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

Fri, 16 Dec 2016 09:16:26 +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/16/t14818761955pxrsl9n9dkzicx.htm/, Retrieved Fri, 03 May 2024 03:24:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300094, Retrieved Fri, 03 May 2024 03:24:04 +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] [] [2016-12-16 08:16:26] [94ac3c9a028ddd47e8862e80eac9f626] [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=300094&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=300094&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300094&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	0.963438	6.4629	0
2	0.91142	6.114	0
3	0.851318	5.7108	0
4	0.790405	5.3022	2e-06
5	0.729847	4.896	6e-06
6	0.66775	4.4794	2.5e-05
7	0.604519	4.0552	9.8e-05
8	0.533854	3.5812	0.000417
9	0.459487	3.0823	0.00175
10	0.384909	2.582	0.006574
11	0.308819	2.0716	0.022031
12	0.231873	1.5555	0.063422
13	0.158176	1.0611	0.147158
14	0.090376	0.6063	0.273694
15	0.029002	0.1946	0.42331
16	-0.026901	-0.1805	0.428802

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.963438 & 6.4629 & 0 \tabularnewline
2 & 0.91142 & 6.114 & 0 \tabularnewline
3 & 0.851318 & 5.7108 & 0 \tabularnewline
4 & 0.790405 & 5.3022 & 2e-06 \tabularnewline
5 & 0.729847 & 4.896 & 6e-06 \tabularnewline
6 & 0.66775 & 4.4794 & 2.5e-05 \tabularnewline
7 & 0.604519 & 4.0552 & 9.8e-05 \tabularnewline
8 & 0.533854 & 3.5812 & 0.000417 \tabularnewline
9 & 0.459487 & 3.0823 & 0.00175 \tabularnewline
10 & 0.384909 & 2.582 & 0.006574 \tabularnewline
11 & 0.308819 & 2.0716 & 0.022031 \tabularnewline
12 & 0.231873 & 1.5555 & 0.063422 \tabularnewline
13 & 0.158176 & 1.0611 & 0.147158 \tabularnewline
14 & 0.090376 & 0.6063 & 0.273694 \tabularnewline
15 & 0.029002 & 0.1946 & 0.42331 \tabularnewline
16 & -0.026901 & -0.1805 & 0.428802 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300094&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]0.963438[/C][C]6.4629[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.91142[/C][C]6.114[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.851318[/C][C]5.7108[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.790405[/C][C]5.3022[/C][C]2e-06[/C][/ROW]
[ROW][C]5[/C][C]0.729847[/C][C]4.896[/C][C]6e-06[/C][/ROW]
[ROW][C]6[/C][C]0.66775[/C][C]4.4794[/C][C]2.5e-05[/C][/ROW]
[ROW][C]7[/C][C]0.604519[/C][C]4.0552[/C][C]9.8e-05[/C][/ROW]
[ROW][C]8[/C][C]0.533854[/C][C]3.5812[/C][C]0.000417[/C][/ROW]
[ROW][C]9[/C][C]0.459487[/C][C]3.0823[/C][C]0.00175[/C][/ROW]
[ROW][C]10[/C][C]0.384909[/C][C]2.582[/C][C]0.006574[/C][/ROW]
[ROW][C]11[/C][C]0.308819[/C][C]2.0716[/C][C]0.022031[/C][/ROW]
[ROW][C]12[/C][C]0.231873[/C][C]1.5555[/C][C]0.063422[/C][/ROW]
[ROW][C]13[/C][C]0.158176[/C][C]1.0611[/C][C]0.147158[/C][/ROW]
[ROW][C]14[/C][C]0.090376[/C][C]0.6063[/C][C]0.273694[/C][/ROW]
[ROW][C]15[/C][C]0.029002[/C][C]0.1946[/C][C]0.42331[/C][/ROW]
[ROW][C]16[/C][C]-0.026901[/C][C]-0.1805[/C][C]0.428802[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300094&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300094&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	0.963438	6.4629	0
2	0.91142	6.114	0
3	0.851318	5.7108	0
4	0.790405	5.3022	2e-06
5	0.729847	4.896	6e-06
6	0.66775	4.4794	2.5e-05
7	0.604519	4.0552	9.8e-05
8	0.533854	3.5812	0.000417
9	0.459487	3.0823	0.00175
10	0.384909	2.582	0.006574
11	0.308819	2.0716	0.022031
12	0.231873	1.5555	0.063422
13	0.158176	1.0611	0.147158
14	0.090376	0.6063	0.273694
15	0.029002	0.1946	0.42331
16	-0.026901	-0.1805	0.428802

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.963438	6.4629	0
2	-0.233925	-1.5692	0.061802
3	-0.100438	-0.6738	0.251955
4	-0.007506	-0.0504	0.480032
5	-0.02382	-0.1598	0.436881
6	-0.063152	-0.4236	0.336924
7	-0.046839	-0.3142	0.37741
8	-0.141674	-0.9504	0.173498
9	-0.063118	-0.4234	0.337007
10	-0.025978	-0.1743	0.431218
11	-0.079891	-0.5359	0.297324
12	-0.0721	-0.4837	0.315487
13	-0.004514	-0.0303	0.487988
14	0.009411	0.0631	0.47497
15	0.0073	0.049	0.480579
16	-0.008774	-0.0589	0.476663

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.963438 & 6.4629 & 0 \tabularnewline
2 & -0.233925 & -1.5692 & 0.061802 \tabularnewline
3 & -0.100438 & -0.6738 & 0.251955 \tabularnewline
4 & -0.007506 & -0.0504 & 0.480032 \tabularnewline
5 & -0.02382 & -0.1598 & 0.436881 \tabularnewline
6 & -0.063152 & -0.4236 & 0.336924 \tabularnewline
7 & -0.046839 & -0.3142 & 0.37741 \tabularnewline
8 & -0.141674 & -0.9504 & 0.173498 \tabularnewline
9 & -0.063118 & -0.4234 & 0.337007 \tabularnewline
10 & -0.025978 & -0.1743 & 0.431218 \tabularnewline
11 & -0.079891 & -0.5359 & 0.297324 \tabularnewline
12 & -0.0721 & -0.4837 & 0.315487 \tabularnewline
13 & -0.004514 & -0.0303 & 0.487988 \tabularnewline
14 & 0.009411 & 0.0631 & 0.47497 \tabularnewline
15 & 0.0073 & 0.049 & 0.480579 \tabularnewline
16 & -0.008774 & -0.0589 & 0.476663 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300094&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]0.963438[/C][C]6.4629[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.233925[/C][C]-1.5692[/C][C]0.061802[/C][/ROW]
[ROW][C]3[/C][C]-0.100438[/C][C]-0.6738[/C][C]0.251955[/C][/ROW]
[ROW][C]4[/C][C]-0.007506[/C][C]-0.0504[/C][C]0.480032[/C][/ROW]
[ROW][C]5[/C][C]-0.02382[/C][C]-0.1598[/C][C]0.436881[/C][/ROW]
[ROW][C]6[/C][C]-0.063152[/C][C]-0.4236[/C][C]0.336924[/C][/ROW]
[ROW][C]7[/C][C]-0.046839[/C][C]-0.3142[/C][C]0.37741[/C][/ROW]
[ROW][C]8[/C][C]-0.141674[/C][C]-0.9504[/C][C]0.173498[/C][/ROW]
[ROW][C]9[/C][C]-0.063118[/C][C]-0.4234[/C][C]0.337007[/C][/ROW]
[ROW][C]10[/C][C]-0.025978[/C][C]-0.1743[/C][C]0.431218[/C][/ROW]
[ROW][C]11[/C][C]-0.079891[/C][C]-0.5359[/C][C]0.297324[/C][/ROW]
[ROW][C]12[/C][C]-0.0721[/C][C]-0.4837[/C][C]0.315487[/C][/ROW]
[ROW][C]13[/C][C]-0.004514[/C][C]-0.0303[/C][C]0.487988[/C][/ROW]
[ROW][C]14[/C][C]0.009411[/C][C]0.0631[/C][C]0.47497[/C][/ROW]
[ROW][C]15[/C][C]0.0073[/C][C]0.049[/C][C]0.480579[/C][/ROW]
[ROW][C]16[/C][C]-0.008774[/C][C]-0.0589[/C][C]0.476663[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300094&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300094&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	0.963438	6.4629	0
2	-0.233925	-1.5692	0.061802
3	-0.100438	-0.6738	0.251955
4	-0.007506	-0.0504	0.480032
5	-0.02382	-0.1598	0.436881
6	-0.063152	-0.4236	0.336924
7	-0.046839	-0.3142	0.37741
8	-0.141674	-0.9504	0.173498
9	-0.063118	-0.4234	0.337007
10	-0.025978	-0.1743	0.431218
11	-0.079891	-0.5359	0.297324
12	-0.0721	-0.4837	0.315487
13	-0.004514	-0.0303	0.487988
14	0.009411	0.0631	0.47497
15	0.0073	0.049	0.480579
16	-0.008774	-0.0589	0.476663

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)
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