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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 19 Dec 2016 21:16:59 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/19/t1482178753o7ofo4kpmkp5yg7.htm/, Retrieved Fri, 17 May 2024 01:17:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301482, Retrieved Fri, 17 May 2024 01:17:56 +0000

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

-       [(Partial) Autocorrelation Function] [Time series: Part...] [2016-12-19 20:16:59] [16e0888ced5f28ae20ce1ff74f042113] [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=301482&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=301482&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301482&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	0.789149	8.8582	0
2	0.766024	8.5986	0
3	0.772064	8.6664	0
4	0.739432	8.3001	0
5	0.692632	7.7748	0
6	0.644456	7.234	0
7	0.627485	7.0435	0
8	0.593219	6.6589	0
9	0.602945	6.768	0
10	0.567153	6.3663	0
11	0.568773	6.3845	0
12	0.553356	6.2114	0
13	0.471133	5.2885	0
14	0.478595	5.3722	0
15	0.477415	5.359	0
16	0.428236	4.8069	2e-06
17	0.392618	4.4071	1.1e-05
18	0.41285	4.6342	4e-06
19	0.380441	4.2704	1.9e-05
20	0.388402	4.3598	1.3e-05
21	0.422175	4.7389	3e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.789149 & 8.8582 & 0 \tabularnewline
2 & 0.766024 & 8.5986 & 0 \tabularnewline
3 & 0.772064 & 8.6664 & 0 \tabularnewline
4 & 0.739432 & 8.3001 & 0 \tabularnewline
5 & 0.692632 & 7.7748 & 0 \tabularnewline
6 & 0.644456 & 7.234 & 0 \tabularnewline
7 & 0.627485 & 7.0435 & 0 \tabularnewline
8 & 0.593219 & 6.6589 & 0 \tabularnewline
9 & 0.602945 & 6.768 & 0 \tabularnewline
10 & 0.567153 & 6.3663 & 0 \tabularnewline
11 & 0.568773 & 6.3845 & 0 \tabularnewline
12 & 0.553356 & 6.2114 & 0 \tabularnewline
13 & 0.471133 & 5.2885 & 0 \tabularnewline
14 & 0.478595 & 5.3722 & 0 \tabularnewline
15 & 0.477415 & 5.359 & 0 \tabularnewline
16 & 0.428236 & 4.8069 & 2e-06 \tabularnewline
17 & 0.392618 & 4.4071 & 1.1e-05 \tabularnewline
18 & 0.41285 & 4.6342 & 4e-06 \tabularnewline
19 & 0.380441 & 4.2704 & 1.9e-05 \tabularnewline
20 & 0.388402 & 4.3598 & 1.3e-05 \tabularnewline
21 & 0.422175 & 4.7389 & 3e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301482&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]0.789149[/C][C]8.8582[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.766024[/C][C]8.5986[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.772064[/C][C]8.6664[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.739432[/C][C]8.3001[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.692632[/C][C]7.7748[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.644456[/C][C]7.234[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.627485[/C][C]7.0435[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.593219[/C][C]6.6589[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.602945[/C][C]6.768[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.567153[/C][C]6.3663[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.568773[/C][C]6.3845[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.553356[/C][C]6.2114[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.471133[/C][C]5.2885[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.478595[/C][C]5.3722[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.477415[/C][C]5.359[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.428236[/C][C]4.8069[/C][C]2e-06[/C][/ROW]
[ROW][C]17[/C][C]0.392618[/C][C]4.4071[/C][C]1.1e-05[/C][/ROW]
[ROW][C]18[/C][C]0.41285[/C][C]4.6342[/C][C]4e-06[/C][/ROW]
[ROW][C]19[/C][C]0.380441[/C][C]4.2704[/C][C]1.9e-05[/C][/ROW]
[ROW][C]20[/C][C]0.388402[/C][C]4.3598[/C][C]1.3e-05[/C][/ROW]
[ROW][C]21[/C][C]0.422175[/C][C]4.7389[/C][C]3e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301482&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301482&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	0.789149	8.8582	0
2	0.766024	8.5986	0
3	0.772064	8.6664	0
4	0.739432	8.3001	0
5	0.692632	7.7748	0
6	0.644456	7.234	0
7	0.627485	7.0435	0
8	0.593219	6.6589	0
9	0.602945	6.768	0
10	0.567153	6.3663	0
11	0.568773	6.3845	0
12	0.553356	6.2114	0
13	0.471133	5.2885	0
14	0.478595	5.3722	0
15	0.477415	5.359	0
16	0.428236	4.8069	2e-06
17	0.392618	4.4071	1.1e-05
18	0.41285	4.6342	4e-06
19	0.380441	4.2704	1.9e-05
20	0.388402	4.3598	1.3e-05
21	0.422175	4.7389	3e-06

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.789149	8.8582	0
2	0.379774	4.2629	2e-05
3	0.30181	3.3878	0.00047
4	0.116239	1.3048	0.097173
5	-0.022358	-0.251	0.401124
6	-0.099239	-1.114	0.133709
7	-0.007833	-0.0879	0.465037
8	-0.011683	-0.1311	0.447934
9	0.1558	1.7489	0.041376
10	0.026781	0.3006	0.382103
11	0.091183	1.0235	0.15401
12	-0.002064	-0.0232	0.490777
13	-0.258381	-2.9003	0.0022
14	-0.038306	-0.43	0.33397
15	0.074735	0.8389	0.201557
16	0.004066	0.0456	0.481835
17	0.010225	0.1148	0.454402
18	0.116815	1.3112	0.09608
19	-0.045262	-0.5081	0.306149
20	0.062956	0.7067	0.240535
21	0.153016	1.7176	0.044163

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.789149 & 8.8582 & 0 \tabularnewline
2 & 0.379774 & 4.2629 & 2e-05 \tabularnewline
3 & 0.30181 & 3.3878 & 0.00047 \tabularnewline
4 & 0.116239 & 1.3048 & 0.097173 \tabularnewline
5 & -0.022358 & -0.251 & 0.401124 \tabularnewline
6 & -0.099239 & -1.114 & 0.133709 \tabularnewline
7 & -0.007833 & -0.0879 & 0.465037 \tabularnewline
8 & -0.011683 & -0.1311 & 0.447934 \tabularnewline
9 & 0.1558 & 1.7489 & 0.041376 \tabularnewline
10 & 0.026781 & 0.3006 & 0.382103 \tabularnewline
11 & 0.091183 & 1.0235 & 0.15401 \tabularnewline
12 & -0.002064 & -0.0232 & 0.490777 \tabularnewline
13 & -0.258381 & -2.9003 & 0.0022 \tabularnewline
14 & -0.038306 & -0.43 & 0.33397 \tabularnewline
15 & 0.074735 & 0.8389 & 0.201557 \tabularnewline
16 & 0.004066 & 0.0456 & 0.481835 \tabularnewline
17 & 0.010225 & 0.1148 & 0.454402 \tabularnewline
18 & 0.116815 & 1.3112 & 0.09608 \tabularnewline
19 & -0.045262 & -0.5081 & 0.306149 \tabularnewline
20 & 0.062956 & 0.7067 & 0.240535 \tabularnewline
21 & 0.153016 & 1.7176 & 0.044163 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301482&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]0.789149[/C][C]8.8582[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.379774[/C][C]4.2629[/C][C]2e-05[/C][/ROW]
[ROW][C]3[/C][C]0.30181[/C][C]3.3878[/C][C]0.00047[/C][/ROW]
[ROW][C]4[/C][C]0.116239[/C][C]1.3048[/C][C]0.097173[/C][/ROW]
[ROW][C]5[/C][C]-0.022358[/C][C]-0.251[/C][C]0.401124[/C][/ROW]
[ROW][C]6[/C][C]-0.099239[/C][C]-1.114[/C][C]0.133709[/C][/ROW]
[ROW][C]7[/C][C]-0.007833[/C][C]-0.0879[/C][C]0.465037[/C][/ROW]
[ROW][C]8[/C][C]-0.011683[/C][C]-0.1311[/C][C]0.447934[/C][/ROW]
[ROW][C]9[/C][C]0.1558[/C][C]1.7489[/C][C]0.041376[/C][/ROW]
[ROW][C]10[/C][C]0.026781[/C][C]0.3006[/C][C]0.382103[/C][/ROW]
[ROW][C]11[/C][C]0.091183[/C][C]1.0235[/C][C]0.15401[/C][/ROW]
[ROW][C]12[/C][C]-0.002064[/C][C]-0.0232[/C][C]0.490777[/C][/ROW]
[ROW][C]13[/C][C]-0.258381[/C][C]-2.9003[/C][C]0.0022[/C][/ROW]
[ROW][C]14[/C][C]-0.038306[/C][C]-0.43[/C][C]0.33397[/C][/ROW]
[ROW][C]15[/C][C]0.074735[/C][C]0.8389[/C][C]0.201557[/C][/ROW]
[ROW][C]16[/C][C]0.004066[/C][C]0.0456[/C][C]0.481835[/C][/ROW]
[ROW][C]17[/C][C]0.010225[/C][C]0.1148[/C][C]0.454402[/C][/ROW]
[ROW][C]18[/C][C]0.116815[/C][C]1.3112[/C][C]0.09608[/C][/ROW]
[ROW][C]19[/C][C]-0.045262[/C][C]-0.5081[/C][C]0.306149[/C][/ROW]
[ROW][C]20[/C][C]0.062956[/C][C]0.7067[/C][C]0.240535[/C][/ROW]
[ROW][C]21[/C][C]0.153016[/C][C]1.7176[/C][C]0.044163[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301482&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301482&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	0.789149	8.8582	0
2	0.379774	4.2629	2e-05
3	0.30181	3.3878	0.00047
4	0.116239	1.3048	0.097173
5	-0.022358	-0.251	0.401124
6	-0.099239	-1.114	0.133709
7	-0.007833	-0.0879	0.465037
8	-0.011683	-0.1311	0.447934
9	0.1558	1.7489	0.041376
10	0.026781	0.3006	0.382103
11	0.091183	1.0235	0.15401
12	-0.002064	-0.0232	0.490777
13	-0.258381	-2.9003	0.0022
14	-0.038306	-0.43	0.33397
15	0.074735	0.8389	0.201557
16	0.004066	0.0456	0.481835
17	0.010225	0.1148	0.454402
18	0.116815	1.3112	0.09608
19	-0.045262	-0.5081	0.306149
20	0.062956	0.7067	0.240535
21	0.153016	1.7176	0.044163

Figure 1

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Figure 2

PNG link

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Figure 3

PNG link

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Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 1 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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 <- '12'
par4 <- '0'
par3 <- '0'
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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code