-0.7982[/C][C]0.214628[/C][/ROW]
[ROW][C]7[/C][C]-0.020022[/C][C]-0.1298[/C][C]0.448688[/C][/ROW]
[ROW][C]8[/C][C]0.068939[/C][C]0.4468[/C][C]0.328666[/C][/ROW]
[ROW][C]9[/C][C]0.065512[/C][C]0.4246[/C][C]0.336659[/C][/ROW]
[ROW][C]10[/C][C]0.096016[/C][C]0.6223[/C][C]0.268569[/C][/ROW]
[ROW][C]11[/C][C]-0.09911[/C][C]-0.6423[/C][C]0.262083[/C][/ROW]
[ROW][C]12[/C][C]-0.047213[/C][C]-0.306[/C][C]0.380567[/C][/ROW]
[ROW][C]13[/C][C]6e-06[/C][C]0[/C][C]0.499985[/C][/ROW]
[ROW][C]14[/C][C]-0.039206[/C][C]-0.2541[/C][C]0.400335[/C][/ROW]
[ROW][C]15[/C][C]0.105357[/C][C]0.6828[/C][C]0.249244[/C][/ROW]
[ROW][C]16[/C][C]-0.121189[/C][C]-0.7854[/C][C]0.218315[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301149&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301149&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	-0.632604	-4.0997	9.3e-05
2	-0.227186	-1.4723	0.074193
3	-0.637699	-4.1328	8.4e-05
4	-0.064035	-0.415	0.34013
5	0.063617	0.4123	0.341114
6	-0.123162	-0.7982	0.214628
7	-0.020022	-0.1298	0.448688
8	0.068939	0.4468	0.328666
9	0.065512	0.4246	0.336659
10	0.096016	0.6223	0.268569
11	-0.09911	-0.6423	0.262083
12	-0.047213	-0.306	0.380567
13	6e-06	0	0.499985
14	-0.039206	-0.2541	0.400335
15	0.105357	0.6828	0.249244
16	-0.121189	-0.7854	0.218315

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 = 1 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 1 ; 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 <- '1'
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)
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,'ACF(k)',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,'PACF(k)',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