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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 19 Dec 2017 12:41:18 +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/2017/Dec/19/t1513683855ihno1a0l59dqp2t.htm/, Retrieved Wed, 15 May 2024 04:58:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310302, Retrieved Wed, 15 May 2024 04:58:29 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

110

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [gil is homo ] [2017-12-19 11:41:18] [d41d8cd98f00b204e9800998ecf8427e] [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	2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310302&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=310302&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310302&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	2 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.19462	2.0132	0.023304
2	0.142533	1.4744	0.071659
3	0.285931	2.9577	0.001908
4	0.186175	1.9258	0.028391
5	0.031843	0.3294	0.371255
6	0.290985	3.01	0.00163
7	0.120726	1.2488	0.107232
8	0.141683	1.4656	0.072848
9	0.158361	1.6381	0.052169
10	0.082065	0.8489	0.198921
11	0.039218	0.4057	0.342897
12	0.256712	2.6554	0.004565
13	-0.011335	-0.1173	0.453439
14	0.179137	1.853	0.033319
15	0.067111	0.6942	0.244531
16	0.061554	0.6367	0.262835
17	0.055005	0.569	0.285283
18	0.057375	0.5935	0.277053
19	-0.107557	-1.1126	0.134191
20	0.140663	1.455	0.074294

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.19462 & 2.0132 & 0.023304 \tabularnewline
2 & 0.142533 & 1.4744 & 0.071659 \tabularnewline
3 & 0.285931 & 2.9577 & 0.001908 \tabularnewline
4 & 0.186175 & 1.9258 & 0.028391 \tabularnewline
5 & 0.031843 & 0.3294 & 0.371255 \tabularnewline
6 & 0.290985 & 3.01 & 0.00163 \tabularnewline
7 & 0.120726 & 1.2488 & 0.107232 \tabularnewline
8 & 0.141683 & 1.4656 & 0.072848 \tabularnewline
9 & 0.158361 & 1.6381 & 0.052169 \tabularnewline
10 & 0.082065 & 0.8489 & 0.198921 \tabularnewline
11 & 0.039218 & 0.4057 & 0.342897 \tabularnewline
12 & 0.256712 & 2.6554 & 0.004565 \tabularnewline
13 & -0.011335 & -0.1173 & 0.453439 \tabularnewline
14 & 0.179137 & 1.853 & 0.033319 \tabularnewline
15 & 0.067111 & 0.6942 & 0.244531 \tabularnewline
16 & 0.061554 & 0.6367 & 0.262835 \tabularnewline
17 & 0.055005 & 0.569 & 0.285283 \tabularnewline
18 & 0.057375 & 0.5935 & 0.277053 \tabularnewline
19 & -0.107557 & -1.1126 & 0.134191 \tabularnewline
20 & 0.140663 & 1.455 & 0.074294 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310302&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]0.19462[/C][C]2.0132[/C][C]0.023304[/C][/ROW]
[ROW][C]2[/C][C]0.142533[/C][C]1.4744[/C][C]0.071659[/C][/ROW]
[ROW][C]3[/C][C]0.285931[/C][C]2.9577[/C][C]0.001908[/C][/ROW]
[ROW][C]4[/C][C]0.186175[/C][C]1.9258[/C][C]0.028391[/C][/ROW]
[ROW][C]5[/C][C]0.031843[/C][C]0.3294[/C][C]0.371255[/C][/ROW]
[ROW][C]6[/C][C]0.290985[/C][C]3.01[/C][C]0.00163[/C][/ROW]
[ROW][C]7[/C][C]0.120726[/C][C]1.2488[/C][C]0.107232[/C][/ROW]
[ROW][C]8[/C][C]0.141683[/C][C]1.4656[/C][C]0.072848[/C][/ROW]
[ROW][C]9[/C][C]0.158361[/C][C]1.6381[/C][C]0.052169[/C][/ROW]
[ROW][C]10[/C][C]0.082065[/C][C]0.8489[/C][C]0.198921[/C][/ROW]
[ROW][C]11[/C][C]0.039218[/C][C]0.4057[/C][C]0.342897[/C][/ROW]
[ROW][C]12[/C][C]0.256712[/C][C]2.6554[/C][C]0.004565[/C][/ROW]
[ROW][C]13[/C][C]-0.011335[/C][C]-0.1173[/C][C]0.453439[/C][/ROW]
[ROW][C]14[/C][C]0.179137[/C][C]1.853[/C][C]0.033319[/C][/ROW]
[ROW][C]15[/C][C]0.067111[/C][C]0.6942[/C][C]0.244531[/C][/ROW]
[ROW][C]16[/C][C]0.061554[/C][C]0.6367[/C][C]0.262835[/C][/ROW]
[ROW][C]17[/C][C]0.055005[/C][C]0.569[/C][C]0.285283[/C][/ROW]
[ROW][C]18[/C][C]0.057375[/C][C]0.5935[/C][C]0.277053[/C][/ROW]
[ROW][C]19[/C][C]-0.107557[/C][C]-1.1126[/C][C]0.134191[/C][/ROW]
[ROW][C]20[/C][C]0.140663[/C][C]1.455[/C][C]0.074294[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310302&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310302&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	0.19462	2.0132	0.023304
2	0.142533	1.4744	0.071659
3	0.285931	2.9577	0.001908
4	0.186175	1.9258	0.028391
5	0.031843	0.3294	0.371255
6	0.290985	3.01	0.00163
7	0.120726	1.2488	0.107232
8	0.141683	1.4656	0.072848
9	0.158361	1.6381	0.052169
10	0.082065	0.8489	0.198921
11	0.039218	0.4057	0.342897
12	0.256712	2.6554	0.004565
13	-0.011335	-0.1173	0.453439
14	0.179137	1.853	0.033319
15	0.067111	0.6942	0.244531
16	0.061554	0.6367	0.262835
17	0.055005	0.569	0.285283
18	0.057375	0.5935	0.277053
19	-0.107557	-1.1126	0.134191
20	0.140663	1.455	0.074294

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.19462	2.0132	0.023304
2	0.108776	1.1252	0.131513
3	0.252476	2.6116	0.005152
4	0.096653	0.9998	0.159835
5	-0.068454	-0.7081	0.240214
6	0.230139	2.3806	0.009527
7	-0.016157	-0.1671	0.433792
8	0.101594	1.0509	0.147838
9	0.018485	0.1912	0.424361
10	-0.047782	-0.4943	0.311067
11	-0.008072	-0.0835	0.466807
12	0.165486	1.7118	0.044915
13	-0.124078	-1.2835	0.10105
14	0.173736	1.7971	0.037567
15	-0.133335	-1.3792	0.085351
16	0.040008	0.4138	0.339908
17	0.015592	0.1613	0.436085
18	-0.110079	-1.1387	0.128692
19	-0.080826	-0.8361	0.202488
20	0.09295	0.9615	0.16924

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.19462 & 2.0132 & 0.023304 \tabularnewline
2 & 0.108776 & 1.1252 & 0.131513 \tabularnewline
3 & 0.252476 & 2.6116 & 0.005152 \tabularnewline
4 & 0.096653 & 0.9998 & 0.159835 \tabularnewline
5 & -0.068454 & -0.7081 & 0.240214 \tabularnewline
6 & 0.230139 & 2.3806 & 0.009527 \tabularnewline
7 & -0.016157 & -0.1671 & 0.433792 \tabularnewline
8 & 0.101594 & 1.0509 & 0.147838 \tabularnewline
9 & 0.018485 & 0.1912 & 0.424361 \tabularnewline
10 & -0.047782 & -0.4943 & 0.311067 \tabularnewline
11 & -0.008072 & -0.0835 & 0.466807 \tabularnewline
12 & 0.165486 & 1.7118 & 0.044915 \tabularnewline
13 & -0.124078 & -1.2835 & 0.10105 \tabularnewline
14 & 0.173736 & 1.7971 & 0.037567 \tabularnewline
15 & -0.133335 & -1.3792 & 0.085351 \tabularnewline
16 & 0.040008 & 0.4138 & 0.339908 \tabularnewline
17 & 0.015592 & 0.1613 & 0.436085 \tabularnewline
18 & -0.110079 & -1.1387 & 0.128692 \tabularnewline
19 & -0.080826 & -0.8361 & 0.202488 \tabularnewline
20 & 0.09295 & 0.9615 & 0.16924 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310302&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]0.19462[/C][C]2.0132[/C][C]0.023304[/C][/ROW]
[ROW][C]2[/C][C]0.108776[/C][C]1.1252[/C][C]0.131513[/C][/ROW]
[ROW][C]3[/C][C]0.252476[/C][C]2.6116[/C][C]0.005152[/C][/ROW]
[ROW][C]4[/C][C]0.096653[/C][C]0.9998[/C][C]0.159835[/C][/ROW]
[ROW][C]5[/C][C]-0.068454[/C][C]-0.7081[/C][C]0.240214[/C][/ROW]
[ROW][C]6[/C][C]0.230139[/C][C]2.3806[/C][C]0.009527[/C][/ROW]
[ROW][C]7[/C][C]-0.016157[/C][C]-0.1671[/C][C]0.433792[/C][/ROW]
[ROW][C]8[/C][C]0.101594[/C][C]1.0509[/C][C]0.147838[/C][/ROW]
[ROW][C]9[/C][C]0.018485[/C][C]0.1912[/C][C]0.424361[/C][/ROW]
[ROW][C]10[/C][C]-0.047782[/C][C]-0.4943[/C][C]0.311067[/C][/ROW]
[ROW][C]11[/C][C]-0.008072[/C][C]-0.0835[/C][C]0.466807[/C][/ROW]
[ROW][C]12[/C][C]0.165486[/C][C]1.7118[/C][C]0.044915[/C][/ROW]
[ROW][C]13[/C][C]-0.124078[/C][C]-1.2835[/C][C]0.10105[/C][/ROW]
[ROW][C]14[/C][C]0.173736[/C][C]1.7971[/C][C]0.037567[/C][/ROW]
[ROW][C]15[/C][C]-0.133335[/C][C]-1.3792[/C][C]0.085351[/C][/ROW]
[ROW][C]16[/C][C]0.040008[/C][C]0.4138[/C][C]0.339908[/C][/ROW]
[ROW][C]17[/C][C]0.015592[/C][C]0.1613[/C][C]0.436085[/C][/ROW]
[ROW][C]18[/C][C]-0.110079[/C][C]-1.1387[/C][C]0.128692[/C][/ROW]
[ROW][C]19[/C][C]-0.080826[/C][C]-0.8361[/C][C]0.202488[/C][/ROW]
[ROW][C]20[/C][C]0.09295[/C][C]0.9615[/C][C]0.16924[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310302&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310302&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	0.19462	2.0132	0.023304
2	0.108776	1.1252	0.131513
3	0.252476	2.6116	0.005152
4	0.096653	0.9998	0.159835
5	-0.068454	-0.7081	0.240214
6	0.230139	2.3806	0.009527
7	-0.016157	-0.1671	0.433792
8	0.101594	1.0509	0.147838
9	0.018485	0.1912	0.424361
10	-0.047782	-0.4943	0.311067
11	-0.008072	-0.0835	0.466807
12	0.165486	1.7118	0.044915
13	-0.124078	-1.2835	0.10105
14	0.173736	1.7971	0.037567
15	-0.133335	-1.3792	0.085351
16	0.040008	0.4138	0.339908
17	0.015592	0.1613	0.436085
18	-0.110079	-1.1387	0.128692
19	-0.080826	-0.8361	0.202488
20	0.09295	0.9615	0.16924

Figure 1

PNG link

Postscript link

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Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code