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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 20 Dec 2016 16:16:02 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/20/t1482246971ykvmtnkzt8xiceo.htm/, Retrieved Sat, 27 Apr 2024 18:40:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301707, Retrieved Sat, 27 Apr 2024 18:40:52 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-12-20 15:16:02] [361c8dad91b3f1ef2e651cd04783c23b] [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=301707&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=301707&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301707&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	0.677816	5.0268	3e-06
2	0.430459	3.1924	0.001167
3	0.262889	1.9496	0.028162
4	-0.020914	-0.1551	0.438655
5	-0.218512	-1.6205	0.05542
6	-0.252773	-1.8746	0.03308
7	-0.195143	-1.4472	0.076756
8	-0.226076	-1.6766	0.049646
9	-0.084212	-0.6245	0.26743
10	0.09621	0.7135	0.239272
11	0.093261	0.6916	0.246036
12	0.088851	0.6589	0.256343
13	0.118339	0.8776	0.191982
14	0.056585	0.4196	0.33819
15	-0.117342	-0.8702	0.193979
16	-0.204341	-1.5154	0.067695
17	-0.251918	-1.8683	0.033527

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.677816 & 5.0268 & 3e-06 \tabularnewline
2 & 0.430459 & 3.1924 & 0.001167 \tabularnewline
3 & 0.262889 & 1.9496 & 0.028162 \tabularnewline
4 & -0.020914 & -0.1551 & 0.438655 \tabularnewline
5 & -0.218512 & -1.6205 & 0.05542 \tabularnewline
6 & -0.252773 & -1.8746 & 0.03308 \tabularnewline
7 & -0.195143 & -1.4472 & 0.076756 \tabularnewline
8 & -0.226076 & -1.6766 & 0.049646 \tabularnewline
9 & -0.084212 & -0.6245 & 0.26743 \tabularnewline
10 & 0.09621 & 0.7135 & 0.239272 \tabularnewline
11 & 0.093261 & 0.6916 & 0.246036 \tabularnewline
12 & 0.088851 & 0.6589 & 0.256343 \tabularnewline
13 & 0.118339 & 0.8776 & 0.191982 \tabularnewline
14 & 0.056585 & 0.4196 & 0.33819 \tabularnewline
15 & -0.117342 & -0.8702 & 0.193979 \tabularnewline
16 & -0.204341 & -1.5154 & 0.067695 \tabularnewline
17 & -0.251918 & -1.8683 & 0.033527 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301707&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]0.677816[/C][C]5.0268[/C][C]3e-06[/C][/ROW]
[ROW][C]2[/C][C]0.430459[/C][C]3.1924[/C][C]0.001167[/C][/ROW]
[ROW][C]3[/C][C]0.262889[/C][C]1.9496[/C][C]0.028162[/C][/ROW]
[ROW][C]4[/C][C]-0.020914[/C][C]-0.1551[/C][C]0.438655[/C][/ROW]
[ROW][C]5[/C][C]-0.218512[/C][C]-1.6205[/C][C]0.05542[/C][/ROW]
[ROW][C]6[/C][C]-0.252773[/C][C]-1.8746[/C][C]0.03308[/C][/ROW]
[ROW][C]7[/C][C]-0.195143[/C][C]-1.4472[/C][C]0.076756[/C][/ROW]
[ROW][C]8[/C][C]-0.226076[/C][C]-1.6766[/C][C]0.049646[/C][/ROW]
[ROW][C]9[/C][C]-0.084212[/C][C]-0.6245[/C][C]0.26743[/C][/ROW]
[ROW][C]10[/C][C]0.09621[/C][C]0.7135[/C][C]0.239272[/C][/ROW]
[ROW][C]11[/C][C]0.093261[/C][C]0.6916[/C][C]0.246036[/C][/ROW]
[ROW][C]12[/C][C]0.088851[/C][C]0.6589[/C][C]0.256343[/C][/ROW]
[ROW][C]13[/C][C]0.118339[/C][C]0.8776[/C][C]0.191982[/C][/ROW]
[ROW][C]14[/C][C]0.056585[/C][C]0.4196[/C][C]0.33819[/C][/ROW]
[ROW][C]15[/C][C]-0.117342[/C][C]-0.8702[/C][C]0.193979[/C][/ROW]
[ROW][C]16[/C][C]-0.204341[/C][C]-1.5154[/C][C]0.067695[/C][/ROW]
[ROW][C]17[/C][C]-0.251918[/C][C]-1.8683[/C][C]0.033527[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301707&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301707&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	0.677816	5.0268	3e-06
2	0.430459	3.1924	0.001167
3	0.262889	1.9496	0.028162
4	-0.020914	-0.1551	0.438655
5	-0.218512	-1.6205	0.05542
6	-0.252773	-1.8746	0.03308
7	-0.195143	-1.4472	0.076756
8	-0.226076	-1.6766	0.049646
9	-0.084212	-0.6245	0.26743
10	0.09621	0.7135	0.239272
11	0.093261	0.6916	0.246036
12	0.088851	0.6589	0.256343
13	0.118339	0.8776	0.191982
14	0.056585	0.4196	0.33819
15	-0.117342	-0.8702	0.193979
16	-0.204341	-1.5154	0.067695
17	-0.251918	-1.8683	0.033527

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.677816	5.0268	3e-06
2	-0.053602	-0.3975	0.346259
3	-0.015195	-0.1127	0.455344
4	-0.333538	-2.4736	0.008246
5	-0.122167	-0.906	0.18444
6	0.052731	0.3911	0.348631
7	0.153772	1.1404	0.12953
8	-0.193249	-1.4332	0.078734
9	0.167736	1.244	0.109395
10	0.098771	0.7325	0.233486
11	-0.091509	-0.6787	0.250103
12	-0.094945	-0.7041	0.24216
13	0.037253	0.2763	0.391686
14	-0.008145	-0.0604	0.476026
15	-0.179515	-1.3313	0.094288
16	-0.134663	-0.9987	0.16116
17	-0.032934	-0.2442	0.403974

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.677816 & 5.0268 & 3e-06 \tabularnewline
2 & -0.053602 & -0.3975 & 0.346259 \tabularnewline
3 & -0.015195 & -0.1127 & 0.455344 \tabularnewline
4 & -0.333538 & -2.4736 & 0.008246 \tabularnewline
5 & -0.122167 & -0.906 & 0.18444 \tabularnewline
6 & 0.052731 & 0.3911 & 0.348631 \tabularnewline
7 & 0.153772 & 1.1404 & 0.12953 \tabularnewline
8 & -0.193249 & -1.4332 & 0.078734 \tabularnewline
9 & 0.167736 & 1.244 & 0.109395 \tabularnewline
10 & 0.098771 & 0.7325 & 0.233486 \tabularnewline
11 & -0.091509 & -0.6787 & 0.250103 \tabularnewline
12 & -0.094945 & -0.7041 & 0.24216 \tabularnewline
13 & 0.037253 & 0.2763 & 0.391686 \tabularnewline
14 & -0.008145 & -0.0604 & 0.476026 \tabularnewline
15 & -0.179515 & -1.3313 & 0.094288 \tabularnewline
16 & -0.134663 & -0.9987 & 0.16116 \tabularnewline
17 & -0.032934 & -0.2442 & 0.403974 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301707&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]0.677816[/C][C]5.0268[/C][C]3e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.053602[/C][C]-0.3975[/C][C]0.346259[/C][/ROW]
[ROW][C]3[/C][C]-0.015195[/C][C]-0.1127[/C][C]0.455344[/C][/ROW]
[ROW][C]4[/C][C]-0.333538[/C][C]-2.4736[/C][C]0.008246[/C][/ROW]
[ROW][C]5[/C][C]-0.122167[/C][C]-0.906[/C][C]0.18444[/C][/ROW]
[ROW][C]6[/C][C]0.052731[/C][C]0.3911[/C][C]0.348631[/C][/ROW]
[ROW][C]7[/C][C]0.153772[/C][C]1.1404[/C][C]0.12953[/C][/ROW]
[ROW][C]8[/C][C]-0.193249[/C][C]-1.4332[/C][C]0.078734[/C][/ROW]
[ROW][C]9[/C][C]0.167736[/C][C]1.244[/C][C]0.109395[/C][/ROW]
[ROW][C]10[/C][C]0.098771[/C][C]0.7325[/C][C]0.233486[/C][/ROW]
[ROW][C]11[/C][C]-0.091509[/C][C]-0.6787[/C][C]0.250103[/C][/ROW]
[ROW][C]12[/C][C]-0.094945[/C][C]-0.7041[/C][C]0.24216[/C][/ROW]
[ROW][C]13[/C][C]0.037253[/C][C]0.2763[/C][C]0.391686[/C][/ROW]
[ROW][C]14[/C][C]-0.008145[/C][C]-0.0604[/C][C]0.476026[/C][/ROW]
[ROW][C]15[/C][C]-0.179515[/C][C]-1.3313[/C][C]0.094288[/C][/ROW]
[ROW][C]16[/C][C]-0.134663[/C][C]-0.9987[/C][C]0.16116[/C][/ROW]
[ROW][C]17[/C][C]-0.032934[/C][C]-0.2442[/C][C]0.403974[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301707&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301707&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	0.677816	5.0268	3e-06
2	-0.053602	-0.3975	0.346259
3	-0.015195	-0.1127	0.455344
4	-0.333538	-2.4736	0.008246
5	-0.122167	-0.906	0.18444
6	0.052731	0.3911	0.348631
7	0.153772	1.1404	0.12953
8	-0.193249	-1.4332	0.078734
9	0.167736	1.244	0.109395
10	0.098771	0.7325	0.233486
11	-0.091509	-0.6787	0.250103
12	-0.094945	-0.7041	0.24216
13	0.037253	0.2763	0.391686
14	-0.008145	-0.0604	0.476026
15	-0.179515	-1.3313	0.094288
16	-0.134663	-0.9987	0.16116
17	-0.032934	-0.2442	0.403974

Figure 1

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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 = 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')

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Input Parameters & R Code