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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

Mon, 05 Dec 2011 14:07:19 -0500

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/2011/Dec/05/t1323112049m6b4uu9f255giky.htm/, Retrieved Fri, 03 May 2024 09:00:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151189, Retrieved Fri, 03 May 2024 09:00:19 +0000

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Original text written by user:

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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] [] [2011-12-05 19:07:19] [c80accbb627afb8a1e74b91ef6a0d2c4] [Current]

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Dataseries X:

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Boxplots

0.224565646
0.261571480
0.253029834
0.033938060
0.353208554
0.033295045
0.002171707
0.084136132
0.077468368
0.010160325
0.079746191
0.263485597
0.460389066
0.132348066
0.529154319
0.032287005
0.472190992
0.037985170
0.019795866
0.053763887
0.086771175
0.143764004
0.202780264
0.006932185
0.124637036
0.116166293
0.037363442
0.416532177
0.612491026
0.012781084
0.163992436
0.212717925
0.092409609
0.150134816
0.047430792
0.022017328
0.350262865
0.013821921
0.578796918
0.030264300
0.090627282
0.029354226
0.182663201
0.372085552
0.235142217
0.311617946
0.030548270
0.068424450
0.043757662
0.238109173
0.465951209
0.127494709
0.010810575
0.230141979
0.426687450
0.175605499
0.005595384
0.203565169
0.236888269
0.153586896
0.027445414
0.026240968
0.299075759
0.171469487
0.016355307
0.220064442
0.137054994
0.034683689
0.085767702
0.119746590
0.223347602
0.026601623
0.063485064
0.467803972
0.012650088
0.048496183
0.047170846
0.043196485
0.095073370
0.538513979
0.045034181
0.427235474
0.289835816
0.150884924
0.176887675
0.369202741
0.178461483
0.077501113
0.281105892
0.051375864
0.357311398
0.561861189
0.028342902
0.326209843
0.303994601
0.020530542
0.278139180
0.582716856
0.071720238
0.237546024

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	'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151189&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151189&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151189&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	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.111146	-1.1115	0.134518
2	-0.033464	-0.3346	0.369298
3	0.046645	0.4664	0.320956
4	-0.059057	-0.5906	0.27807
5	-0.05469	-0.5469	0.292834
6	0.072602	0.726	0.23476
7	-0.106102	-1.061	0.145619
8	0.012345	0.1234	0.451
9	-0.01351	-0.1351	0.446401
10	-0.063785	-0.6378	0.262515
11	0.047853	0.4785	0.316659
12	0.237794	2.3779	0.009655
13	-0.138828	-1.3883	0.084069
14	0.009977	0.0998	0.460365
15	0.093046	0.9305	0.177187
16	0.112398	1.124	0.131856
17	-0.011747	-0.1175	0.45336
18	-0.021043	-0.2104	0.41688
19	-0.13859	-1.3859	0.08443
20	-0.027638	-0.2764	0.391413

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.111146 & -1.1115 & 0.134518 \tabularnewline
2 & -0.033464 & -0.3346 & 0.369298 \tabularnewline
3 & 0.046645 & 0.4664 & 0.320956 \tabularnewline
4 & -0.059057 & -0.5906 & 0.27807 \tabularnewline
5 & -0.05469 & -0.5469 & 0.292834 \tabularnewline
6 & 0.072602 & 0.726 & 0.23476 \tabularnewline
7 & -0.106102 & -1.061 & 0.145619 \tabularnewline
8 & 0.012345 & 0.1234 & 0.451 \tabularnewline
9 & -0.01351 & -0.1351 & 0.446401 \tabularnewline
10 & -0.063785 & -0.6378 & 0.262515 \tabularnewline
11 & 0.047853 & 0.4785 & 0.316659 \tabularnewline
12 & 0.237794 & 2.3779 & 0.009655 \tabularnewline
13 & -0.138828 & -1.3883 & 0.084069 \tabularnewline
14 & 0.009977 & 0.0998 & 0.460365 \tabularnewline
15 & 0.093046 & 0.9305 & 0.177187 \tabularnewline
16 & 0.112398 & 1.124 & 0.131856 \tabularnewline
17 & -0.011747 & -0.1175 & 0.45336 \tabularnewline
18 & -0.021043 & -0.2104 & 0.41688 \tabularnewline
19 & -0.13859 & -1.3859 & 0.08443 \tabularnewline
20 & -0.027638 & -0.2764 & 0.391413 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151189&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]-0.111146[/C][C]-1.1115[/C][C]0.134518[/C][/ROW]
[ROW][C]2[/C][C]-0.033464[/C][C]-0.3346[/C][C]0.369298[/C][/ROW]
[ROW][C]3[/C][C]0.046645[/C][C]0.4664[/C][C]0.320956[/C][/ROW]
[ROW][C]4[/C][C]-0.059057[/C][C]-0.5906[/C][C]0.27807[/C][/ROW]
[ROW][C]5[/C][C]-0.05469[/C][C]-0.5469[/C][C]0.292834[/C][/ROW]
[ROW][C]6[/C][C]0.072602[/C][C]0.726[/C][C]0.23476[/C][/ROW]
[ROW][C]7[/C][C]-0.106102[/C][C]-1.061[/C][C]0.145619[/C][/ROW]
[ROW][C]8[/C][C]0.012345[/C][C]0.1234[/C][C]0.451[/C][/ROW]
[ROW][C]9[/C][C]-0.01351[/C][C]-0.1351[/C][C]0.446401[/C][/ROW]
[ROW][C]10[/C][C]-0.063785[/C][C]-0.6378[/C][C]0.262515[/C][/ROW]
[ROW][C]11[/C][C]0.047853[/C][C]0.4785[/C][C]0.316659[/C][/ROW]
[ROW][C]12[/C][C]0.237794[/C][C]2.3779[/C][C]0.009655[/C][/ROW]
[ROW][C]13[/C][C]-0.138828[/C][C]-1.3883[/C][C]0.084069[/C][/ROW]
[ROW][C]14[/C][C]0.009977[/C][C]0.0998[/C][C]0.460365[/C][/ROW]
[ROW][C]15[/C][C]0.093046[/C][C]0.9305[/C][C]0.177187[/C][/ROW]
[ROW][C]16[/C][C]0.112398[/C][C]1.124[/C][C]0.131856[/C][/ROW]
[ROW][C]17[/C][C]-0.011747[/C][C]-0.1175[/C][C]0.45336[/C][/ROW]
[ROW][C]18[/C][C]-0.021043[/C][C]-0.2104[/C][C]0.41688[/C][/ROW]
[ROW][C]19[/C][C]-0.13859[/C][C]-1.3859[/C][C]0.08443[/C][/ROW]
[ROW][C]20[/C][C]-0.027638[/C][C]-0.2764[/C][C]0.391413[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151189&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151189&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	-0.111146	-1.1115	0.134518
2	-0.033464	-0.3346	0.369298
3	0.046645	0.4664	0.320956
4	-0.059057	-0.5906	0.27807
5	-0.05469	-0.5469	0.292834
6	0.072602	0.726	0.23476
7	-0.106102	-1.061	0.145619
8	0.012345	0.1234	0.451
9	-0.01351	-0.1351	0.446401
10	-0.063785	-0.6378	0.262515
11	0.047853	0.4785	0.316659
12	0.237794	2.3779	0.009655
13	-0.138828	-1.3883	0.084069
14	0.009977	0.0998	0.460365
15	0.093046	0.9305	0.177187
16	0.112398	1.124	0.131856
17	-0.011747	-0.1175	0.45336
18	-0.021043	-0.2104	0.41688
19	-0.13859	-1.3859	0.08443
20	-0.027638	-0.2764	0.391413

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.111146	-1.1115	0.134518
2	-0.046391	-0.4639	0.321861
3	0.038149	0.3815	0.351825
4	-0.051701	-0.517	0.303144
5	-0.065155	-0.6516	0.258093
6	0.05443	0.5443	0.293722
7	-0.094108	-0.9411	0.174466
8	-0.004001	-0.04	0.484082
9	-0.031873	-0.3187	0.375298
10	-0.060399	-0.604	0.27361
11	0.029523	0.2952	0.384214
12	0.237159	2.3716	0.009813
13	-0.078622	-0.7862	0.216798
14	-0.020243	-0.2024	0.419995
15	0.082076	0.8208	0.206867
16	0.185054	1.8505	0.033594
17	0.021519	0.2152	0.41503
18	-0.053413	-0.5341	0.297217
19	-0.109372	-1.0937	0.138353
20	-0.051681	-0.5168	0.303216

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.111146 & -1.1115 & 0.134518 \tabularnewline
2 & -0.046391 & -0.4639 & 0.321861 \tabularnewline
3 & 0.038149 & 0.3815 & 0.351825 \tabularnewline
4 & -0.051701 & -0.517 & 0.303144 \tabularnewline
5 & -0.065155 & -0.6516 & 0.258093 \tabularnewline
6 & 0.05443 & 0.5443 & 0.293722 \tabularnewline
7 & -0.094108 & -0.9411 & 0.174466 \tabularnewline
8 & -0.004001 & -0.04 & 0.484082 \tabularnewline
9 & -0.031873 & -0.3187 & 0.375298 \tabularnewline
10 & -0.060399 & -0.604 & 0.27361 \tabularnewline
11 & 0.029523 & 0.2952 & 0.384214 \tabularnewline
12 & 0.237159 & 2.3716 & 0.009813 \tabularnewline
13 & -0.078622 & -0.7862 & 0.216798 \tabularnewline
14 & -0.020243 & -0.2024 & 0.419995 \tabularnewline
15 & 0.082076 & 0.8208 & 0.206867 \tabularnewline
16 & 0.185054 & 1.8505 & 0.033594 \tabularnewline
17 & 0.021519 & 0.2152 & 0.41503 \tabularnewline
18 & -0.053413 & -0.5341 & 0.297217 \tabularnewline
19 & -0.109372 & -1.0937 & 0.138353 \tabularnewline
20 & -0.051681 & -0.5168 & 0.303216 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151189&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]-0.111146[/C][C]-1.1115[/C][C]0.134518[/C][/ROW]
[ROW][C]2[/C][C]-0.046391[/C][C]-0.4639[/C][C]0.321861[/C][/ROW]
[ROW][C]3[/C][C]0.038149[/C][C]0.3815[/C][C]0.351825[/C][/ROW]
[ROW][C]4[/C][C]-0.051701[/C][C]-0.517[/C][C]0.303144[/C][/ROW]
[ROW][C]5[/C][C]-0.065155[/C][C]-0.6516[/C][C]0.258093[/C][/ROW]
[ROW][C]6[/C][C]0.05443[/C][C]0.5443[/C][C]0.293722[/C][/ROW]
[ROW][C]7[/C][C]-0.094108[/C][C]-0.9411[/C][C]0.174466[/C][/ROW]
[ROW][C]8[/C][C]-0.004001[/C][C]-0.04[/C][C]0.484082[/C][/ROW]
[ROW][C]9[/C][C]-0.031873[/C][C]-0.3187[/C][C]0.375298[/C][/ROW]
[ROW][C]10[/C][C]-0.060399[/C][C]-0.604[/C][C]0.27361[/C][/ROW]
[ROW][C]11[/C][C]0.029523[/C][C]0.2952[/C][C]0.384214[/C][/ROW]
[ROW][C]12[/C][C]0.237159[/C][C]2.3716[/C][C]0.009813[/C][/ROW]
[ROW][C]13[/C][C]-0.078622[/C][C]-0.7862[/C][C]0.216798[/C][/ROW]
[ROW][C]14[/C][C]-0.020243[/C][C]-0.2024[/C][C]0.419995[/C][/ROW]
[ROW][C]15[/C][C]0.082076[/C][C]0.8208[/C][C]0.206867[/C][/ROW]
[ROW][C]16[/C][C]0.185054[/C][C]1.8505[/C][C]0.033594[/C][/ROW]
[ROW][C]17[/C][C]0.021519[/C][C]0.2152[/C][C]0.41503[/C][/ROW]
[ROW][C]18[/C][C]-0.053413[/C][C]-0.5341[/C][C]0.297217[/C][/ROW]
[ROW][C]19[/C][C]-0.109372[/C][C]-1.0937[/C][C]0.138353[/C][/ROW]
[ROW][C]20[/C][C]-0.051681[/C][C]-0.5168[/C][C]0.303216[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151189&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151189&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	-0.111146	-1.1115	0.134518
2	-0.046391	-0.4639	0.321861
3	0.038149	0.3815	0.351825
4	-0.051701	-0.517	0.303144
5	-0.065155	-0.6516	0.258093
6	0.05443	0.5443	0.293722
7	-0.094108	-0.9411	0.174466
8	-0.004001	-0.04	0.484082
9	-0.031873	-0.3187	0.375298
10	-0.060399	-0.604	0.27361
11	0.029523	0.2952	0.384214
12	0.237159	2.3716	0.009813
13	-0.078622	-0.7862	0.216798
14	-0.020243	-0.2024	0.419995
15	0.082076	0.8208	0.206867
16	0.185054	1.8505	0.033594
17	0.021519	0.2152	0.41503
18	-0.053413	-0.5341	0.297217
19	-0.109372	-1.0937	0.138353
20	-0.051681	-0.5168	0.303216

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)
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