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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 23 Jan 2017 10:12:26 +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/2017/Jan/23/t1485162754s7b60bs6uvafe4g.htm/, Retrieved Wed, 15 May 2024 16:26:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=304222, Retrieved Wed, 15 May 2024 16:26:54 +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] [] [2017-01-23 09:12:26] [2a4cd29e98d45e730e96e92769c461dd] [Current]

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Dataseries X:

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Histogram

Boxplots

0.7923
-2.468
-2.996
3.119
0.04315
0.731
2.45
2.119
-1.429
-1.644
-3.065
-1.461
1.141
1.329
0.3396
0.8429
2.225
-1.924
0.4999
-0.6433

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=304222&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=304222&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=304222&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	2 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.136179	0.609	0.274686
2	-0.135228	-0.6048	0.276069
3	-0.087392	-0.3908	0.350028
4	-0.316189	-1.414	0.086364
5	-0.451763	-2.0203	0.028472
6	-0.089296	-0.3993	0.346937
7	0.074143	0.3316	0.371828
8	0.160486	0.7177	0.240616
9	0.381933	1.7081	0.051551
10	0.064493	0.2884	0.387995
11	-0.120857	-0.5405	0.297414
12	-0.033576	-0.1502	0.441073
13	0.050584	0.2262	0.411664

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.136179 & 0.609 & 0.274686 \tabularnewline
2 & -0.135228 & -0.6048 & 0.276069 \tabularnewline
3 & -0.087392 & -0.3908 & 0.350028 \tabularnewline
4 & -0.316189 & -1.414 & 0.086364 \tabularnewline
5 & -0.451763 & -2.0203 & 0.028472 \tabularnewline
6 & -0.089296 & -0.3993 & 0.346937 \tabularnewline
7 & 0.074143 & 0.3316 & 0.371828 \tabularnewline
8 & 0.160486 & 0.7177 & 0.240616 \tabularnewline
9 & 0.381933 & 1.7081 & 0.051551 \tabularnewline
10 & 0.064493 & 0.2884 & 0.387995 \tabularnewline
11 & -0.120857 & -0.5405 & 0.297414 \tabularnewline
12 & -0.033576 & -0.1502 & 0.441073 \tabularnewline
13 & 0.050584 & 0.2262 & 0.411664 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=304222&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]0.136179[/C][C]0.609[/C][C]0.274686[/C][/ROW]
[ROW][C]2[/C][C]-0.135228[/C][C]-0.6048[/C][C]0.276069[/C][/ROW]
[ROW][C]3[/C][C]-0.087392[/C][C]-0.3908[/C][C]0.350028[/C][/ROW]
[ROW][C]4[/C][C]-0.316189[/C][C]-1.414[/C][C]0.086364[/C][/ROW]
[ROW][C]5[/C][C]-0.451763[/C][C]-2.0203[/C][C]0.028472[/C][/ROW]
[ROW][C]6[/C][C]-0.089296[/C][C]-0.3993[/C][C]0.346937[/C][/ROW]
[ROW][C]7[/C][C]0.074143[/C][C]0.3316[/C][C]0.371828[/C][/ROW]
[ROW][C]8[/C][C]0.160486[/C][C]0.7177[/C][C]0.240616[/C][/ROW]
[ROW][C]9[/C][C]0.381933[/C][C]1.7081[/C][C]0.051551[/C][/ROW]
[ROW][C]10[/C][C]0.064493[/C][C]0.2884[/C][C]0.387995[/C][/ROW]
[ROW][C]11[/C][C]-0.120857[/C][C]-0.5405[/C][C]0.297414[/C][/ROW]
[ROW][C]12[/C][C]-0.033576[/C][C]-0.1502[/C][C]0.441073[/C][/ROW]
[ROW][C]13[/C][C]0.050584[/C][C]0.2262[/C][C]0.411664[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=304222&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=304222&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	0.136179	0.609	0.274686
2	-0.135228	-0.6048	0.276069
3	-0.087392	-0.3908	0.350028
4	-0.316189	-1.414	0.086364
5	-0.451763	-2.0203	0.028472
6	-0.089296	-0.3993	0.346937
7	0.074143	0.3316	0.371828
8	0.160486	0.7177	0.240616
9	0.381933	1.7081	0.051551
10	0.064493	0.2884	0.387995
11	-0.120857	-0.5405	0.297414
12	-0.033576	-0.1502	0.441073
13	0.050584	0.2262	0.411664

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.136179	0.609	0.274686
2	-0.156679	-0.7007	0.245785
3	-0.046748	-0.2091	0.418256
4	-0.331727	-1.4835	0.076761
5	-0.448116	-2.004	0.029399
6	-0.207874	-0.9296	0.181822
7	-0.219913	-0.9835	0.16856
8	-0.144426	-0.6459	0.262845
9	0.064454	0.2882	0.388062
10	-0.302358	-1.3522	0.095704
11	-0.31216	-1.396	0.089007
12	-0.239295	-1.0702	0.148647
13	0.096353	0.4309	0.335574

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.136179 & 0.609 & 0.274686 \tabularnewline
2 & -0.156679 & -0.7007 & 0.245785 \tabularnewline
3 & -0.046748 & -0.2091 & 0.418256 \tabularnewline
4 & -0.331727 & -1.4835 & 0.076761 \tabularnewline
5 & -0.448116 & -2.004 & 0.029399 \tabularnewline
6 & -0.207874 & -0.9296 & 0.181822 \tabularnewline
7 & -0.219913 & -0.9835 & 0.16856 \tabularnewline
8 & -0.144426 & -0.6459 & 0.262845 \tabularnewline
9 & 0.064454 & 0.2882 & 0.388062 \tabularnewline
10 & -0.302358 & -1.3522 & 0.095704 \tabularnewline
11 & -0.31216 & -1.396 & 0.089007 \tabularnewline
12 & -0.239295 & -1.0702 & 0.148647 \tabularnewline
13 & 0.096353 & 0.4309 & 0.335574 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=304222&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]0.136179[/C][C]0.609[/C][C]0.274686[/C][/ROW]
[ROW][C]2[/C][C]-0.156679[/C][C]-0.7007[/C][C]0.245785[/C][/ROW]
[ROW][C]3[/C][C]-0.046748[/C][C]-0.2091[/C][C]0.418256[/C][/ROW]
[ROW][C]4[/C][C]-0.331727[/C][C]-1.4835[/C][C]0.076761[/C][/ROW]
[ROW][C]5[/C][C]-0.448116[/C][C]-2.004[/C][C]0.029399[/C][/ROW]
[ROW][C]6[/C][C]-0.207874[/C][C]-0.9296[/C][C]0.181822[/C][/ROW]
[ROW][C]7[/C][C]-0.219913[/C][C]-0.9835[/C][C]0.16856[/C][/ROW]
[ROW][C]8[/C][C]-0.144426[/C][C]-0.6459[/C][C]0.262845[/C][/ROW]
[ROW][C]9[/C][C]0.064454[/C][C]0.2882[/C][C]0.388062[/C][/ROW]
[ROW][C]10[/C][C]-0.302358[/C][C]-1.3522[/C][C]0.095704[/C][/ROW]
[ROW][C]11[/C][C]-0.31216[/C][C]-1.396[/C][C]0.089007[/C][/ROW]
[ROW][C]12[/C][C]-0.239295[/C][C]-1.0702[/C][C]0.148647[/C][/ROW]
[ROW][C]13[/C][C]0.096353[/C][C]0.4309[/C][C]0.335574[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=304222&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=304222&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	0.136179	0.609	0.274686
2	-0.156679	-0.7007	0.245785
3	-0.046748	-0.2091	0.418256
4	-0.331727	-1.4835	0.076761
5	-0.448116	-2.004	0.029399
6	-0.207874	-0.9296	0.181822
7	-0.219913	-0.9835	0.16856
8	-0.144426	-0.6459	0.262845
9	0.064454	0.2882	0.388062
10	-0.302358	-1.3522	0.095704
11	-0.31216	-1.396	0.089007
12	-0.239295	-1.0702	0.148647
13	0.096353	0.4309	0.335574

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