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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 20 Dec 2016 19:51:28 +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/t1482259913x2ntmq2fe6n6are.htm/, Retrieved Sun, 28 Apr 2024 17:27:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301773, Retrieved Sun, 28 Apr 2024 17:27:49 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-12-20 18:51:28] [672675941468e072e71d9fb024f2b817] [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=301773&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=301773&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301773&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	0.722488	5.1596	2e-06
2	0.725312	5.1798	2e-06
3	0.616389	4.4019	2.7e-05
4	0.739652	5.2822	1e-06
5	0.482198	3.4436	0.000578
6	0.493171	3.5219	0.000456
7	0.400482	2.86	0.003062
8	0.516057	3.6854	0.000277
9	0.287365	2.0522	0.02265
10	0.305747	2.1835	0.016814
11	0.231255	1.6515	0.052391
12	0.340575	2.4322	0.009278
13	0.141301	1.0091	0.158848
14	0.158322	1.1306	0.131747
15	0.090135	0.6437	0.261331
16	0.181273	1.2946	0.100653
17	-0.001866	-0.0133	0.494711

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.722488 & 5.1596 & 2e-06 \tabularnewline
2 & 0.725312 & 5.1798 & 2e-06 \tabularnewline
3 & 0.616389 & 4.4019 & 2.7e-05 \tabularnewline
4 & 0.739652 & 5.2822 & 1e-06 \tabularnewline
5 & 0.482198 & 3.4436 & 0.000578 \tabularnewline
6 & 0.493171 & 3.5219 & 0.000456 \tabularnewline
7 & 0.400482 & 2.86 & 0.003062 \tabularnewline
8 & 0.516057 & 3.6854 & 0.000277 \tabularnewline
9 & 0.287365 & 2.0522 & 0.02265 \tabularnewline
10 & 0.305747 & 2.1835 & 0.016814 \tabularnewline
11 & 0.231255 & 1.6515 & 0.052391 \tabularnewline
12 & 0.340575 & 2.4322 & 0.009278 \tabularnewline
13 & 0.141301 & 1.0091 & 0.158848 \tabularnewline
14 & 0.158322 & 1.1306 & 0.131747 \tabularnewline
15 & 0.090135 & 0.6437 & 0.261331 \tabularnewline
16 & 0.181273 & 1.2946 & 0.100653 \tabularnewline
17 & -0.001866 & -0.0133 & 0.494711 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301773&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]0.722488[/C][C]5.1596[/C][C]2e-06[/C][/ROW]
[ROW][C]2[/C][C]0.725312[/C][C]5.1798[/C][C]2e-06[/C][/ROW]
[ROW][C]3[/C][C]0.616389[/C][C]4.4019[/C][C]2.7e-05[/C][/ROW]
[ROW][C]4[/C][C]0.739652[/C][C]5.2822[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]0.482198[/C][C]3.4436[/C][C]0.000578[/C][/ROW]
[ROW][C]6[/C][C]0.493171[/C][C]3.5219[/C][C]0.000456[/C][/ROW]
[ROW][C]7[/C][C]0.400482[/C][C]2.86[/C][C]0.003062[/C][/ROW]
[ROW][C]8[/C][C]0.516057[/C][C]3.6854[/C][C]0.000277[/C][/ROW]
[ROW][C]9[/C][C]0.287365[/C][C]2.0522[/C][C]0.02265[/C][/ROW]
[ROW][C]10[/C][C]0.305747[/C][C]2.1835[/C][C]0.016814[/C][/ROW]
[ROW][C]11[/C][C]0.231255[/C][C]1.6515[/C][C]0.052391[/C][/ROW]
[ROW][C]12[/C][C]0.340575[/C][C]2.4322[/C][C]0.009278[/C][/ROW]
[ROW][C]13[/C][C]0.141301[/C][C]1.0091[/C][C]0.158848[/C][/ROW]
[ROW][C]14[/C][C]0.158322[/C][C]1.1306[/C][C]0.131747[/C][/ROW]
[ROW][C]15[/C][C]0.090135[/C][C]0.6437[/C][C]0.261331[/C][/ROW]
[ROW][C]16[/C][C]0.181273[/C][C]1.2946[/C][C]0.100653[/C][/ROW]
[ROW][C]17[/C][C]-0.001866[/C][C]-0.0133[/C][C]0.494711[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301773&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301773&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	0.722488	5.1596	2e-06
2	0.725312	5.1798	2e-06
3	0.616389	4.4019	2.7e-05
4	0.739652	5.2822	1e-06
5	0.482198	3.4436	0.000578
6	0.493171	3.5219	0.000456
7	0.400482	2.86	0.003062
8	0.516057	3.6854	0.000277
9	0.287365	2.0522	0.02265
10	0.305747	2.1835	0.016814
11	0.231255	1.6515	0.052391
12	0.340575	2.4322	0.009278
13	0.141301	1.0091	0.158848
14	0.158322	1.1306	0.131747
15	0.090135	0.6437	0.261331
16	0.181273	1.2946	0.100653
17	-0.001866	-0.0133	0.494711

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.722488	5.1596	2e-06
2	0.425352	3.0376	0.001877
3	0.020293	0.1449	0.442671
4	0.439483	3.1385	0.001411
5	-0.502262	-3.5869	0.000375
6	0.023361	0.1668	0.434081
7	0.077749	0.5552	0.290579
8	0.146103	1.0434	0.150846
9	-0.192189	-1.3725	0.087957
10	-0.056521	-0.4036	0.344082
11	0.052704	0.3764	0.354097
12	0.071576	0.5112	0.305724
13	-0.069874	-0.499	0.309962
14	-0.098734	-0.7051	0.241976
15	-0.015091	-0.1078	0.4573
16	0.007425	0.053	0.47896
17	-0.042331	-0.3023	0.381824

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.722488 & 5.1596 & 2e-06 \tabularnewline
2 & 0.425352 & 3.0376 & 0.001877 \tabularnewline
3 & 0.020293 & 0.1449 & 0.442671 \tabularnewline
4 & 0.439483 & 3.1385 & 0.001411 \tabularnewline
5 & -0.502262 & -3.5869 & 0.000375 \tabularnewline
6 & 0.023361 & 0.1668 & 0.434081 \tabularnewline
7 & 0.077749 & 0.5552 & 0.290579 \tabularnewline
8 & 0.146103 & 1.0434 & 0.150846 \tabularnewline
9 & -0.192189 & -1.3725 & 0.087957 \tabularnewline
10 & -0.056521 & -0.4036 & 0.344082 \tabularnewline
11 & 0.052704 & 0.3764 & 0.354097 \tabularnewline
12 & 0.071576 & 0.5112 & 0.305724 \tabularnewline
13 & -0.069874 & -0.499 & 0.309962 \tabularnewline
14 & -0.098734 & -0.7051 & 0.241976 \tabularnewline
15 & -0.015091 & -0.1078 & 0.4573 \tabularnewline
16 & 0.007425 & 0.053 & 0.47896 \tabularnewline
17 & -0.042331 & -0.3023 & 0.381824 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301773&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]0.722488[/C][C]5.1596[/C][C]2e-06[/C][/ROW]
[ROW][C]2[/C][C]0.425352[/C][C]3.0376[/C][C]0.001877[/C][/ROW]
[ROW][C]3[/C][C]0.020293[/C][C]0.1449[/C][C]0.442671[/C][/ROW]
[ROW][C]4[/C][C]0.439483[/C][C]3.1385[/C][C]0.001411[/C][/ROW]
[ROW][C]5[/C][C]-0.502262[/C][C]-3.5869[/C][C]0.000375[/C][/ROW]
[ROW][C]6[/C][C]0.023361[/C][C]0.1668[/C][C]0.434081[/C][/ROW]
[ROW][C]7[/C][C]0.077749[/C][C]0.5552[/C][C]0.290579[/C][/ROW]
[ROW][C]8[/C][C]0.146103[/C][C]1.0434[/C][C]0.150846[/C][/ROW]
[ROW][C]9[/C][C]-0.192189[/C][C]-1.3725[/C][C]0.087957[/C][/ROW]
[ROW][C]10[/C][C]-0.056521[/C][C]-0.4036[/C][C]0.344082[/C][/ROW]
[ROW][C]11[/C][C]0.052704[/C][C]0.3764[/C][C]0.354097[/C][/ROW]
[ROW][C]12[/C][C]0.071576[/C][C]0.5112[/C][C]0.305724[/C][/ROW]
[ROW][C]13[/C][C]-0.069874[/C][C]-0.499[/C][C]0.309962[/C][/ROW]
[ROW][C]14[/C][C]-0.098734[/C][C]-0.7051[/C][C]0.241976[/C][/ROW]
[ROW][C]15[/C][C]-0.015091[/C][C]-0.1078[/C][C]0.4573[/C][/ROW]
[ROW][C]16[/C][C]0.007425[/C][C]0.053[/C][C]0.47896[/C][/ROW]
[ROW][C]17[/C][C]-0.042331[/C][C]-0.3023[/C][C]0.381824[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301773&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301773&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	0.722488	5.1596	2e-06
2	0.425352	3.0376	0.001877
3	0.020293	0.1449	0.442671
4	0.439483	3.1385	0.001411
5	-0.502262	-3.5869	0.000375
6	0.023361	0.1668	0.434081
7	0.077749	0.5552	0.290579
8	0.146103	1.0434	0.150846
9	-0.192189	-1.3725	0.087957
10	-0.056521	-0.4036	0.344082
11	0.052704	0.3764	0.354097
12	0.071576	0.5112	0.305724
13	-0.069874	-0.499	0.309962
14	-0.098734	-0.7051	0.241976
15	-0.015091	-0.1078	0.4573
16	0.007425	0.053	0.47896
17	-0.042331	-0.3023	0.381824

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 = 12 ; par2 = Single ; par3 = multiplicative ; 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')

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Input Parameters & R Code