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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 30 Nov 2016 20:32:27 +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/Nov/30/t1480534380j5mhq20nbkg3u4t.htm/, Retrieved Sun, 19 May 2024 00:04:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297481, Retrieved Sun, 19 May 2024 00:04:26 +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 N2...] [2016-11-30 19:32:27] [4c05fa0998bf98e29c2e453b139976f4] [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=297481&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=297481&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297481&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	-0.049832	-0.5344	0.297052
2	0.11409	1.2235	0.111824
3	0.080803	0.8665	0.194005
4	-0.137071	-1.4699	0.072156
5	-0.056332	-0.6041	0.273487
6	-0.220534	-2.365	0.009853
7	-0.101934	-1.0931	0.138312
8	-0.164297	-1.7619	0.040372
9	0.039949	0.4284	0.334578
10	0.125407	1.3448	0.090662
11	-0.114697	-1.23	0.110606
12	0.447696	4.801	2e-06
13	0.001475	0.0158	0.493704
14	-0.013598	-0.1458	0.442157
15	-0.015962	-0.1712	0.432194
16	-0.214983	-2.3054	0.011467
17	-0.024883	-0.2668	0.395036
18	-0.155097	-1.6632	0.049495
19	-0.102266	-1.0967	0.137535
20	-0.106932	-1.1467	0.12694

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.049832 & -0.5344 & 0.297052 \tabularnewline
2 & 0.11409 & 1.2235 & 0.111824 \tabularnewline
3 & 0.080803 & 0.8665 & 0.194005 \tabularnewline
4 & -0.137071 & -1.4699 & 0.072156 \tabularnewline
5 & -0.056332 & -0.6041 & 0.273487 \tabularnewline
6 & -0.220534 & -2.365 & 0.009853 \tabularnewline
7 & -0.101934 & -1.0931 & 0.138312 \tabularnewline
8 & -0.164297 & -1.7619 & 0.040372 \tabularnewline
9 & 0.039949 & 0.4284 & 0.334578 \tabularnewline
10 & 0.125407 & 1.3448 & 0.090662 \tabularnewline
11 & -0.114697 & -1.23 & 0.110606 \tabularnewline
12 & 0.447696 & 4.801 & 2e-06 \tabularnewline
13 & 0.001475 & 0.0158 & 0.493704 \tabularnewline
14 & -0.013598 & -0.1458 & 0.442157 \tabularnewline
15 & -0.015962 & -0.1712 & 0.432194 \tabularnewline
16 & -0.214983 & -2.3054 & 0.011467 \tabularnewline
17 & -0.024883 & -0.2668 & 0.395036 \tabularnewline
18 & -0.155097 & -1.6632 & 0.049495 \tabularnewline
19 & -0.102266 & -1.0967 & 0.137535 \tabularnewline
20 & -0.106932 & -1.1467 & 0.12694 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297481&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]-0.049832[/C][C]-0.5344[/C][C]0.297052[/C][/ROW]
[ROW][C]2[/C][C]0.11409[/C][C]1.2235[/C][C]0.111824[/C][/ROW]
[ROW][C]3[/C][C]0.080803[/C][C]0.8665[/C][C]0.194005[/C][/ROW]
[ROW][C]4[/C][C]-0.137071[/C][C]-1.4699[/C][C]0.072156[/C][/ROW]
[ROW][C]5[/C][C]-0.056332[/C][C]-0.6041[/C][C]0.273487[/C][/ROW]
[ROW][C]6[/C][C]-0.220534[/C][C]-2.365[/C][C]0.009853[/C][/ROW]
[ROW][C]7[/C][C]-0.101934[/C][C]-1.0931[/C][C]0.138312[/C][/ROW]
[ROW][C]8[/C][C]-0.164297[/C][C]-1.7619[/C][C]0.040372[/C][/ROW]
[ROW][C]9[/C][C]0.039949[/C][C]0.4284[/C][C]0.334578[/C][/ROW]
[ROW][C]10[/C][C]0.125407[/C][C]1.3448[/C][C]0.090662[/C][/ROW]
[ROW][C]11[/C][C]-0.114697[/C][C]-1.23[/C][C]0.110606[/C][/ROW]
[ROW][C]12[/C][C]0.447696[/C][C]4.801[/C][C]2e-06[/C][/ROW]
[ROW][C]13[/C][C]0.001475[/C][C]0.0158[/C][C]0.493704[/C][/ROW]
[ROW][C]14[/C][C]-0.013598[/C][C]-0.1458[/C][C]0.442157[/C][/ROW]
[ROW][C]15[/C][C]-0.015962[/C][C]-0.1712[/C][C]0.432194[/C][/ROW]
[ROW][C]16[/C][C]-0.214983[/C][C]-2.3054[/C][C]0.011467[/C][/ROW]
[ROW][C]17[/C][C]-0.024883[/C][C]-0.2668[/C][C]0.395036[/C][/ROW]
[ROW][C]18[/C][C]-0.155097[/C][C]-1.6632[/C][C]0.049495[/C][/ROW]
[ROW][C]19[/C][C]-0.102266[/C][C]-1.0967[/C][C]0.137535[/C][/ROW]
[ROW][C]20[/C][C]-0.106932[/C][C]-1.1467[/C][C]0.12694[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297481&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297481&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	-0.049832	-0.5344	0.297052
2	0.11409	1.2235	0.111824
3	0.080803	0.8665	0.194005
4	-0.137071	-1.4699	0.072156
5	-0.056332	-0.6041	0.273487
6	-0.220534	-2.365	0.009853
7	-0.101934	-1.0931	0.138312
8	-0.164297	-1.7619	0.040372
9	0.039949	0.4284	0.334578
10	0.125407	1.3448	0.090662
11	-0.114697	-1.23	0.110606
12	0.447696	4.801	2e-06
13	0.001475	0.0158	0.493704
14	-0.013598	-0.1458	0.442157
15	-0.015962	-0.1712	0.432194
16	-0.214983	-2.3054	0.011467
17	-0.024883	-0.2668	0.395036
18	-0.155097	-1.6632	0.049495
19	-0.102266	-1.0967	0.137535
20	-0.106932	-1.1467	0.12694

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.049832	-0.5344	0.297052
2	0.111885	1.1998	0.116335
3	0.092817	0.9954	0.160827
4	-0.144658	-1.5513	0.061791
5	-0.093719	-1.005	0.158497
6	-0.210952	-2.2622	0.012782
7	-0.093812	-1.006	0.158259
8	-0.148018	-1.5873	0.057593
9	0.060347	0.6471	0.259414
10	0.138883	1.4894	0.069565
11	-0.146137	-1.5671	0.059914
12	0.350953	3.7636	0.000133
13	0.000431	0.0046	0.49816
14	-0.126743	-1.3592	0.088377
15	-0.140764	-1.5095	0.066953
16	-0.16421	-1.761	0.040452
17	0.015368	0.1648	0.434693
18	0.02001	0.2146	0.415238
19	-0.059843	-0.6417	0.261158
20	-0.052892	-0.5672	0.28584

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.049832 & -0.5344 & 0.297052 \tabularnewline
2 & 0.111885 & 1.1998 & 0.116335 \tabularnewline
3 & 0.092817 & 0.9954 & 0.160827 \tabularnewline
4 & -0.144658 & -1.5513 & 0.061791 \tabularnewline
5 & -0.093719 & -1.005 & 0.158497 \tabularnewline
6 & -0.210952 & -2.2622 & 0.012782 \tabularnewline
7 & -0.093812 & -1.006 & 0.158259 \tabularnewline
8 & -0.148018 & -1.5873 & 0.057593 \tabularnewline
9 & 0.060347 & 0.6471 & 0.259414 \tabularnewline
10 & 0.138883 & 1.4894 & 0.069565 \tabularnewline
11 & -0.146137 & -1.5671 & 0.059914 \tabularnewline
12 & 0.350953 & 3.7636 & 0.000133 \tabularnewline
13 & 0.000431 & 0.0046 & 0.49816 \tabularnewline
14 & -0.126743 & -1.3592 & 0.088377 \tabularnewline
15 & -0.140764 & -1.5095 & 0.066953 \tabularnewline
16 & -0.16421 & -1.761 & 0.040452 \tabularnewline
17 & 0.015368 & 0.1648 & 0.434693 \tabularnewline
18 & 0.02001 & 0.2146 & 0.415238 \tabularnewline
19 & -0.059843 & -0.6417 & 0.261158 \tabularnewline
20 & -0.052892 & -0.5672 & 0.28584 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297481&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]-0.049832[/C][C]-0.5344[/C][C]0.297052[/C][/ROW]
[ROW][C]2[/C][C]0.111885[/C][C]1.1998[/C][C]0.116335[/C][/ROW]
[ROW][C]3[/C][C]0.092817[/C][C]0.9954[/C][C]0.160827[/C][/ROW]
[ROW][C]4[/C][C]-0.144658[/C][C]-1.5513[/C][C]0.061791[/C][/ROW]
[ROW][C]5[/C][C]-0.093719[/C][C]-1.005[/C][C]0.158497[/C][/ROW]
[ROW][C]6[/C][C]-0.210952[/C][C]-2.2622[/C][C]0.012782[/C][/ROW]
[ROW][C]7[/C][C]-0.093812[/C][C]-1.006[/C][C]0.158259[/C][/ROW]
[ROW][C]8[/C][C]-0.148018[/C][C]-1.5873[/C][C]0.057593[/C][/ROW]
[ROW][C]9[/C][C]0.060347[/C][C]0.6471[/C][C]0.259414[/C][/ROW]
[ROW][C]10[/C][C]0.138883[/C][C]1.4894[/C][C]0.069565[/C][/ROW]
[ROW][C]11[/C][C]-0.146137[/C][C]-1.5671[/C][C]0.059914[/C][/ROW]
[ROW][C]12[/C][C]0.350953[/C][C]3.7636[/C][C]0.000133[/C][/ROW]
[ROW][C]13[/C][C]0.000431[/C][C]0.0046[/C][C]0.49816[/C][/ROW]
[ROW][C]14[/C][C]-0.126743[/C][C]-1.3592[/C][C]0.088377[/C][/ROW]
[ROW][C]15[/C][C]-0.140764[/C][C]-1.5095[/C][C]0.066953[/C][/ROW]
[ROW][C]16[/C][C]-0.16421[/C][C]-1.761[/C][C]0.040452[/C][/ROW]
[ROW][C]17[/C][C]0.015368[/C][C]0.1648[/C][C]0.434693[/C][/ROW]
[ROW][C]18[/C][C]0.02001[/C][C]0.2146[/C][C]0.415238[/C][/ROW]
[ROW][C]19[/C][C]-0.059843[/C][C]-0.6417[/C][C]0.261158[/C][/ROW]
[ROW][C]20[/C][C]-0.052892[/C][C]-0.5672[/C][C]0.28584[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297481&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297481&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	-0.049832	-0.5344	0.297052
2	0.111885	1.1998	0.116335
3	0.092817	0.9954	0.160827
4	-0.144658	-1.5513	0.061791
5	-0.093719	-1.005	0.158497
6	-0.210952	-2.2622	0.012782
7	-0.093812	-1.006	0.158259
8	-0.148018	-1.5873	0.057593
9	0.060347	0.6471	0.259414
10	0.138883	1.4894	0.069565
11	-0.146137	-1.5671	0.059914
12	0.350953	3.7636	0.000133
13	0.000431	0.0046	0.49816
14	-0.126743	-1.3592	0.088377
15	-0.140764	-1.5095	0.066953
16	-0.16421	-1.761	0.040452
17	0.015368	0.1648	0.434693
18	0.02001	0.2146	0.415238
19	-0.059843	-0.6417	0.261158
20	-0.052892	-0.5672	0.28584

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 = 1 ; par2 = 0 ; par3 = 0 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code