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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 18 Oct 2016 12:14:23 +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/Oct/18/t1476789439eqoqp7rfvh33dsh.htm/, Retrieved Sat, 27 Apr 2024 20:21:01 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 27 Apr 2024 20:21:01 +0200

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Estimated Impact

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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	'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.351632	-5.2979	0
2	0.195612	2.9472	0.001771
3	-0.107374	-1.6177	0.053553
4	-0.06566	-0.9893	0.161794
5	-0.110298	-1.6618	0.048966
6	-0.073427	-1.1063	0.134885
7	-0.140383	-2.1151	0.017756
8	-0.029684	-0.4472	0.327568
9	-0.05743	-0.8653	0.1939
10	0.156034	2.3509	0.009793
11	-0.196918	-2.9669	0.001665
12	0.670054	10.0954	0
13	-0.289906	-4.3679	1e-05
14	0.22601	3.4052	0.000391
15	-0.072276	-1.0889	0.138667
16	-0.085212	-1.2838	0.100253
17	-0.039979	-0.6024	0.273771
18	-0.123001	-1.8532	0.032576
19	-0.115337	-1.7377	0.041808
20	-0.037983	-0.5723	0.28385
21	-0.055348	-0.8339	0.202606
22	0.139437	2.1008	0.01838
23	-0.129297	-1.9481	0.02632

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.351632 & -5.2979 & 0 \tabularnewline
2 & 0.195612 & 2.9472 & 0.001771 \tabularnewline
3 & -0.107374 & -1.6177 & 0.053553 \tabularnewline
4 & -0.06566 & -0.9893 & 0.161794 \tabularnewline
5 & -0.110298 & -1.6618 & 0.048966 \tabularnewline
6 & -0.073427 & -1.1063 & 0.134885 \tabularnewline
7 & -0.140383 & -2.1151 & 0.017756 \tabularnewline
8 & -0.029684 & -0.4472 & 0.327568 \tabularnewline
9 & -0.05743 & -0.8653 & 0.1939 \tabularnewline
10 & 0.156034 & 2.3509 & 0.009793 \tabularnewline
11 & -0.196918 & -2.9669 & 0.001665 \tabularnewline
12 & 0.670054 & 10.0954 & 0 \tabularnewline
13 & -0.289906 & -4.3679 & 1e-05 \tabularnewline
14 & 0.22601 & 3.4052 & 0.000391 \tabularnewline
15 & -0.072276 & -1.0889 & 0.138667 \tabularnewline
16 & -0.085212 & -1.2838 & 0.100253 \tabularnewline
17 & -0.039979 & -0.6024 & 0.273771 \tabularnewline
18 & -0.123001 & -1.8532 & 0.032576 \tabularnewline
19 & -0.115337 & -1.7377 & 0.041808 \tabularnewline
20 & -0.037983 & -0.5723 & 0.28385 \tabularnewline
21 & -0.055348 & -0.8339 & 0.202606 \tabularnewline
22 & 0.139437 & 2.1008 & 0.01838 \tabularnewline
23 & -0.129297 & -1.9481 & 0.02632 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]-0.351632[/C][C]-5.2979[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.195612[/C][C]2.9472[/C][C]0.001771[/C][/ROW]
[ROW][C]3[/C][C]-0.107374[/C][C]-1.6177[/C][C]0.053553[/C][/ROW]
[ROW][C]4[/C][C]-0.06566[/C][C]-0.9893[/C][C]0.161794[/C][/ROW]
[ROW][C]5[/C][C]-0.110298[/C][C]-1.6618[/C][C]0.048966[/C][/ROW]
[ROW][C]6[/C][C]-0.073427[/C][C]-1.1063[/C][C]0.134885[/C][/ROW]
[ROW][C]7[/C][C]-0.140383[/C][C]-2.1151[/C][C]0.017756[/C][/ROW]
[ROW][C]8[/C][C]-0.029684[/C][C]-0.4472[/C][C]0.327568[/C][/ROW]
[ROW][C]9[/C][C]-0.05743[/C][C]-0.8653[/C][C]0.1939[/C][/ROW]
[ROW][C]10[/C][C]0.156034[/C][C]2.3509[/C][C]0.009793[/C][/ROW]
[ROW][C]11[/C][C]-0.196918[/C][C]-2.9669[/C][C]0.001665[/C][/ROW]
[ROW][C]12[/C][C]0.670054[/C][C]10.0954[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.289906[/C][C]-4.3679[/C][C]1e-05[/C][/ROW]
[ROW][C]14[/C][C]0.22601[/C][C]3.4052[/C][C]0.000391[/C][/ROW]
[ROW][C]15[/C][C]-0.072276[/C][C]-1.0889[/C][C]0.138667[/C][/ROW]
[ROW][C]16[/C][C]-0.085212[/C][C]-1.2838[/C][C]0.100253[/C][/ROW]
[ROW][C]17[/C][C]-0.039979[/C][C]-0.6024[/C][C]0.273771[/C][/ROW]
[ROW][C]18[/C][C]-0.123001[/C][C]-1.8532[/C][C]0.032576[/C][/ROW]
[ROW][C]19[/C][C]-0.115337[/C][C]-1.7377[/C][C]0.041808[/C][/ROW]
[ROW][C]20[/C][C]-0.037983[/C][C]-0.5723[/C][C]0.28385[/C][/ROW]
[ROW][C]21[/C][C]-0.055348[/C][C]-0.8339[/C][C]0.202606[/C][/ROW]
[ROW][C]22[/C][C]0.139437[/C][C]2.1008[/C][C]0.01838[/C][/ROW]
[ROW][C]23[/C][C]-0.129297[/C][C]-1.9481[/C][C]0.02632[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	-0.351632	-5.2979	0
2	0.195612	2.9472	0.001771
3	-0.107374	-1.6177	0.053553
4	-0.06566	-0.9893	0.161794
5	-0.110298	-1.6618	0.048966
6	-0.073427	-1.1063	0.134885
7	-0.140383	-2.1151	0.017756
8	-0.029684	-0.4472	0.327568
9	-0.05743	-0.8653	0.1939
10	0.156034	2.3509	0.009793
11	-0.196918	-2.9669	0.001665
12	0.670054	10.0954	0
13	-0.289906	-4.3679	1e-05
14	0.22601	3.4052	0.000391
15	-0.072276	-1.0889	0.138667
16	-0.085212	-1.2838	0.100253
17	-0.039979	-0.6024	0.273771
18	-0.123001	-1.8532	0.032576
19	-0.115337	-1.7377	0.041808
20	-0.037983	-0.5723	0.28385
21	-0.055348	-0.8339	0.202606
22	0.139437	2.1008	0.01838
23	-0.129297	-1.9481	0.02632

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.351632	-5.2979	0
2	0.082121	1.2373	0.108632
3	-0.017649	-0.2659	0.395275
4	-0.139414	-2.1005	0.018395
5	-0.18636	-2.8078	0.002711
6	-0.168121	-2.533	0.005992
7	-0.248066	-3.7375	0.000118
8	-0.233952	-3.5248	0.000256
9	-0.255929	-3.856	7.5e-05
10	-0.074901	-1.1285	0.130149
11	-0.410141	-6.1794	0
12	0.454721	6.8511	0
13	0.069729	1.0506	0.147286
14	0.049753	0.7496	0.227134
15	0.147788	2.2266	0.013477
16	0.055218	0.8319	0.203157
17	0.138348	2.0844	0.01912
18	0.034285	0.5166	0.302986
19	0.049668	0.7483	0.227518
20	0.000417	0.0063	0.497494
21	-0.052921	-0.7973	0.213045
22	0.00331	0.0499	0.480137
23	-0.078013	-1.1754	0.120537

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.351632 & -5.2979 & 0 \tabularnewline
2 & 0.082121 & 1.2373 & 0.108632 \tabularnewline
3 & -0.017649 & -0.2659 & 0.395275 \tabularnewline
4 & -0.139414 & -2.1005 & 0.018395 \tabularnewline
5 & -0.18636 & -2.8078 & 0.002711 \tabularnewline
6 & -0.168121 & -2.533 & 0.005992 \tabularnewline
7 & -0.248066 & -3.7375 & 0.000118 \tabularnewline
8 & -0.233952 & -3.5248 & 0.000256 \tabularnewline
9 & -0.255929 & -3.856 & 7.5e-05 \tabularnewline
10 & -0.074901 & -1.1285 & 0.130149 \tabularnewline
11 & -0.410141 & -6.1794 & 0 \tabularnewline
12 & 0.454721 & 6.8511 & 0 \tabularnewline
13 & 0.069729 & 1.0506 & 0.147286 \tabularnewline
14 & 0.049753 & 0.7496 & 0.227134 \tabularnewline
15 & 0.147788 & 2.2266 & 0.013477 \tabularnewline
16 & 0.055218 & 0.8319 & 0.203157 \tabularnewline
17 & 0.138348 & 2.0844 & 0.01912 \tabularnewline
18 & 0.034285 & 0.5166 & 0.302986 \tabularnewline
19 & 0.049668 & 0.7483 & 0.227518 \tabularnewline
20 & 0.000417 & 0.0063 & 0.497494 \tabularnewline
21 & -0.052921 & -0.7973 & 0.213045 \tabularnewline
22 & 0.00331 & 0.0499 & 0.480137 \tabularnewline
23 & -0.078013 & -1.1754 & 0.120537 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]-0.351632[/C][C]-5.2979[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.082121[/C][C]1.2373[/C][C]0.108632[/C][/ROW]
[ROW][C]3[/C][C]-0.017649[/C][C]-0.2659[/C][C]0.395275[/C][/ROW]
[ROW][C]4[/C][C]-0.139414[/C][C]-2.1005[/C][C]0.018395[/C][/ROW]
[ROW][C]5[/C][C]-0.18636[/C][C]-2.8078[/C][C]0.002711[/C][/ROW]
[ROW][C]6[/C][C]-0.168121[/C][C]-2.533[/C][C]0.005992[/C][/ROW]
[ROW][C]7[/C][C]-0.248066[/C][C]-3.7375[/C][C]0.000118[/C][/ROW]
[ROW][C]8[/C][C]-0.233952[/C][C]-3.5248[/C][C]0.000256[/C][/ROW]
[ROW][C]9[/C][C]-0.255929[/C][C]-3.856[/C][C]7.5e-05[/C][/ROW]
[ROW][C]10[/C][C]-0.074901[/C][C]-1.1285[/C][C]0.130149[/C][/ROW]
[ROW][C]11[/C][C]-0.410141[/C][C]-6.1794[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.454721[/C][C]6.8511[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.069729[/C][C]1.0506[/C][C]0.147286[/C][/ROW]
[ROW][C]14[/C][C]0.049753[/C][C]0.7496[/C][C]0.227134[/C][/ROW]
[ROW][C]15[/C][C]0.147788[/C][C]2.2266[/C][C]0.013477[/C][/ROW]
[ROW][C]16[/C][C]0.055218[/C][C]0.8319[/C][C]0.203157[/C][/ROW]
[ROW][C]17[/C][C]0.138348[/C][C]2.0844[/C][C]0.01912[/C][/ROW]
[ROW][C]18[/C][C]0.034285[/C][C]0.5166[/C][C]0.302986[/C][/ROW]
[ROW][C]19[/C][C]0.049668[/C][C]0.7483[/C][C]0.227518[/C][/ROW]
[ROW][C]20[/C][C]0.000417[/C][C]0.0063[/C][C]0.497494[/C][/ROW]
[ROW][C]21[/C][C]-0.052921[/C][C]-0.7973[/C][C]0.213045[/C][/ROW]
[ROW][C]22[/C][C]0.00331[/C][C]0.0499[/C][C]0.480137[/C][/ROW]
[ROW][C]23[/C][C]-0.078013[/C][C]-1.1754[/C][C]0.120537[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	-0.351632	-5.2979	0
2	0.082121	1.2373	0.108632
3	-0.017649	-0.2659	0.395275
4	-0.139414	-2.1005	0.018395
5	-0.18636	-2.8078	0.002711
6	-0.168121	-2.533	0.005992
7	-0.248066	-3.7375	0.000118
8	-0.233952	-3.5248	0.000256
9	-0.255929	-3.856	7.5e-05
10	-0.074901	-1.1285	0.130149
11	-0.410141	-6.1794	0
12	0.454721	6.8511	0
13	0.069729	1.0506	0.147286
14	0.049753	0.7496	0.227134
15	0.147788	2.2266	0.013477
16	0.055218	0.8319	0.203157
17	0.138348	2.0844	0.01912
18	0.034285	0.5166	0.302986
19	0.049668	0.7483	0.227518
20	0.000417	0.0063	0.497494
21	-0.052921	-0.7973	0.213045
22	0.00331	0.0499	0.480137
23	-0.078013	-1.1754	0.120537

Figure 1

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Postscript link

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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 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),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,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),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