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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 20 Dec 2016 19:55:03 +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/t1482260177gv4n76rijppltcx.htm/, Retrieved Sun, 28 Apr 2024 11:38:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301775, Retrieved Sun, 28 Apr 2024 11:38:08 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-12-20 18:55:03] [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=301775&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=301775&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301775&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	-0.630865	-4.4609	2.3e-05
2	0.334975	2.3686	0.01088
3	-0.637162	-4.5054	2e-05
4	0.895622	6.333	0
5	-0.581775	-4.1138	7.3e-05
6	0.317673	2.2463	0.014567
7	-0.590917	-4.1784	5.9e-05
8	0.81513	5.7638	0
9	-0.531057	-3.7551	0.000226
10	0.293537	2.0756	0.021546
11	-0.534854	-3.782	0.000208
12	0.719613	5.0884	3e-06
13	-0.460113	-3.2535	0.001023
14	0.253073	1.7895	0.039796
15	-0.457139	-3.2325	0.001087
16	0.61725	4.3646	3.2e-05
17	-0.41037	-2.9018	0.002753

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.630865 & -4.4609 & 2.3e-05 \tabularnewline
2 & 0.334975 & 2.3686 & 0.01088 \tabularnewline
3 & -0.637162 & -4.5054 & 2e-05 \tabularnewline
4 & 0.895622 & 6.333 & 0 \tabularnewline
5 & -0.581775 & -4.1138 & 7.3e-05 \tabularnewline
6 & 0.317673 & 2.2463 & 0.014567 \tabularnewline
7 & -0.590917 & -4.1784 & 5.9e-05 \tabularnewline
8 & 0.81513 & 5.7638 & 0 \tabularnewline
9 & -0.531057 & -3.7551 & 0.000226 \tabularnewline
10 & 0.293537 & 2.0756 & 0.021546 \tabularnewline
11 & -0.534854 & -3.782 & 0.000208 \tabularnewline
12 & 0.719613 & 5.0884 & 3e-06 \tabularnewline
13 & -0.460113 & -3.2535 & 0.001023 \tabularnewline
14 & 0.253073 & 1.7895 & 0.039796 \tabularnewline
15 & -0.457139 & -3.2325 & 0.001087 \tabularnewline
16 & 0.61725 & 4.3646 & 3.2e-05 \tabularnewline
17 & -0.41037 & -2.9018 & 0.002753 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301775&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]-0.630865[/C][C]-4.4609[/C][C]2.3e-05[/C][/ROW]
[ROW][C]2[/C][C]0.334975[/C][C]2.3686[/C][C]0.01088[/C][/ROW]
[ROW][C]3[/C][C]-0.637162[/C][C]-4.5054[/C][C]2e-05[/C][/ROW]
[ROW][C]4[/C][C]0.895622[/C][C]6.333[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]-0.581775[/C][C]-4.1138[/C][C]7.3e-05[/C][/ROW]
[ROW][C]6[/C][C]0.317673[/C][C]2.2463[/C][C]0.014567[/C][/ROW]
[ROW][C]7[/C][C]-0.590917[/C][C]-4.1784[/C][C]5.9e-05[/C][/ROW]
[ROW][C]8[/C][C]0.81513[/C][C]5.7638[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]-0.531057[/C][C]-3.7551[/C][C]0.000226[/C][/ROW]
[ROW][C]10[/C][C]0.293537[/C][C]2.0756[/C][C]0.021546[/C][/ROW]
[ROW][C]11[/C][C]-0.534854[/C][C]-3.782[/C][C]0.000208[/C][/ROW]
[ROW][C]12[/C][C]0.719613[/C][C]5.0884[/C][C]3e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.460113[/C][C]-3.2535[/C][C]0.001023[/C][/ROW]
[ROW][C]14[/C][C]0.253073[/C][C]1.7895[/C][C]0.039796[/C][/ROW]
[ROW][C]15[/C][C]-0.457139[/C][C]-3.2325[/C][C]0.001087[/C][/ROW]
[ROW][C]16[/C][C]0.61725[/C][C]4.3646[/C][C]3.2e-05[/C][/ROW]
[ROW][C]17[/C][C]-0.41037[/C][C]-2.9018[/C][C]0.002753[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301775&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301775&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	-0.630865	-4.4609	2.3e-05
2	0.334975	2.3686	0.01088
3	-0.637162	-4.5054	2e-05
4	0.895622	6.333	0
5	-0.581775	-4.1138	7.3e-05
6	0.317673	2.2463	0.014567
7	-0.590917	-4.1784	5.9e-05
8	0.81513	5.7638	0
9	-0.531057	-3.7551	0.000226
10	0.293537	2.0756	0.021546
11	-0.534854	-3.782	0.000208
12	0.719613	5.0884	3e-06
13	-0.460113	-3.2535	0.001023
14	0.253073	1.7895	0.039796
15	-0.457139	-3.2325	0.001087
16	0.61725	4.3646	3.2e-05
17	-0.41037	-2.9018	0.002753

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.630865	-4.4609	2.3e-05
2	-0.104676	-0.7402	0.231329
3	-0.788954	-5.5787	0
4	0.535949	3.7897	0.000203
5	0.041049	0.2903	0.386408
6	-0.195944	-1.3855	0.08602
7	0.053723	0.3799	0.352822
8	0.058144	0.4111	0.341365
9	-0.023417	-0.1656	0.434576
10	-0.05314	-0.3758	0.354345
11	0.065926	0.4662	0.321561
12	-0.102921	-0.7278	0.235077
13	0.04889	0.3457	0.365508
14	-0.036117	-0.2554	0.399736
15	0.072537	0.5129	0.305135
16	-0.018964	-0.1341	0.446933
17	-0.13153	-0.9301	0.178406

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.630865 & -4.4609 & 2.3e-05 \tabularnewline
2 & -0.104676 & -0.7402 & 0.231329 \tabularnewline
3 & -0.788954 & -5.5787 & 0 \tabularnewline
4 & 0.535949 & 3.7897 & 0.000203 \tabularnewline
5 & 0.041049 & 0.2903 & 0.386408 \tabularnewline
6 & -0.195944 & -1.3855 & 0.08602 \tabularnewline
7 & 0.053723 & 0.3799 & 0.352822 \tabularnewline
8 & 0.058144 & 0.4111 & 0.341365 \tabularnewline
9 & -0.023417 & -0.1656 & 0.434576 \tabularnewline
10 & -0.05314 & -0.3758 & 0.354345 \tabularnewline
11 & 0.065926 & 0.4662 & 0.321561 \tabularnewline
12 & -0.102921 & -0.7278 & 0.235077 \tabularnewline
13 & 0.04889 & 0.3457 & 0.365508 \tabularnewline
14 & -0.036117 & -0.2554 & 0.399736 \tabularnewline
15 & 0.072537 & 0.5129 & 0.305135 \tabularnewline
16 & -0.018964 & -0.1341 & 0.446933 \tabularnewline
17 & -0.13153 & -0.9301 & 0.178406 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301775&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]-0.630865[/C][C]-4.4609[/C][C]2.3e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.104676[/C][C]-0.7402[/C][C]0.231329[/C][/ROW]
[ROW][C]3[/C][C]-0.788954[/C][C]-5.5787[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.535949[/C][C]3.7897[/C][C]0.000203[/C][/ROW]
[ROW][C]5[/C][C]0.041049[/C][C]0.2903[/C][C]0.386408[/C][/ROW]
[ROW][C]6[/C][C]-0.195944[/C][C]-1.3855[/C][C]0.08602[/C][/ROW]
[ROW][C]7[/C][C]0.053723[/C][C]0.3799[/C][C]0.352822[/C][/ROW]
[ROW][C]8[/C][C]0.058144[/C][C]0.4111[/C][C]0.341365[/C][/ROW]
[ROW][C]9[/C][C]-0.023417[/C][C]-0.1656[/C][C]0.434576[/C][/ROW]
[ROW][C]10[/C][C]-0.05314[/C][C]-0.3758[/C][C]0.354345[/C][/ROW]
[ROW][C]11[/C][C]0.065926[/C][C]0.4662[/C][C]0.321561[/C][/ROW]
[ROW][C]12[/C][C]-0.102921[/C][C]-0.7278[/C][C]0.235077[/C][/ROW]
[ROW][C]13[/C][C]0.04889[/C][C]0.3457[/C][C]0.365508[/C][/ROW]
[ROW][C]14[/C][C]-0.036117[/C][C]-0.2554[/C][C]0.399736[/C][/ROW]
[ROW][C]15[/C][C]0.072537[/C][C]0.5129[/C][C]0.305135[/C][/ROW]
[ROW][C]16[/C][C]-0.018964[/C][C]-0.1341[/C][C]0.446933[/C][/ROW]
[ROW][C]17[/C][C]-0.13153[/C][C]-0.9301[/C][C]0.178406[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301775&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301775&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	-0.630865	-4.4609	2.3e-05
2	-0.104676	-0.7402	0.231329
3	-0.788954	-5.5787	0
4	0.535949	3.7897	0.000203
5	0.041049	0.2903	0.386408
6	-0.195944	-1.3855	0.08602
7	0.053723	0.3799	0.352822
8	0.058144	0.4111	0.341365
9	-0.023417	-0.1656	0.434576
10	-0.05314	-0.3758	0.354345
11	0.065926	0.4662	0.321561
12	-0.102921	-0.7278	0.235077
13	0.04889	0.3457	0.365508
14	-0.036117	-0.2554	0.399736
15	0.072537	0.5129	0.305135
16	-0.018964	-0.1341	0.446933
17	-0.13153	-0.9301	0.178406

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 = 12 ; par2 = Single ; par3 = multiplicative ; par4 = 12 ;

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
par2 <- '1'
par1 <- 'Default'
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