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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

Sun, 18 Dec 2016 09:40:42 +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/t1482050542hhk0dabu960osr8.htm/, Retrieved Wed, 08 May 2024 19:36:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300980, Retrieved Wed, 08 May 2024 19:36:05 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

121

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

-       [(Partial) Autocorrelation Function] [Autocorrelation N...] [2016-12-18 08:40:42] [08c254f01fc4fb8b56d19f4878327019] [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=300980&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=300980&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300980&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	-0.629098	-6.7463	0
2	0.156742	1.6809	0.047752
3	0.018079	0.1939	0.423306
4	-0.030579	-0.3279	0.371784
5	0.044447	0.4766	0.317263
6	-0.073905	-0.7925	0.214838
7	0.077442	0.8305	0.203996
8	-0.07832	-0.8399	0.201357
9	0.073889	0.7924	0.214889
10	-0.05963	-0.6395	0.261898
11	0.018524	0.1986	0.421446
12	0.032648	0.3501	0.363448
13	-0.033635	-0.3607	0.359493
14	0.024193	0.2594	0.397879
15	-0.065941	-0.7071	0.240456
16	0.111242	1.1929	0.117675
17	-0.154318	-1.6549	0.050338
18	0.132309	1.4189	0.079322
19	-0.058765	-0.6302	0.264912
20	0.040962	0.4393	0.330644

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.629098 & -6.7463 & 0 \tabularnewline
2 & 0.156742 & 1.6809 & 0.047752 \tabularnewline
3 & 0.018079 & 0.1939 & 0.423306 \tabularnewline
4 & -0.030579 & -0.3279 & 0.371784 \tabularnewline
5 & 0.044447 & 0.4766 & 0.317263 \tabularnewline
6 & -0.073905 & -0.7925 & 0.214838 \tabularnewline
7 & 0.077442 & 0.8305 & 0.203996 \tabularnewline
8 & -0.07832 & -0.8399 & 0.201357 \tabularnewline
9 & 0.073889 & 0.7924 & 0.214889 \tabularnewline
10 & -0.05963 & -0.6395 & 0.261898 \tabularnewline
11 & 0.018524 & 0.1986 & 0.421446 \tabularnewline
12 & 0.032648 & 0.3501 & 0.363448 \tabularnewline
13 & -0.033635 & -0.3607 & 0.359493 \tabularnewline
14 & 0.024193 & 0.2594 & 0.397879 \tabularnewline
15 & -0.065941 & -0.7071 & 0.240456 \tabularnewline
16 & 0.111242 & 1.1929 & 0.117675 \tabularnewline
17 & -0.154318 & -1.6549 & 0.050338 \tabularnewline
18 & 0.132309 & 1.4189 & 0.079322 \tabularnewline
19 & -0.058765 & -0.6302 & 0.264912 \tabularnewline
20 & 0.040962 & 0.4393 & 0.330644 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300980&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]-0.629098[/C][C]-6.7463[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.156742[/C][C]1.6809[/C][C]0.047752[/C][/ROW]
[ROW][C]3[/C][C]0.018079[/C][C]0.1939[/C][C]0.423306[/C][/ROW]
[ROW][C]4[/C][C]-0.030579[/C][C]-0.3279[/C][C]0.371784[/C][/ROW]
[ROW][C]5[/C][C]0.044447[/C][C]0.4766[/C][C]0.317263[/C][/ROW]
[ROW][C]6[/C][C]-0.073905[/C][C]-0.7925[/C][C]0.214838[/C][/ROW]
[ROW][C]7[/C][C]0.077442[/C][C]0.8305[/C][C]0.203996[/C][/ROW]
[ROW][C]8[/C][C]-0.07832[/C][C]-0.8399[/C][C]0.201357[/C][/ROW]
[ROW][C]9[/C][C]0.073889[/C][C]0.7924[/C][C]0.214889[/C][/ROW]
[ROW][C]10[/C][C]-0.05963[/C][C]-0.6395[/C][C]0.261898[/C][/ROW]
[ROW][C]11[/C][C]0.018524[/C][C]0.1986[/C][C]0.421446[/C][/ROW]
[ROW][C]12[/C][C]0.032648[/C][C]0.3501[/C][C]0.363448[/C][/ROW]
[ROW][C]13[/C][C]-0.033635[/C][C]-0.3607[/C][C]0.359493[/C][/ROW]
[ROW][C]14[/C][C]0.024193[/C][C]0.2594[/C][C]0.397879[/C][/ROW]
[ROW][C]15[/C][C]-0.065941[/C][C]-0.7071[/C][C]0.240456[/C][/ROW]
[ROW][C]16[/C][C]0.111242[/C][C]1.1929[/C][C]0.117675[/C][/ROW]
[ROW][C]17[/C][C]-0.154318[/C][C]-1.6549[/C][C]0.050338[/C][/ROW]
[ROW][C]18[/C][C]0.132309[/C][C]1.4189[/C][C]0.079322[/C][/ROW]
[ROW][C]19[/C][C]-0.058765[/C][C]-0.6302[/C][C]0.264912[/C][/ROW]
[ROW][C]20[/C][C]0.040962[/C][C]0.4393[/C][C]0.330644[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300980&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300980&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	-0.629098	-6.7463	0
2	0.156742	1.6809	0.047752
3	0.018079	0.1939	0.423306
4	-0.030579	-0.3279	0.371784
5	0.044447	0.4766	0.317263
6	-0.073905	-0.7925	0.214838
7	0.077442	0.8305	0.203996
8	-0.07832	-0.8399	0.201357
9	0.073889	0.7924	0.214889
10	-0.05963	-0.6395	0.261898
11	0.018524	0.1986	0.421446
12	0.032648	0.3501	0.363448
13	-0.033635	-0.3607	0.359493
14	0.024193	0.2594	0.397879
15	-0.065941	-0.7071	0.240456
16	0.111242	1.1929	0.117675
17	-0.154318	-1.6549	0.050338
18	0.132309	1.4189	0.079322
19	-0.058765	-0.6302	0.264912
20	0.040962	0.4393	0.330644

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.629098	-6.7463	0
2	-0.395578	-4.2421	2.3e-05
3	-0.182791	-1.9602	0.026195
4	-0.083698	-0.8976	0.185647
5	0.029187	0.313	0.377423
6	-0.036422	-0.3906	0.348416
7	0.009268	0.0994	0.460502
8	-0.059118	-0.634	0.263679
9	0.00149	0.016	0.493642
10	-0.025026	-0.2684	0.394445
11	-0.03888	-0.4169	0.338748
12	0.020295	0.2176	0.414048
13	0.037371	0.4008	0.344669
14	0.042988	0.461	0.322835
15	-0.072327	-0.7756	0.219783
16	0.022766	0.2441	0.403779
17	-0.120999	-1.2976	0.098517
18	-0.047544	-0.5099	0.305565
19	-0.011239	-0.1205	0.45214
20	0.084323	0.9043	0.183873

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.629098 & -6.7463 & 0 \tabularnewline
2 & -0.395578 & -4.2421 & 2.3e-05 \tabularnewline
3 & -0.182791 & -1.9602 & 0.026195 \tabularnewline
4 & -0.083698 & -0.8976 & 0.185647 \tabularnewline
5 & 0.029187 & 0.313 & 0.377423 \tabularnewline
6 & -0.036422 & -0.3906 & 0.348416 \tabularnewline
7 & 0.009268 & 0.0994 & 0.460502 \tabularnewline
8 & -0.059118 & -0.634 & 0.263679 \tabularnewline
9 & 0.00149 & 0.016 & 0.493642 \tabularnewline
10 & -0.025026 & -0.2684 & 0.394445 \tabularnewline
11 & -0.03888 & -0.4169 & 0.338748 \tabularnewline
12 & 0.020295 & 0.2176 & 0.414048 \tabularnewline
13 & 0.037371 & 0.4008 & 0.344669 \tabularnewline
14 & 0.042988 & 0.461 & 0.322835 \tabularnewline
15 & -0.072327 & -0.7756 & 0.219783 \tabularnewline
16 & 0.022766 & 0.2441 & 0.403779 \tabularnewline
17 & -0.120999 & -1.2976 & 0.098517 \tabularnewline
18 & -0.047544 & -0.5099 & 0.305565 \tabularnewline
19 & -0.011239 & -0.1205 & 0.45214 \tabularnewline
20 & 0.084323 & 0.9043 & 0.183873 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300980&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]-0.629098[/C][C]-6.7463[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.395578[/C][C]-4.2421[/C][C]2.3e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.182791[/C][C]-1.9602[/C][C]0.026195[/C][/ROW]
[ROW][C]4[/C][C]-0.083698[/C][C]-0.8976[/C][C]0.185647[/C][/ROW]
[ROW][C]5[/C][C]0.029187[/C][C]0.313[/C][C]0.377423[/C][/ROW]
[ROW][C]6[/C][C]-0.036422[/C][C]-0.3906[/C][C]0.348416[/C][/ROW]
[ROW][C]7[/C][C]0.009268[/C][C]0.0994[/C][C]0.460502[/C][/ROW]
[ROW][C]8[/C][C]-0.059118[/C][C]-0.634[/C][C]0.263679[/C][/ROW]
[ROW][C]9[/C][C]0.00149[/C][C]0.016[/C][C]0.493642[/C][/ROW]
[ROW][C]10[/C][C]-0.025026[/C][C]-0.2684[/C][C]0.394445[/C][/ROW]
[ROW][C]11[/C][C]-0.03888[/C][C]-0.4169[/C][C]0.338748[/C][/ROW]
[ROW][C]12[/C][C]0.020295[/C][C]0.2176[/C][C]0.414048[/C][/ROW]
[ROW][C]13[/C][C]0.037371[/C][C]0.4008[/C][C]0.344669[/C][/ROW]
[ROW][C]14[/C][C]0.042988[/C][C]0.461[/C][C]0.322835[/C][/ROW]
[ROW][C]15[/C][C]-0.072327[/C][C]-0.7756[/C][C]0.219783[/C][/ROW]
[ROW][C]16[/C][C]0.022766[/C][C]0.2441[/C][C]0.403779[/C][/ROW]
[ROW][C]17[/C][C]-0.120999[/C][C]-1.2976[/C][C]0.098517[/C][/ROW]
[ROW][C]18[/C][C]-0.047544[/C][C]-0.5099[/C][C]0.305565[/C][/ROW]
[ROW][C]19[/C][C]-0.011239[/C][C]-0.1205[/C][C]0.45214[/C][/ROW]
[ROW][C]20[/C][C]0.084323[/C][C]0.9043[/C][C]0.183873[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300980&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300980&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	-0.629098	-6.7463	0
2	-0.395578	-4.2421	2.3e-05
3	-0.182791	-1.9602	0.026195
4	-0.083698	-0.8976	0.185647
5	0.029187	0.313	0.377423
6	-0.036422	-0.3906	0.348416
7	0.009268	0.0994	0.460502
8	-0.059118	-0.634	0.263679
9	0.00149	0.016	0.493642
10	-0.025026	-0.2684	0.394445
11	-0.03888	-0.4169	0.338748
12	0.020295	0.2176	0.414048
13	0.037371	0.4008	0.344669
14	0.042988	0.461	0.322835
15	-0.072327	-0.7756	0.219783
16	0.022766	0.2441	0.403779
17	-0.120999	-1.2976	0.098517
18	-0.047544	-0.5099	0.305565
19	-0.011239	-0.1205	0.45214
20	0.084323	0.9043	0.183873

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 = 2 ; par4 = 0 ; par5 = 1 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; 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 <- '1'
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