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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 13 Dec 2016 12:42:39 +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/t14816294066k06y78fofqjxxb.htm/, Retrieved Sun, 05 May 2024 04:56:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299075, Retrieved Sun, 05 May 2024 04:56:53 +0000

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

-       [(Partial) Autocorrelation Function] [Autocorrelatie oo...] [2016-12-13 11:42:39] [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=299075&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=299075&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299075&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	0.700838	7.2833	0
2	0.516517	5.3678	0
3	0.288439	2.9975	0.001689
4	0.044412	0.4615	0.322668
5	-0.120255	-1.2497	0.10705
6	-0.212546	-2.2088	0.014649
7	-0.135204	-1.4051	0.081433
8	-0.043008	-0.447	0.327901
9	0.211663	2.1997	0.014981
10	0.427146	4.439	1.1e-05
11	0.549572	5.7113	0
12	0.624991	6.4951	0
13	0.54123	5.6246	0
14	0.417726	4.3411	1.6e-05
15	0.133855	1.3911	0.083533
16	-0.070837	-0.7362	0.231613
17	-0.157347	-1.6352	0.05246
18	-0.248204	-2.5794	0.005621
19	-0.203199	-2.1117	0.018509
20	-0.100582	-1.0453	0.149113

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.700838 & 7.2833 & 0 \tabularnewline
2 & 0.516517 & 5.3678 & 0 \tabularnewline
3 & 0.288439 & 2.9975 & 0.001689 \tabularnewline
4 & 0.044412 & 0.4615 & 0.322668 \tabularnewline
5 & -0.120255 & -1.2497 & 0.10705 \tabularnewline
6 & -0.212546 & -2.2088 & 0.014649 \tabularnewline
7 & -0.135204 & -1.4051 & 0.081433 \tabularnewline
8 & -0.043008 & -0.447 & 0.327901 \tabularnewline
9 & 0.211663 & 2.1997 & 0.014981 \tabularnewline
10 & 0.427146 & 4.439 & 1.1e-05 \tabularnewline
11 & 0.549572 & 5.7113 & 0 \tabularnewline
12 & 0.624991 & 6.4951 & 0 \tabularnewline
13 & 0.54123 & 5.6246 & 0 \tabularnewline
14 & 0.417726 & 4.3411 & 1.6e-05 \tabularnewline
15 & 0.133855 & 1.3911 & 0.083533 \tabularnewline
16 & -0.070837 & -0.7362 & 0.231613 \tabularnewline
17 & -0.157347 & -1.6352 & 0.05246 \tabularnewline
18 & -0.248204 & -2.5794 & 0.005621 \tabularnewline
19 & -0.203199 & -2.1117 & 0.018509 \tabularnewline
20 & -0.100582 & -1.0453 & 0.149113 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299075&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]0.700838[/C][C]7.2833[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.516517[/C][C]5.3678[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.288439[/C][C]2.9975[/C][C]0.001689[/C][/ROW]
[ROW][C]4[/C][C]0.044412[/C][C]0.4615[/C][C]0.322668[/C][/ROW]
[ROW][C]5[/C][C]-0.120255[/C][C]-1.2497[/C][C]0.10705[/C][/ROW]
[ROW][C]6[/C][C]-0.212546[/C][C]-2.2088[/C][C]0.014649[/C][/ROW]
[ROW][C]7[/C][C]-0.135204[/C][C]-1.4051[/C][C]0.081433[/C][/ROW]
[ROW][C]8[/C][C]-0.043008[/C][C]-0.447[/C][C]0.327901[/C][/ROW]
[ROW][C]9[/C][C]0.211663[/C][C]2.1997[/C][C]0.014981[/C][/ROW]
[ROW][C]10[/C][C]0.427146[/C][C]4.439[/C][C]1.1e-05[/C][/ROW]
[ROW][C]11[/C][C]0.549572[/C][C]5.7113[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.624991[/C][C]6.4951[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.54123[/C][C]5.6246[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.417726[/C][C]4.3411[/C][C]1.6e-05[/C][/ROW]
[ROW][C]15[/C][C]0.133855[/C][C]1.3911[/C][C]0.083533[/C][/ROW]
[ROW][C]16[/C][C]-0.070837[/C][C]-0.7362[/C][C]0.231613[/C][/ROW]
[ROW][C]17[/C][C]-0.157347[/C][C]-1.6352[/C][C]0.05246[/C][/ROW]
[ROW][C]18[/C][C]-0.248204[/C][C]-2.5794[/C][C]0.005621[/C][/ROW]
[ROW][C]19[/C][C]-0.203199[/C][C]-2.1117[/C][C]0.018509[/C][/ROW]
[ROW][C]20[/C][C]-0.100582[/C][C]-1.0453[/C][C]0.149113[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299075&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299075&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	0.700838	7.2833	0
2	0.516517	5.3678	0
3	0.288439	2.9975	0.001689
4	0.044412	0.4615	0.322668
5	-0.120255	-1.2497	0.10705
6	-0.212546	-2.2088	0.014649
7	-0.135204	-1.4051	0.081433
8	-0.043008	-0.447	0.327901
9	0.211663	2.1997	0.014981
10	0.427146	4.439	1.1e-05
11	0.549572	5.7113	0
12	0.624991	6.4951	0
13	0.54123	5.6246	0
14	0.417726	4.3411	1.6e-05
15	0.133855	1.3911	0.083533
16	-0.070837	-0.7362	0.231613
17	-0.157347	-1.6352	0.05246
18	-0.248204	-2.5794	0.005621
19	-0.203199	-2.1117	0.018509
20	-0.100582	-1.0453	0.149113

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.700838	7.2833	0
2	0.049806	0.5176	0.302898
3	-0.17817	-1.8516	0.033408
4	-0.228649	-2.3762	0.009627
5	-0.076296	-0.7929	0.214789
6	0.003049	0.0317	0.487389
7	0.240628	2.5007	0.006949
8	0.099727	1.0364	0.151166
9	0.352149	3.6596	0.000196
10	0.232946	2.4208	0.008576
11	0.080645	0.8381	0.201916
12	0.092886	0.9653	0.168275
13	-0.047919	-0.498	0.309751
14	0.011367	0.1181	0.453092
15	-0.237021	-2.4632	0.007675
16	-0.093649	-0.9732	0.166308
17	0.176071	1.8298	0.035021
18	-0.025738	-0.2675	0.394806
19	-0.061195	-0.636	0.263076
20	-0.066833	-0.6946	0.244414

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.700838 & 7.2833 & 0 \tabularnewline
2 & 0.049806 & 0.5176 & 0.302898 \tabularnewline
3 & -0.17817 & -1.8516 & 0.033408 \tabularnewline
4 & -0.228649 & -2.3762 & 0.009627 \tabularnewline
5 & -0.076296 & -0.7929 & 0.214789 \tabularnewline
6 & 0.003049 & 0.0317 & 0.487389 \tabularnewline
7 & 0.240628 & 2.5007 & 0.006949 \tabularnewline
8 & 0.099727 & 1.0364 & 0.151166 \tabularnewline
9 & 0.352149 & 3.6596 & 0.000196 \tabularnewline
10 & 0.232946 & 2.4208 & 0.008576 \tabularnewline
11 & 0.080645 & 0.8381 & 0.201916 \tabularnewline
12 & 0.092886 & 0.9653 & 0.168275 \tabularnewline
13 & -0.047919 & -0.498 & 0.309751 \tabularnewline
14 & 0.011367 & 0.1181 & 0.453092 \tabularnewline
15 & -0.237021 & -2.4632 & 0.007675 \tabularnewline
16 & -0.093649 & -0.9732 & 0.166308 \tabularnewline
17 & 0.176071 & 1.8298 & 0.035021 \tabularnewline
18 & -0.025738 & -0.2675 & 0.394806 \tabularnewline
19 & -0.061195 & -0.636 & 0.263076 \tabularnewline
20 & -0.066833 & -0.6946 & 0.244414 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299075&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]0.700838[/C][C]7.2833[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.049806[/C][C]0.5176[/C][C]0.302898[/C][/ROW]
[ROW][C]3[/C][C]-0.17817[/C][C]-1.8516[/C][C]0.033408[/C][/ROW]
[ROW][C]4[/C][C]-0.228649[/C][C]-2.3762[/C][C]0.009627[/C][/ROW]
[ROW][C]5[/C][C]-0.076296[/C][C]-0.7929[/C][C]0.214789[/C][/ROW]
[ROW][C]6[/C][C]0.003049[/C][C]0.0317[/C][C]0.487389[/C][/ROW]
[ROW][C]7[/C][C]0.240628[/C][C]2.5007[/C][C]0.006949[/C][/ROW]
[ROW][C]8[/C][C]0.099727[/C][C]1.0364[/C][C]0.151166[/C][/ROW]
[ROW][C]9[/C][C]0.352149[/C][C]3.6596[/C][C]0.000196[/C][/ROW]
[ROW][C]10[/C][C]0.232946[/C][C]2.4208[/C][C]0.008576[/C][/ROW]
[ROW][C]11[/C][C]0.080645[/C][C]0.8381[/C][C]0.201916[/C][/ROW]
[ROW][C]12[/C][C]0.092886[/C][C]0.9653[/C][C]0.168275[/C][/ROW]
[ROW][C]13[/C][C]-0.047919[/C][C]-0.498[/C][C]0.309751[/C][/ROW]
[ROW][C]14[/C][C]0.011367[/C][C]0.1181[/C][C]0.453092[/C][/ROW]
[ROW][C]15[/C][C]-0.237021[/C][C]-2.4632[/C][C]0.007675[/C][/ROW]
[ROW][C]16[/C][C]-0.093649[/C][C]-0.9732[/C][C]0.166308[/C][/ROW]
[ROW][C]17[/C][C]0.176071[/C][C]1.8298[/C][C]0.035021[/C][/ROW]
[ROW][C]18[/C][C]-0.025738[/C][C]-0.2675[/C][C]0.394806[/C][/ROW]
[ROW][C]19[/C][C]-0.061195[/C][C]-0.636[/C][C]0.263076[/C][/ROW]
[ROW][C]20[/C][C]-0.066833[/C][C]-0.6946[/C][C]0.244414[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299075&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299075&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	0.700838	7.2833	0
2	0.049806	0.5176	0.302898
3	-0.17817	-1.8516	0.033408
4	-0.228649	-2.3762	0.009627
5	-0.076296	-0.7929	0.214789
6	0.003049	0.0317	0.487389
7	0.240628	2.5007	0.006949
8	0.099727	1.0364	0.151166
9	0.352149	3.6596	0.000196
10	0.232946	2.4208	0.008576
11	0.080645	0.8381	0.201916
12	0.092886	0.9653	0.168275
13	-0.047919	-0.498	0.309751
14	0.011367	0.1181	0.453092
15	-0.237021	-2.4632	0.007675
16	-0.093649	-0.9732	0.166308
17	0.176071	1.8298	0.035021
18	-0.025738	-0.2675	0.394806
19	-0.061195	-0.636	0.263076
20	-0.066833	-0.6946	0.244414

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

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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)
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