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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 18 Dec 2016 16:31:47 +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/18/t1482075124bzk6b7aqv6i1b09.htm/, Retrieved Wed, 08 May 2024 22:06:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301139, Retrieved Wed, 08 May 2024 22:06:19 +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] [] [2016-12-18 15:31:47] [1a4fa2544711480e714211476e711237] [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=301139&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=301139&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301139&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	0.769265	4.9257	7e-06
2	0.60551	3.8772	0.000187
3	0.494595	3.167	0.001453
4	0.406472	2.6027	0.006408
5	0.290756	1.8617	0.034909
6	0.208316	1.3339	0.094804
7	0.16239	1.0398	0.152262
8	0.104536	0.6694	0.25351
9	0.071788	0.4597	0.324092
10	0.04341	0.278	0.391221
11	0.029925	0.1916	0.424495
12	0.011816	0.0757	0.47003
13	-0.003321	-0.0213	0.491569
14	-0.007276	-0.0466	0.481534
15	-0.018244	-0.1168	0.453787
16	-0.038333	-0.2455	0.403665

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.769265 & 4.9257 & 7e-06 \tabularnewline
2 & 0.60551 & 3.8772 & 0.000187 \tabularnewline
3 & 0.494595 & 3.167 & 0.001453 \tabularnewline
4 & 0.406472 & 2.6027 & 0.006408 \tabularnewline
5 & 0.290756 & 1.8617 & 0.034909 \tabularnewline
6 & 0.208316 & 1.3339 & 0.094804 \tabularnewline
7 & 0.16239 & 1.0398 & 0.152262 \tabularnewline
8 & 0.104536 & 0.6694 & 0.25351 \tabularnewline
9 & 0.071788 & 0.4597 & 0.324092 \tabularnewline
10 & 0.04341 & 0.278 & 0.391221 \tabularnewline
11 & 0.029925 & 0.1916 & 0.424495 \tabularnewline
12 & 0.011816 & 0.0757 & 0.47003 \tabularnewline
13 & -0.003321 & -0.0213 & 0.491569 \tabularnewline
14 & -0.007276 & -0.0466 & 0.481534 \tabularnewline
15 & -0.018244 & -0.1168 & 0.453787 \tabularnewline
16 & -0.038333 & -0.2455 & 0.403665 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301139&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]0.769265[/C][C]4.9257[/C][C]7e-06[/C][/ROW]
[ROW][C]2[/C][C]0.60551[/C][C]3.8772[/C][C]0.000187[/C][/ROW]
[ROW][C]3[/C][C]0.494595[/C][C]3.167[/C][C]0.001453[/C][/ROW]
[ROW][C]4[/C][C]0.406472[/C][C]2.6027[/C][C]0.006408[/C][/ROW]
[ROW][C]5[/C][C]0.290756[/C][C]1.8617[/C][C]0.034909[/C][/ROW]
[ROW][C]6[/C][C]0.208316[/C][C]1.3339[/C][C]0.094804[/C][/ROW]
[ROW][C]7[/C][C]0.16239[/C][C]1.0398[/C][C]0.152262[/C][/ROW]
[ROW][C]8[/C][C]0.104536[/C][C]0.6694[/C][C]0.25351[/C][/ROW]
[ROW][C]9[/C][C]0.071788[/C][C]0.4597[/C][C]0.324092[/C][/ROW]
[ROW][C]10[/C][C]0.04341[/C][C]0.278[/C][C]0.391221[/C][/ROW]
[ROW][C]11[/C][C]0.029925[/C][C]0.1916[/C][C]0.424495[/C][/ROW]
[ROW][C]12[/C][C]0.011816[/C][C]0.0757[/C][C]0.47003[/C][/ROW]
[ROW][C]13[/C][C]-0.003321[/C][C]-0.0213[/C][C]0.491569[/C][/ROW]
[ROW][C]14[/C][C]-0.007276[/C][C]-0.0466[/C][C]0.481534[/C][/ROW]
[ROW][C]15[/C][C]-0.018244[/C][C]-0.1168[/C][C]0.453787[/C][/ROW]
[ROW][C]16[/C][C]-0.038333[/C][C]-0.2455[/C][C]0.403665[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301139&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301139&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	0.769265	4.9257	7e-06
2	0.60551	3.8772	0.000187
3	0.494595	3.167	0.001453
4	0.406472	2.6027	0.006408
5	0.290756	1.8617	0.034909
6	0.208316	1.3339	0.094804
7	0.16239	1.0398	0.152262
8	0.104536	0.6694	0.25351
9	0.071788	0.4597	0.324092
10	0.04341	0.278	0.391221
11	0.029925	0.1916	0.424495
12	0.011816	0.0757	0.47003
13	-0.003321	-0.0213	0.491569
14	-0.007276	-0.0466	0.481534
15	-0.018244	-0.1168	0.453787
16	-0.038333	-0.2455	0.403665

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.769265	4.9257	7e-06
2	0.033659	0.2155	0.415213
3	0.045571	0.2918	0.385956
4	0.011398	0.073	0.471088
5	-0.102503	-0.6563	0.257636
6	-0.003559	-0.0228	0.490964
7	0.028583	0.183	0.427843
8	-0.050052	-0.3205	0.375113
9	0.028207	0.1806	0.42878
10	-0.015982	-0.1023	0.459496
11	0.008694	0.0557	0.477938
12	-0.010296	-0.0659	0.473878
13	-0.015167	-0.0971	0.461554
14	0.010442	0.0669	0.473508
15	-0.020855	-0.1335	0.44721
16	-0.036813	-0.2357	0.407412

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.769265 & 4.9257 & 7e-06 \tabularnewline
2 & 0.033659 & 0.2155 & 0.415213 \tabularnewline
3 & 0.045571 & 0.2918 & 0.385956 \tabularnewline
4 & 0.011398 & 0.073 & 0.471088 \tabularnewline
5 & -0.102503 & -0.6563 & 0.257636 \tabularnewline
6 & -0.003559 & -0.0228 & 0.490964 \tabularnewline
7 & 0.028583 & 0.183 & 0.427843 \tabularnewline
8 & -0.050052 & -0.3205 & 0.375113 \tabularnewline
9 & 0.028207 & 0.1806 & 0.42878 \tabularnewline
10 & -0.015982 & -0.1023 & 0.459496 \tabularnewline
11 & 0.008694 & 0.0557 & 0.477938 \tabularnewline
12 & -0.010296 & -0.0659 & 0.473878 \tabularnewline
13 & -0.015167 & -0.0971 & 0.461554 \tabularnewline
14 & 0.010442 & 0.0669 & 0.473508 \tabularnewline
15 & -0.020855 & -0.1335 & 0.44721 \tabularnewline
16 & -0.036813 & -0.2357 & 0.407412 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301139&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]0.769265[/C][C]4.9257[/C][C]7e-06[/C][/ROW]
[ROW][C]2[/C][C]0.033659[/C][C]0.2155[/C][C]0.415213[/C][/ROW]
[ROW][C]3[/C][C]0.045571[/C][C]0.2918[/C][C]0.385956[/C][/ROW]
[ROW][C]4[/C][C]0.011398[/C][C]0.073[/C][C]0.471088[/C][/ROW]
[ROW][C]5[/C][C]-0.102503[/C][C]-0.6563[/C][C]0.257636[/C][/ROW]
[ROW][C]6[/C][C]-0.003559[/C][C]-0.0228[/C][C]0.490964[/C][/ROW]
[ROW][C]7[/C][C]0.028583[/C][C]0.183[/C][C]0.427843[/C][/ROW]
[ROW][C]8[/C][C]-0.050052[/C][C]-0.3205[/C][C]0.375113[/C][/ROW]
[ROW][C]9[/C][C]0.028207[/C][C]0.1806[/C][C]0.42878[/C][/ROW]
[ROW][C]10[/C][C]-0.015982[/C][C]-0.1023[/C][C]0.459496[/C][/ROW]
[ROW][C]11[/C][C]0.008694[/C][C]0.0557[/C][C]0.477938[/C][/ROW]
[ROW][C]12[/C][C]-0.010296[/C][C]-0.0659[/C][C]0.473878[/C][/ROW]
[ROW][C]13[/C][C]-0.015167[/C][C]-0.0971[/C][C]0.461554[/C][/ROW]
[ROW][C]14[/C][C]0.010442[/C][C]0.0669[/C][C]0.473508[/C][/ROW]
[ROW][C]15[/C][C]-0.020855[/C][C]-0.1335[/C][C]0.44721[/C][/ROW]
[ROW][C]16[/C][C]-0.036813[/C][C]-0.2357[/C][C]0.407412[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301139&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301139&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	0.769265	4.9257	7e-06
2	0.033659	0.2155	0.415213
3	0.045571	0.2918	0.385956
4	0.011398	0.073	0.471088
5	-0.102503	-0.6563	0.257636
6	-0.003559	-0.0228	0.490964
7	0.028583	0.183	0.427843
8	-0.050052	-0.3205	0.375113
9	0.028207	0.1806	0.42878
10	-0.015982	-0.1023	0.459496
11	0.008694	0.0557	0.477938
12	-0.010296	-0.0659	0.473878
13	-0.015167	-0.0971	0.461554
14	0.010442	0.0669	0.473508
15	-0.020855	-0.1335	0.44721
16	-0.036813	-0.2357	0.407412

Figure 1

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Figure 2

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Figure 3

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Parameters (Session):

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