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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 13 Dec 2016 12:47:29 +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/13/t1481629685br0sx5f50kwajzx.htm/, Retrieved Sun, 05 May 2024 02:57:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299077, Retrieved Sun, 05 May 2024 02:57:26 +0000

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-       [(Partial) Autocorrelation Function] [Autocorrelatie d=1] [2016-12-13 11:47:29] [e8b5e2ae4a4517822f644e6c122e1af0] [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=299077&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=299077&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299077&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	-0.188779	-1.9527	0.026731
2	0.070664	0.7309	0.233204
3	0.026577	0.2749	0.391955
4	-0.131542	-1.3607	0.088237
5	-0.123724	-1.2798	0.10169
6	-0.283622	-2.9338	0.002049
7	-0.027929	-0.2889	0.38661
8	-0.275419	-2.849	0.002631
9	0.064537	0.6676	0.25292
10	0.15984	1.6534	0.05059
11	0.07562	0.7822	0.217908
12	0.269151	2.7841	0.003174
13	0.070922	0.7336	0.232391
14	0.268915	2.7817	0.003196
15	-0.132779	-1.3735	0.086237
16	-0.19619	-2.0294	0.02245
17	0.004232	0.0438	0.482582
18	-0.228713	-2.3658	0.009895
19	-0.099327	-1.0274	0.153264
20	-0.131871	-1.3641	0.087701

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.188779 & -1.9527 & 0.026731 \tabularnewline
2 & 0.070664 & 0.7309 & 0.233204 \tabularnewline
3 & 0.026577 & 0.2749 & 0.391955 \tabularnewline
4 & -0.131542 & -1.3607 & 0.088237 \tabularnewline
5 & -0.123724 & -1.2798 & 0.10169 \tabularnewline
6 & -0.283622 & -2.9338 & 0.002049 \tabularnewline
7 & -0.027929 & -0.2889 & 0.38661 \tabularnewline
8 & -0.275419 & -2.849 & 0.002631 \tabularnewline
9 & 0.064537 & 0.6676 & 0.25292 \tabularnewline
10 & 0.15984 & 1.6534 & 0.05059 \tabularnewline
11 & 0.07562 & 0.7822 & 0.217908 \tabularnewline
12 & 0.269151 & 2.7841 & 0.003174 \tabularnewline
13 & 0.070922 & 0.7336 & 0.232391 \tabularnewline
14 & 0.268915 & 2.7817 & 0.003196 \tabularnewline
15 & -0.132779 & -1.3735 & 0.086237 \tabularnewline
16 & -0.19619 & -2.0294 & 0.02245 \tabularnewline
17 & 0.004232 & 0.0438 & 0.482582 \tabularnewline
18 & -0.228713 & -2.3658 & 0.009895 \tabularnewline
19 & -0.099327 & -1.0274 & 0.153264 \tabularnewline
20 & -0.131871 & -1.3641 & 0.087701 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299077&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]-0.188779[/C][C]-1.9527[/C][C]0.026731[/C][/ROW]
[ROW][C]2[/C][C]0.070664[/C][C]0.7309[/C][C]0.233204[/C][/ROW]
[ROW][C]3[/C][C]0.026577[/C][C]0.2749[/C][C]0.391955[/C][/ROW]
[ROW][C]4[/C][C]-0.131542[/C][C]-1.3607[/C][C]0.088237[/C][/ROW]
[ROW][C]5[/C][C]-0.123724[/C][C]-1.2798[/C][C]0.10169[/C][/ROW]
[ROW][C]6[/C][C]-0.283622[/C][C]-2.9338[/C][C]0.002049[/C][/ROW]
[ROW][C]7[/C][C]-0.027929[/C][C]-0.2889[/C][C]0.38661[/C][/ROW]
[ROW][C]8[/C][C]-0.275419[/C][C]-2.849[/C][C]0.002631[/C][/ROW]
[ROW][C]9[/C][C]0.064537[/C][C]0.6676[/C][C]0.25292[/C][/ROW]
[ROW][C]10[/C][C]0.15984[/C][C]1.6534[/C][C]0.05059[/C][/ROW]
[ROW][C]11[/C][C]0.07562[/C][C]0.7822[/C][C]0.217908[/C][/ROW]
[ROW][C]12[/C][C]0.269151[/C][C]2.7841[/C][C]0.003174[/C][/ROW]
[ROW][C]13[/C][C]0.070922[/C][C]0.7336[/C][C]0.232391[/C][/ROW]
[ROW][C]14[/C][C]0.268915[/C][C]2.7817[/C][C]0.003196[/C][/ROW]
[ROW][C]15[/C][C]-0.132779[/C][C]-1.3735[/C][C]0.086237[/C][/ROW]
[ROW][C]16[/C][C]-0.19619[/C][C]-2.0294[/C][C]0.02245[/C][/ROW]
[ROW][C]17[/C][C]0.004232[/C][C]0.0438[/C][C]0.482582[/C][/ROW]
[ROW][C]18[/C][C]-0.228713[/C][C]-2.3658[/C][C]0.009895[/C][/ROW]
[ROW][C]19[/C][C]-0.099327[/C][C]-1.0274[/C][C]0.153264[/C][/ROW]
[ROW][C]20[/C][C]-0.131871[/C][C]-1.3641[/C][C]0.087701[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299077&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299077&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	-0.188779	-1.9527	0.026731
2	0.070664	0.7309	0.233204
3	0.026577	0.2749	0.391955
4	-0.131542	-1.3607	0.088237
5	-0.123724	-1.2798	0.10169
6	-0.283622	-2.9338	0.002049
7	-0.027929	-0.2889	0.38661
8	-0.275419	-2.849	0.002631
9	0.064537	0.6676	0.25292
10	0.15984	1.6534	0.05059
11	0.07562	0.7822	0.217908
12	0.269151	2.7841	0.003174
13	0.070922	0.7336	0.232391
14	0.268915	2.7817	0.003196
15	-0.132779	-1.3735	0.086237
16	-0.19619	-2.0294	0.02245
17	0.004232	0.0438	0.482582
18	-0.228713	-2.3658	0.009895
19	-0.099327	-1.0274	0.153264
20	-0.131871	-1.3641	0.087701

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.188779	-1.9527	0.026731
2	0.03632	0.3757	0.353941
3	0.048063	0.4972	0.310045
4	-0.125691	-1.3002	0.098171
5	-0.18392	-1.9025	0.029898
6	-0.35638	-3.6864	0.000179
7	-0.17929	-1.8546	0.033204
8	-0.402714	-4.1657	3.2e-05
9	-0.26748	-2.7668	0.003335
10	-0.106133	-1.0978	0.137367
11	-0.124055	-1.2832	0.10109
12	0.020904	0.2162	0.414608
13	-0.035527	-0.3675	0.356989
14	0.214863	2.2226	0.014174
15	0.065376	0.6762	0.250171
16	-0.201234	-2.0816	0.019883
17	-0.001637	-0.0169	0.49326
18	0.036042	0.3728	0.35501
19	0.040522	0.4192	0.337969
20	0.02004	0.2073	0.418088

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.188779 & -1.9527 & 0.026731 \tabularnewline
2 & 0.03632 & 0.3757 & 0.353941 \tabularnewline
3 & 0.048063 & 0.4972 & 0.310045 \tabularnewline
4 & -0.125691 & -1.3002 & 0.098171 \tabularnewline
5 & -0.18392 & -1.9025 & 0.029898 \tabularnewline
6 & -0.35638 & -3.6864 & 0.000179 \tabularnewline
7 & -0.17929 & -1.8546 & 0.033204 \tabularnewline
8 & -0.402714 & -4.1657 & 3.2e-05 \tabularnewline
9 & -0.26748 & -2.7668 & 0.003335 \tabularnewline
10 & -0.106133 & -1.0978 & 0.137367 \tabularnewline
11 & -0.124055 & -1.2832 & 0.10109 \tabularnewline
12 & 0.020904 & 0.2162 & 0.414608 \tabularnewline
13 & -0.035527 & -0.3675 & 0.356989 \tabularnewline
14 & 0.214863 & 2.2226 & 0.014174 \tabularnewline
15 & 0.065376 & 0.6762 & 0.250171 \tabularnewline
16 & -0.201234 & -2.0816 & 0.019883 \tabularnewline
17 & -0.001637 & -0.0169 & 0.49326 \tabularnewline
18 & 0.036042 & 0.3728 & 0.35501 \tabularnewline
19 & 0.040522 & 0.4192 & 0.337969 \tabularnewline
20 & 0.02004 & 0.2073 & 0.418088 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299077&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]-0.188779[/C][C]-1.9527[/C][C]0.026731[/C][/ROW]
[ROW][C]2[/C][C]0.03632[/C][C]0.3757[/C][C]0.353941[/C][/ROW]
[ROW][C]3[/C][C]0.048063[/C][C]0.4972[/C][C]0.310045[/C][/ROW]
[ROW][C]4[/C][C]-0.125691[/C][C]-1.3002[/C][C]0.098171[/C][/ROW]
[ROW][C]5[/C][C]-0.18392[/C][C]-1.9025[/C][C]0.029898[/C][/ROW]
[ROW][C]6[/C][C]-0.35638[/C][C]-3.6864[/C][C]0.000179[/C][/ROW]
[ROW][C]7[/C][C]-0.17929[/C][C]-1.8546[/C][C]0.033204[/C][/ROW]
[ROW][C]8[/C][C]-0.402714[/C][C]-4.1657[/C][C]3.2e-05[/C][/ROW]
[ROW][C]9[/C][C]-0.26748[/C][C]-2.7668[/C][C]0.003335[/C][/ROW]
[ROW][C]10[/C][C]-0.106133[/C][C]-1.0978[/C][C]0.137367[/C][/ROW]
[ROW][C]11[/C][C]-0.124055[/C][C]-1.2832[/C][C]0.10109[/C][/ROW]
[ROW][C]12[/C][C]0.020904[/C][C]0.2162[/C][C]0.414608[/C][/ROW]
[ROW][C]13[/C][C]-0.035527[/C][C]-0.3675[/C][C]0.356989[/C][/ROW]
[ROW][C]14[/C][C]0.214863[/C][C]2.2226[/C][C]0.014174[/C][/ROW]
[ROW][C]15[/C][C]0.065376[/C][C]0.6762[/C][C]0.250171[/C][/ROW]
[ROW][C]16[/C][C]-0.201234[/C][C]-2.0816[/C][C]0.019883[/C][/ROW]
[ROW][C]17[/C][C]-0.001637[/C][C]-0.0169[/C][C]0.49326[/C][/ROW]
[ROW][C]18[/C][C]0.036042[/C][C]0.3728[/C][C]0.35501[/C][/ROW]
[ROW][C]19[/C][C]0.040522[/C][C]0.4192[/C][C]0.337969[/C][/ROW]
[ROW][C]20[/C][C]0.02004[/C][C]0.2073[/C][C]0.418088[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299077&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299077&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	-0.188779	-1.9527	0.026731
2	0.03632	0.3757	0.353941
3	0.048063	0.4972	0.310045
4	-0.125691	-1.3002	0.098171
5	-0.18392	-1.9025	0.029898
6	-0.35638	-3.6864	0.000179
7	-0.17929	-1.8546	0.033204
8	-0.402714	-4.1657	3.2e-05
9	-0.26748	-2.7668	0.003335
10	-0.106133	-1.0978	0.137367
11	-0.124055	-1.2832	0.10109
12	0.020904	0.2162	0.414608
13	-0.035527	-0.3675	0.356989
14	0.214863	2.2226	0.014174
15	0.065376	0.6762	0.250171
16	-0.201234	-2.0816	0.019883
17	-0.001637	-0.0169	0.49326
18	0.036042	0.3728	0.35501
19	0.040522	0.4192	0.337969
20	0.02004	0.2073	0.418088

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

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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,'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