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*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 12:55:35 +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/t148206216008kaxy1y4xd93tr.htm/, Retrieved Fri, 01 Nov 2024 03:45:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301020, Retrieved Fri, 01 Nov 2024 03:45:00 +0000

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120

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

-     [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2015-11-15 16:35:00] [32b17a345b130fdf5cc88718ed94a974]
- RMPD    [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2016-12-18 11:55:35] [2ea868439aa9f960cb5a0f1a9b97f873] [Current]

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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	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=301020&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=301020&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301020&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	0.963443	10.3766	0
2	0.922472	9.9353	0
3	0.891463	9.6014	0
4	0.858682	9.2483	0
5	0.824202	8.8769	0
6	0.784564	8.45	0
7	0.742085	7.9925	0
8	0.700067	7.54	0
9	0.655937	7.0647	0
10	0.613712	6.6099	0
11	0.572275	6.1636	0
12	0.53151	5.7245	0
13	0.493599	5.3162	0
14	0.455039	4.9009	2e-06
15	0.415875	4.4791	9e-06
16	0.374738	4.0361	4.9e-05
17	0.34193	3.6827	0.000176
18	0.311406	3.3539	0.000538
19	0.286117	3.0816	0.001286
20	0.263516	2.8382	0.002679

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.963443 & 10.3766 & 0 \tabularnewline
2 & 0.922472 & 9.9353 & 0 \tabularnewline
3 & 0.891463 & 9.6014 & 0 \tabularnewline
4 & 0.858682 & 9.2483 & 0 \tabularnewline
5 & 0.824202 & 8.8769 & 0 \tabularnewline
6 & 0.784564 & 8.45 & 0 \tabularnewline
7 & 0.742085 & 7.9925 & 0 \tabularnewline
8 & 0.700067 & 7.54 & 0 \tabularnewline
9 & 0.655937 & 7.0647 & 0 \tabularnewline
10 & 0.613712 & 6.6099 & 0 \tabularnewline
11 & 0.572275 & 6.1636 & 0 \tabularnewline
12 & 0.53151 & 5.7245 & 0 \tabularnewline
13 & 0.493599 & 5.3162 & 0 \tabularnewline
14 & 0.455039 & 4.9009 & 2e-06 \tabularnewline
15 & 0.415875 & 4.4791 & 9e-06 \tabularnewline
16 & 0.374738 & 4.0361 & 4.9e-05 \tabularnewline
17 & 0.34193 & 3.6827 & 0.000176 \tabularnewline
18 & 0.311406 & 3.3539 & 0.000538 \tabularnewline
19 & 0.286117 & 3.0816 & 0.001286 \tabularnewline
20 & 0.263516 & 2.8382 & 0.002679 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301020&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]0.963443[/C][C]10.3766[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.922472[/C][C]9.9353[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.891463[/C][C]9.6014[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.858682[/C][C]9.2483[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.824202[/C][C]8.8769[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.784564[/C][C]8.45[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.742085[/C][C]7.9925[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.700067[/C][C]7.54[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.655937[/C][C]7.0647[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.613712[/C][C]6.6099[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.572275[/C][C]6.1636[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.53151[/C][C]5.7245[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.493599[/C][C]5.3162[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.455039[/C][C]4.9009[/C][C]2e-06[/C][/ROW]
[ROW][C]15[/C][C]0.415875[/C][C]4.4791[/C][C]9e-06[/C][/ROW]
[ROW][C]16[/C][C]0.374738[/C][C]4.0361[/C][C]4.9e-05[/C][/ROW]
[ROW][C]17[/C][C]0.34193[/C][C]3.6827[/C][C]0.000176[/C][/ROW]
[ROW][C]18[/C][C]0.311406[/C][C]3.3539[/C][C]0.000538[/C][/ROW]
[ROW][C]19[/C][C]0.286117[/C][C]3.0816[/C][C]0.001286[/C][/ROW]
[ROW][C]20[/C][C]0.263516[/C][C]2.8382[/C][C]0.002679[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301020&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301020&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	0.963443	10.3766	0
2	0.922472	9.9353	0
3	0.891463	9.6014	0
4	0.858682	9.2483	0
5	0.824202	8.8769	0
6	0.784564	8.45	0
7	0.742085	7.9925	0
8	0.700067	7.54	0
9	0.655937	7.0647	0
10	0.613712	6.6099	0
11	0.572275	6.1636	0
12	0.53151	5.7245	0
13	0.493599	5.3162	0
14	0.455039	4.9009	2e-06
15	0.415875	4.4791	9e-06
16	0.374738	4.0361	4.9e-05
17	0.34193	3.6827	0.000176
18	0.311406	3.3539	0.000538
19	0.286117	3.0816	0.001286
20	0.263516	2.8382	0.002679

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.963443	10.3766	0
2	-0.080101	-0.8627	0.195039
3	0.121947	1.3134	0.095818
4	-0.060247	-0.6489	0.258851
5	-0.017498	-0.1885	0.425421
6	-0.100286	-1.0801	0.141165
7	-0.053823	-0.5797	0.281622
8	-0.033602	-0.3619	0.359043
9	-0.060377	-0.6503	0.258397
10	0.008964	0.0965	0.461628
11	-0.023014	-0.2479	0.402336
12	-0.000665	-0.0072	0.497149
13	0.01428	0.1538	0.439019
14	-0.031911	-0.3437	0.36585
15	-0.025265	-0.2721	0.393009
16	-0.065343	-0.7038	0.241495
17	0.093576	1.0078	0.157813
18	-0.027841	-0.2999	0.382413
19	0.087924	0.947	0.172811
20	0.001163	0.0125	0.495014

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.963443 & 10.3766 & 0 \tabularnewline
2 & -0.080101 & -0.8627 & 0.195039 \tabularnewline
3 & 0.121947 & 1.3134 & 0.095818 \tabularnewline
4 & -0.060247 & -0.6489 & 0.258851 \tabularnewline
5 & -0.017498 & -0.1885 & 0.425421 \tabularnewline
6 & -0.100286 & -1.0801 & 0.141165 \tabularnewline
7 & -0.053823 & -0.5797 & 0.281622 \tabularnewline
8 & -0.033602 & -0.3619 & 0.359043 \tabularnewline
9 & -0.060377 & -0.6503 & 0.258397 \tabularnewline
10 & 0.008964 & 0.0965 & 0.461628 \tabularnewline
11 & -0.023014 & -0.2479 & 0.402336 \tabularnewline
12 & -0.000665 & -0.0072 & 0.497149 \tabularnewline
13 & 0.01428 & 0.1538 & 0.439019 \tabularnewline
14 & -0.031911 & -0.3437 & 0.36585 \tabularnewline
15 & -0.025265 & -0.2721 & 0.393009 \tabularnewline
16 & -0.065343 & -0.7038 & 0.241495 \tabularnewline
17 & 0.093576 & 1.0078 & 0.157813 \tabularnewline
18 & -0.027841 & -0.2999 & 0.382413 \tabularnewline
19 & 0.087924 & 0.947 & 0.172811 \tabularnewline
20 & 0.001163 & 0.0125 & 0.495014 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301020&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]0.963443[/C][C]10.3766[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.080101[/C][C]-0.8627[/C][C]0.195039[/C][/ROW]
[ROW][C]3[/C][C]0.121947[/C][C]1.3134[/C][C]0.095818[/C][/ROW]
[ROW][C]4[/C][C]-0.060247[/C][C]-0.6489[/C][C]0.258851[/C][/ROW]
[ROW][C]5[/C][C]-0.017498[/C][C]-0.1885[/C][C]0.425421[/C][/ROW]
[ROW][C]6[/C][C]-0.100286[/C][C]-1.0801[/C][C]0.141165[/C][/ROW]
[ROW][C]7[/C][C]-0.053823[/C][C]-0.5797[/C][C]0.281622[/C][/ROW]
[ROW][C]8[/C][C]-0.033602[/C][C]-0.3619[/C][C]0.359043[/C][/ROW]
[ROW][C]9[/C][C]-0.060377[/C][C]-0.6503[/C][C]0.258397[/C][/ROW]
[ROW][C]10[/C][C]0.008964[/C][C]0.0965[/C][C]0.461628[/C][/ROW]
[ROW][C]11[/C][C]-0.023014[/C][C]-0.2479[/C][C]0.402336[/C][/ROW]
[ROW][C]12[/C][C]-0.000665[/C][C]-0.0072[/C][C]0.497149[/C][/ROW]
[ROW][C]13[/C][C]0.01428[/C][C]0.1538[/C][C]0.439019[/C][/ROW]
[ROW][C]14[/C][C]-0.031911[/C][C]-0.3437[/C][C]0.36585[/C][/ROW]
[ROW][C]15[/C][C]-0.025265[/C][C]-0.2721[/C][C]0.393009[/C][/ROW]
[ROW][C]16[/C][C]-0.065343[/C][C]-0.7038[/C][C]0.241495[/C][/ROW]
[ROW][C]17[/C][C]0.093576[/C][C]1.0078[/C][C]0.157813[/C][/ROW]
[ROW][C]18[/C][C]-0.027841[/C][C]-0.2999[/C][C]0.382413[/C][/ROW]
[ROW][C]19[/C][C]0.087924[/C][C]0.947[/C][C]0.172811[/C][/ROW]
[ROW][C]20[/C][C]0.001163[/C][C]0.0125[/C][C]0.495014[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301020&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301020&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	0.963443	10.3766	0
2	-0.080101	-0.8627	0.195039
3	0.121947	1.3134	0.095818
4	-0.060247	-0.6489	0.258851
5	-0.017498	-0.1885	0.425421
6	-0.100286	-1.0801	0.141165
7	-0.053823	-0.5797	0.281622
8	-0.033602	-0.3619	0.359043
9	-0.060377	-0.6503	0.258397
10	0.008964	0.0965	0.461628
11	-0.023014	-0.2479	0.402336
12	-0.000665	-0.0072	0.497149
13	0.01428	0.1538	0.439019
14	-0.031911	-0.3437	0.36585
15	-0.025265	-0.2721	0.393009
16	-0.065343	-0.7038	0.241495
17	0.093576	1.0078	0.157813
18	-0.027841	-0.2999	0.382413
19	0.087924	0.947	0.172811
20	0.001163	0.0125	0.495014

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):

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):

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)
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