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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 30 Nov 2016 20:06:50 +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/Nov/30/t1480533612kcl39d096jzruq0.htm/, Retrieved Sun, 19 May 2024 00:06:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297479, Retrieved Sun, 19 May 2024 00:06:01 +0000

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-       [(Partial) Autocorrelation Function] [Autocorrelatie N2...] [2016-11-30 19:06:50] [4c05fa0998bf98e29c2e453b139976f4] [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=297479&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=297479&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297479&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	0.924052	9.9523	0
2	0.855818	9.2174	0
3	0.776976	8.3683	0
4	0.689787	7.4292	0
5	0.621782	6.6968	0
6	0.561041	6.0426	0
7	0.530515	5.7138	0
8	0.508309	5.4747	0
9	0.507344	5.4643	0
10	0.500342	5.3888	0
11	0.474909	5.1149	1e-06
12	0.463306	4.99	1e-06
13	0.383922	4.135	3.4e-05
14	0.30074	3.2391	0.000782
15	0.226631	2.4409	0.008081
16	0.152264	1.6399	0.051864
17	0.108204	1.1654	0.123126
18	0.071037	0.7651	0.222887
19	0.059505	0.6409	0.261431
20	0.055457	0.5973	0.27574

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.924052 & 9.9523 & 0 \tabularnewline
2 & 0.855818 & 9.2174 & 0 \tabularnewline
3 & 0.776976 & 8.3683 & 0 \tabularnewline
4 & 0.689787 & 7.4292 & 0 \tabularnewline
5 & 0.621782 & 6.6968 & 0 \tabularnewline
6 & 0.561041 & 6.0426 & 0 \tabularnewline
7 & 0.530515 & 5.7138 & 0 \tabularnewline
8 & 0.508309 & 5.4747 & 0 \tabularnewline
9 & 0.507344 & 5.4643 & 0 \tabularnewline
10 & 0.500342 & 5.3888 & 0 \tabularnewline
11 & 0.474909 & 5.1149 & 1e-06 \tabularnewline
12 & 0.463306 & 4.99 & 1e-06 \tabularnewline
13 & 0.383922 & 4.135 & 3.4e-05 \tabularnewline
14 & 0.30074 & 3.2391 & 0.000782 \tabularnewline
15 & 0.226631 & 2.4409 & 0.008081 \tabularnewline
16 & 0.152264 & 1.6399 & 0.051864 \tabularnewline
17 & 0.108204 & 1.1654 & 0.123126 \tabularnewline
18 & 0.071037 & 0.7651 & 0.222887 \tabularnewline
19 & 0.059505 & 0.6409 & 0.261431 \tabularnewline
20 & 0.055457 & 0.5973 & 0.27574 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297479&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]0.924052[/C][C]9.9523[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.855818[/C][C]9.2174[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.776976[/C][C]8.3683[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.689787[/C][C]7.4292[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.621782[/C][C]6.6968[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.561041[/C][C]6.0426[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.530515[/C][C]5.7138[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.508309[/C][C]5.4747[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.507344[/C][C]5.4643[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.500342[/C][C]5.3888[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.474909[/C][C]5.1149[/C][C]1e-06[/C][/ROW]
[ROW][C]12[/C][C]0.463306[/C][C]4.99[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.383922[/C][C]4.135[/C][C]3.4e-05[/C][/ROW]
[ROW][C]14[/C][C]0.30074[/C][C]3.2391[/C][C]0.000782[/C][/ROW]
[ROW][C]15[/C][C]0.226631[/C][C]2.4409[/C][C]0.008081[/C][/ROW]
[ROW][C]16[/C][C]0.152264[/C][C]1.6399[/C][C]0.051864[/C][/ROW]
[ROW][C]17[/C][C]0.108204[/C][C]1.1654[/C][C]0.123126[/C][/ROW]
[ROW][C]18[/C][C]0.071037[/C][C]0.7651[/C][C]0.222887[/C][/ROW]
[ROW][C]19[/C][C]0.059505[/C][C]0.6409[/C][C]0.261431[/C][/ROW]
[ROW][C]20[/C][C]0.055457[/C][C]0.5973[/C][C]0.27574[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297479&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297479&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	0.924052	9.9523	0
2	0.855818	9.2174	0
3	0.776976	8.3683	0
4	0.689787	7.4292	0
5	0.621782	6.6968	0
6	0.561041	6.0426	0
7	0.530515	5.7138	0
8	0.508309	5.4747	0
9	0.507344	5.4643	0
10	0.500342	5.3888	0
11	0.474909	5.1149	1e-06
12	0.463306	4.99	1e-06
13	0.383922	4.135	3.4e-05
14	0.30074	3.2391	0.000782
15	0.226631	2.4409	0.008081
16	0.152264	1.6399	0.051864
17	0.108204	1.1654	0.123126
18	0.071037	0.7651	0.222887
19	0.059505	0.6409	0.261431
20	0.055457	0.5973	0.27574

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.924052	9.9523	0
2	0.013316	0.1434	0.443105
3	-0.106893	-1.1513	0.125993
4	-0.109075	-1.1748	0.121246
5	0.080596	0.868	0.193582
6	0.030282	0.3261	0.37245
7	0.163977	1.7661	0.040006
8	0.032921	0.3546	0.361779
9	0.117997	1.2709	0.10316
10	-0.056809	-0.6118	0.270917
11	-0.127672	-1.3751	0.085881
12	0.085759	0.9237	0.178791
13	-0.411283	-4.4297	1.1e-05
14	-0.097555	-1.0507	0.14779
15	0.078744	0.8481	0.199064
16	0.028069	0.3023	0.381477
17	0.111086	1.1964	0.116985
18	-0.007476	-0.0805	0.467983
19	0.00339	0.0365	0.485469
20	-0.000677	-0.0073	0.497096

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.924052 & 9.9523 & 0 \tabularnewline
2 & 0.013316 & 0.1434 & 0.443105 \tabularnewline
3 & -0.106893 & -1.1513 & 0.125993 \tabularnewline
4 & -0.109075 & -1.1748 & 0.121246 \tabularnewline
5 & 0.080596 & 0.868 & 0.193582 \tabularnewline
6 & 0.030282 & 0.3261 & 0.37245 \tabularnewline
7 & 0.163977 & 1.7661 & 0.040006 \tabularnewline
8 & 0.032921 & 0.3546 & 0.361779 \tabularnewline
9 & 0.117997 & 1.2709 & 0.10316 \tabularnewline
10 & -0.056809 & -0.6118 & 0.270917 \tabularnewline
11 & -0.127672 & -1.3751 & 0.085881 \tabularnewline
12 & 0.085759 & 0.9237 & 0.178791 \tabularnewline
13 & -0.411283 & -4.4297 & 1.1e-05 \tabularnewline
14 & -0.097555 & -1.0507 & 0.14779 \tabularnewline
15 & 0.078744 & 0.8481 & 0.199064 \tabularnewline
16 & 0.028069 & 0.3023 & 0.381477 \tabularnewline
17 & 0.111086 & 1.1964 & 0.116985 \tabularnewline
18 & -0.007476 & -0.0805 & 0.467983 \tabularnewline
19 & 0.00339 & 0.0365 & 0.485469 \tabularnewline
20 & -0.000677 & -0.0073 & 0.497096 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297479&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]0.924052[/C][C]9.9523[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.013316[/C][C]0.1434[/C][C]0.443105[/C][/ROW]
[ROW][C]3[/C][C]-0.106893[/C][C]-1.1513[/C][C]0.125993[/C][/ROW]
[ROW][C]4[/C][C]-0.109075[/C][C]-1.1748[/C][C]0.121246[/C][/ROW]
[ROW][C]5[/C][C]0.080596[/C][C]0.868[/C][C]0.193582[/C][/ROW]
[ROW][C]6[/C][C]0.030282[/C][C]0.3261[/C][C]0.37245[/C][/ROW]
[ROW][C]7[/C][C]0.163977[/C][C]1.7661[/C][C]0.040006[/C][/ROW]
[ROW][C]8[/C][C]0.032921[/C][C]0.3546[/C][C]0.361779[/C][/ROW]
[ROW][C]9[/C][C]0.117997[/C][C]1.2709[/C][C]0.10316[/C][/ROW]
[ROW][C]10[/C][C]-0.056809[/C][C]-0.6118[/C][C]0.270917[/C][/ROW]
[ROW][C]11[/C][C]-0.127672[/C][C]-1.3751[/C][C]0.085881[/C][/ROW]
[ROW][C]12[/C][C]0.085759[/C][C]0.9237[/C][C]0.178791[/C][/ROW]
[ROW][C]13[/C][C]-0.411283[/C][C]-4.4297[/C][C]1.1e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.097555[/C][C]-1.0507[/C][C]0.14779[/C][/ROW]
[ROW][C]15[/C][C]0.078744[/C][C]0.8481[/C][C]0.199064[/C][/ROW]
[ROW][C]16[/C][C]0.028069[/C][C]0.3023[/C][C]0.381477[/C][/ROW]
[ROW][C]17[/C][C]0.111086[/C][C]1.1964[/C][C]0.116985[/C][/ROW]
[ROW][C]18[/C][C]-0.007476[/C][C]-0.0805[/C][C]0.467983[/C][/ROW]
[ROW][C]19[/C][C]0.00339[/C][C]0.0365[/C][C]0.485469[/C][/ROW]
[ROW][C]20[/C][C]-0.000677[/C][C]-0.0073[/C][C]0.497096[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297479&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297479&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	0.924052	9.9523	0
2	0.013316	0.1434	0.443105
3	-0.106893	-1.1513	0.125993
4	-0.109075	-1.1748	0.121246
5	0.080596	0.868	0.193582
6	0.030282	0.3261	0.37245
7	0.163977	1.7661	0.040006
8	0.032921	0.3546	0.361779
9	0.117997	1.2709	0.10316
10	-0.056809	-0.6118	0.270917
11	-0.127672	-1.3751	0.085881
12	0.085759	0.9237	0.178791
13	-0.411283	-4.4297	1.1e-05
14	-0.097555	-1.0507	0.14779
15	0.078744	0.8481	0.199064
16	0.028069	0.3023	0.381477
17	0.111086	1.1964	0.116985
18	-0.007476	-0.0805	0.467983
19	0.00339	0.0365	0.485469
20	-0.000677	-0.0073	0.497096

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 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 12 ;

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