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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 15 Aug 2017 14:27:19 +0200

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/Aug/15/t1502800212659mba2qyqok2n2.htm/, Retrieved Sun, 19 May 2024 21:47:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307274, Retrieved Sun, 19 May 2024 21:47:59 +0000

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User-defined keywords

Estimated Impact

114

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

-       [(Partial) Autocorrelation Function] [] [2017-08-15 12:27:19] [eec775fda337aa2da775a098928b5865] [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=307274&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=307274&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307274&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	-0.216906	-2.3662	0.009794
2	-0.052827	-0.5763	0.282758
3	-0.144728	-1.5788	0.058519
4	0.067033	0.7312	0.233035
5	-0.127179	-1.3874	0.083963
6	0.05057	0.5516	0.291112
7	-0.084742	-0.9244	0.178566
8	0.084979	0.927	0.177899
9	-0.162055	-1.7678	0.039828
10	-0.0398	-0.4342	0.332476
11	-0.178014	-1.9419	0.027256
12	0.824288	8.9919	0
13	-0.222699	-2.4294	0.00831
14	-0.040343	-0.4401	0.330336
15	-0.126437	-1.3793	0.085199
16	0.071258	0.7773	0.219252
17	-0.148908	-1.6244	0.053469
18	0.078667	0.8582	0.196265
19	-0.087466	-0.9541	0.170974
20	0.093311	1.0179	0.155396

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.216906 & -2.3662 & 0.009794 \tabularnewline
2 & -0.052827 & -0.5763 & 0.282758 \tabularnewline
3 & -0.144728 & -1.5788 & 0.058519 \tabularnewline
4 & 0.067033 & 0.7312 & 0.233035 \tabularnewline
5 & -0.127179 & -1.3874 & 0.083963 \tabularnewline
6 & 0.05057 & 0.5516 & 0.291112 \tabularnewline
7 & -0.084742 & -0.9244 & 0.178566 \tabularnewline
8 & 0.084979 & 0.927 & 0.177899 \tabularnewline
9 & -0.162055 & -1.7678 & 0.039828 \tabularnewline
10 & -0.0398 & -0.4342 & 0.332476 \tabularnewline
11 & -0.178014 & -1.9419 & 0.027256 \tabularnewline
12 & 0.824288 & 8.9919 & 0 \tabularnewline
13 & -0.222699 & -2.4294 & 0.00831 \tabularnewline
14 & -0.040343 & -0.4401 & 0.330336 \tabularnewline
15 & -0.126437 & -1.3793 & 0.085199 \tabularnewline
16 & 0.071258 & 0.7773 & 0.219252 \tabularnewline
17 & -0.148908 & -1.6244 & 0.053469 \tabularnewline
18 & 0.078667 & 0.8582 & 0.196265 \tabularnewline
19 & -0.087466 & -0.9541 & 0.170974 \tabularnewline
20 & 0.093311 & 1.0179 & 0.155396 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307274&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]-0.216906[/C][C]-2.3662[/C][C]0.009794[/C][/ROW]
[ROW][C]2[/C][C]-0.052827[/C][C]-0.5763[/C][C]0.282758[/C][/ROW]
[ROW][C]3[/C][C]-0.144728[/C][C]-1.5788[/C][C]0.058519[/C][/ROW]
[ROW][C]4[/C][C]0.067033[/C][C]0.7312[/C][C]0.233035[/C][/ROW]
[ROW][C]5[/C][C]-0.127179[/C][C]-1.3874[/C][C]0.083963[/C][/ROW]
[ROW][C]6[/C][C]0.05057[/C][C]0.5516[/C][C]0.291112[/C][/ROW]
[ROW][C]7[/C][C]-0.084742[/C][C]-0.9244[/C][C]0.178566[/C][/ROW]
[ROW][C]8[/C][C]0.084979[/C][C]0.927[/C][C]0.177899[/C][/ROW]
[ROW][C]9[/C][C]-0.162055[/C][C]-1.7678[/C][C]0.039828[/C][/ROW]
[ROW][C]10[/C][C]-0.0398[/C][C]-0.4342[/C][C]0.332476[/C][/ROW]
[ROW][C]11[/C][C]-0.178014[/C][C]-1.9419[/C][C]0.027256[/C][/ROW]
[ROW][C]12[/C][C]0.824288[/C][C]8.9919[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.222699[/C][C]-2.4294[/C][C]0.00831[/C][/ROW]
[ROW][C]14[/C][C]-0.040343[/C][C]-0.4401[/C][C]0.330336[/C][/ROW]
[ROW][C]15[/C][C]-0.126437[/C][C]-1.3793[/C][C]0.085199[/C][/ROW]
[ROW][C]16[/C][C]0.071258[/C][C]0.7773[/C][C]0.219252[/C][/ROW]
[ROW][C]17[/C][C]-0.148908[/C][C]-1.6244[/C][C]0.053469[/C][/ROW]
[ROW][C]18[/C][C]0.078667[/C][C]0.8582[/C][C]0.196265[/C][/ROW]
[ROW][C]19[/C][C]-0.087466[/C][C]-0.9541[/C][C]0.170974[/C][/ROW]
[ROW][C]20[/C][C]0.093311[/C][C]1.0179[/C][C]0.155396[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307274&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307274&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	-0.216906	-2.3662	0.009794
2	-0.052827	-0.5763	0.282758
3	-0.144728	-1.5788	0.058519
4	0.067033	0.7312	0.233035
5	-0.127179	-1.3874	0.083963
6	0.05057	0.5516	0.291112
7	-0.084742	-0.9244	0.178566
8	0.084979	0.927	0.177899
9	-0.162055	-1.7678	0.039828
10	-0.0398	-0.4342	0.332476
11	-0.178014	-1.9419	0.027256
12	0.824288	8.9919	0
13	-0.222699	-2.4294	0.00831
14	-0.040343	-0.4401	0.330336
15	-0.126437	-1.3793	0.085199
16	0.071258	0.7773	0.219252
17	-0.148908	-1.6244	0.053469
18	0.078667	0.8582	0.196265
19	-0.087466	-0.9541	0.170974
20	0.093311	1.0179	0.155396

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.216906	-2.3662	0.009794
2	-0.104807	-1.1433	0.127603
3	-0.191113	-2.0848	0.019613
4	-0.021979	-0.2398	0.405463
5	-0.161887	-1.766	0.039982
6	-0.047081	-0.5136	0.304244
7	-0.123989	-1.3526	0.089381
8	-0.013633	-0.1487	0.441014
9	-0.190288	-2.0758	0.020033
10	-0.202374	-2.2076	0.014593
11	-0.356777	-3.892	8.2e-05
12	0.754905	8.235	0
13	0.022631	0.2469	0.402713
14	0.022006	0.2401	0.40535
15	-0.014819	-0.1617	0.435924
16	0.043267	0.472	0.318899
17	0.008468	0.0924	0.463279
18	0.07716	0.8417	0.200818
19	-0.100726	-1.0988	0.137039
20	-0.019258	-0.2101	0.416982

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.216906 & -2.3662 & 0.009794 \tabularnewline
2 & -0.104807 & -1.1433 & 0.127603 \tabularnewline
3 & -0.191113 & -2.0848 & 0.019613 \tabularnewline
4 & -0.021979 & -0.2398 & 0.405463 \tabularnewline
5 & -0.161887 & -1.766 & 0.039982 \tabularnewline
6 & -0.047081 & -0.5136 & 0.304244 \tabularnewline
7 & -0.123989 & -1.3526 & 0.089381 \tabularnewline
8 & -0.013633 & -0.1487 & 0.441014 \tabularnewline
9 & -0.190288 & -2.0758 & 0.020033 \tabularnewline
10 & -0.202374 & -2.2076 & 0.014593 \tabularnewline
11 & -0.356777 & -3.892 & 8.2e-05 \tabularnewline
12 & 0.754905 & 8.235 & 0 \tabularnewline
13 & 0.022631 & 0.2469 & 0.402713 \tabularnewline
14 & 0.022006 & 0.2401 & 0.40535 \tabularnewline
15 & -0.014819 & -0.1617 & 0.435924 \tabularnewline
16 & 0.043267 & 0.472 & 0.318899 \tabularnewline
17 & 0.008468 & 0.0924 & 0.463279 \tabularnewline
18 & 0.07716 & 0.8417 & 0.200818 \tabularnewline
19 & -0.100726 & -1.0988 & 0.137039 \tabularnewline
20 & -0.019258 & -0.2101 & 0.416982 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307274&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]-0.216906[/C][C]-2.3662[/C][C]0.009794[/C][/ROW]
[ROW][C]2[/C][C]-0.104807[/C][C]-1.1433[/C][C]0.127603[/C][/ROW]
[ROW][C]3[/C][C]-0.191113[/C][C]-2.0848[/C][C]0.019613[/C][/ROW]
[ROW][C]4[/C][C]-0.021979[/C][C]-0.2398[/C][C]0.405463[/C][/ROW]
[ROW][C]5[/C][C]-0.161887[/C][C]-1.766[/C][C]0.039982[/C][/ROW]
[ROW][C]6[/C][C]-0.047081[/C][C]-0.5136[/C][C]0.304244[/C][/ROW]
[ROW][C]7[/C][C]-0.123989[/C][C]-1.3526[/C][C]0.089381[/C][/ROW]
[ROW][C]8[/C][C]-0.013633[/C][C]-0.1487[/C][C]0.441014[/C][/ROW]
[ROW][C]9[/C][C]-0.190288[/C][C]-2.0758[/C][C]0.020033[/C][/ROW]
[ROW][C]10[/C][C]-0.202374[/C][C]-2.2076[/C][C]0.014593[/C][/ROW]
[ROW][C]11[/C][C]-0.356777[/C][C]-3.892[/C][C]8.2e-05[/C][/ROW]
[ROW][C]12[/C][C]0.754905[/C][C]8.235[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.022631[/C][C]0.2469[/C][C]0.402713[/C][/ROW]
[ROW][C]14[/C][C]0.022006[/C][C]0.2401[/C][C]0.40535[/C][/ROW]
[ROW][C]15[/C][C]-0.014819[/C][C]-0.1617[/C][C]0.435924[/C][/ROW]
[ROW][C]16[/C][C]0.043267[/C][C]0.472[/C][C]0.318899[/C][/ROW]
[ROW][C]17[/C][C]0.008468[/C][C]0.0924[/C][C]0.463279[/C][/ROW]
[ROW][C]18[/C][C]0.07716[/C][C]0.8417[/C][C]0.200818[/C][/ROW]
[ROW][C]19[/C][C]-0.100726[/C][C]-1.0988[/C][C]0.137039[/C][/ROW]
[ROW][C]20[/C][C]-0.019258[/C][C]-0.2101[/C][C]0.416982[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307274&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307274&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	-0.216906	-2.3662	0.009794
2	-0.104807	-1.1433	0.127603
3	-0.191113	-2.0848	0.019613
4	-0.021979	-0.2398	0.405463
5	-0.161887	-1.766	0.039982
6	-0.047081	-0.5136	0.304244
7	-0.123989	-1.3526	0.089381
8	-0.013633	-0.1487	0.441014
9	-0.190288	-2.0758	0.020033
10	-0.202374	-2.2076	0.014593
11	-0.356777	-3.892	8.2e-05
12	0.754905	8.235	0
13	0.022631	0.2469	0.402713
14	0.022006	0.2401	0.40535
15	-0.014819	-0.1617	0.435924
16	0.043267	0.472	0.318899
17	0.008468	0.0924	0.463279
18	0.07716	0.8417	0.200818
19	-0.100726	-1.0988	0.137039
20	-0.019258	-0.2101	0.416982

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):

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,'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