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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 13 Dec 2016 13:27:37 +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/Dec/13/t1481632159frm1yk76m23p2ex.htm/, Retrieved Sun, 05 May 2024 01:28:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299086, Retrieved Sun, 05 May 2024 01:28:46 +0000

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User-defined keywords

Estimated Impact

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

-     [Variance Reduction Matrix] [] [2015-10-08 08:22:46] [32b17a345b130fdf5cc88718ed94a974]
- RMPD    [(Partial) Autocorrelation Function] [Autocorrelation] [2016-12-13 12:27:37] [36884fbde1107444791dd71ee0072a5a] [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=299086&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=299086&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299086&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	-0.333501	-3.7286	0.000145
2	-0.134265	-1.5011	0.067923
3	-0.005882	-0.0658	0.473835
4	-0.025663	-0.2869	0.387324
5	-0.080448	-0.8994	0.185076
6	0.217452	2.4312	0.008234
7	-0.203012	-2.2697	0.012468
8	0.082185	0.9189	0.179969
9	0.007704	0.0861	0.465747
10	-0.050547	-0.5651	0.286498
11	0.120072	1.3424	0.090942
12	0.059999	0.6708	0.251789
13	-0.182032	-2.0352	0.021974
14	-0.006507	-0.0728	0.47106
15	-0.012945	-0.1447	0.44258
16	-0.012897	-0.1442	0.442791
17	0.104414	1.1674	0.122638
18	0.14325	1.6016	0.055887
19	-0.150458	-1.6822	0.047516
20	-0.06474	-0.7238	0.235266
21	-0.000647	-0.0072	0.497119

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.333501 & -3.7286 & 0.000145 \tabularnewline
2 & -0.134265 & -1.5011 & 0.067923 \tabularnewline
3 & -0.005882 & -0.0658 & 0.473835 \tabularnewline
4 & -0.025663 & -0.2869 & 0.387324 \tabularnewline
5 & -0.080448 & -0.8994 & 0.185076 \tabularnewline
6 & 0.217452 & 2.4312 & 0.008234 \tabularnewline
7 & -0.203012 & -2.2697 & 0.012468 \tabularnewline
8 & 0.082185 & 0.9189 & 0.179969 \tabularnewline
9 & 0.007704 & 0.0861 & 0.465747 \tabularnewline
10 & -0.050547 & -0.5651 & 0.286498 \tabularnewline
11 & 0.120072 & 1.3424 & 0.090942 \tabularnewline
12 & 0.059999 & 0.6708 & 0.251789 \tabularnewline
13 & -0.182032 & -2.0352 & 0.021974 \tabularnewline
14 & -0.006507 & -0.0728 & 0.47106 \tabularnewline
15 & -0.012945 & -0.1447 & 0.44258 \tabularnewline
16 & -0.012897 & -0.1442 & 0.442791 \tabularnewline
17 & 0.104414 & 1.1674 & 0.122638 \tabularnewline
18 & 0.14325 & 1.6016 & 0.055887 \tabularnewline
19 & -0.150458 & -1.6822 & 0.047516 \tabularnewline
20 & -0.06474 & -0.7238 & 0.235266 \tabularnewline
21 & -0.000647 & -0.0072 & 0.497119 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299086&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]-0.333501[/C][C]-3.7286[/C][C]0.000145[/C][/ROW]
[ROW][C]2[/C][C]-0.134265[/C][C]-1.5011[/C][C]0.067923[/C][/ROW]
[ROW][C]3[/C][C]-0.005882[/C][C]-0.0658[/C][C]0.473835[/C][/ROW]
[ROW][C]4[/C][C]-0.025663[/C][C]-0.2869[/C][C]0.387324[/C][/ROW]
[ROW][C]5[/C][C]-0.080448[/C][C]-0.8994[/C][C]0.185076[/C][/ROW]
[ROW][C]6[/C][C]0.217452[/C][C]2.4312[/C][C]0.008234[/C][/ROW]
[ROW][C]7[/C][C]-0.203012[/C][C]-2.2697[/C][C]0.012468[/C][/ROW]
[ROW][C]8[/C][C]0.082185[/C][C]0.9189[/C][C]0.179969[/C][/ROW]
[ROW][C]9[/C][C]0.007704[/C][C]0.0861[/C][C]0.465747[/C][/ROW]
[ROW][C]10[/C][C]-0.050547[/C][C]-0.5651[/C][C]0.286498[/C][/ROW]
[ROW][C]11[/C][C]0.120072[/C][C]1.3424[/C][C]0.090942[/C][/ROW]
[ROW][C]12[/C][C]0.059999[/C][C]0.6708[/C][C]0.251789[/C][/ROW]
[ROW][C]13[/C][C]-0.182032[/C][C]-2.0352[/C][C]0.021974[/C][/ROW]
[ROW][C]14[/C][C]-0.006507[/C][C]-0.0728[/C][C]0.47106[/C][/ROW]
[ROW][C]15[/C][C]-0.012945[/C][C]-0.1447[/C][C]0.44258[/C][/ROW]
[ROW][C]16[/C][C]-0.012897[/C][C]-0.1442[/C][C]0.442791[/C][/ROW]
[ROW][C]17[/C][C]0.104414[/C][C]1.1674[/C][C]0.122638[/C][/ROW]
[ROW][C]18[/C][C]0.14325[/C][C]1.6016[/C][C]0.055887[/C][/ROW]
[ROW][C]19[/C][C]-0.150458[/C][C]-1.6822[/C][C]0.047516[/C][/ROW]
[ROW][C]20[/C][C]-0.06474[/C][C]-0.7238[/C][C]0.235266[/C][/ROW]
[ROW][C]21[/C][C]-0.000647[/C][C]-0.0072[/C][C]0.497119[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299086&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299086&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	-0.333501	-3.7286	0.000145
2	-0.134265	-1.5011	0.067923
3	-0.005882	-0.0658	0.473835
4	-0.025663	-0.2869	0.387324
5	-0.080448	-0.8994	0.185076
6	0.217452	2.4312	0.008234
7	-0.203012	-2.2697	0.012468
8	0.082185	0.9189	0.179969
9	0.007704	0.0861	0.465747
10	-0.050547	-0.5651	0.286498
11	0.120072	1.3424	0.090942
12	0.059999	0.6708	0.251789
13	-0.182032	-2.0352	0.021974
14	-0.006507	-0.0728	0.47106
15	-0.012945	-0.1447	0.44258
16	-0.012897	-0.1442	0.442791
17	0.104414	1.1674	0.122638
18	0.14325	1.6016	0.055887
19	-0.150458	-1.6822	0.047516
20	-0.06474	-0.7238	0.235266
21	-0.000647	-0.0072	0.497119

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.333501	-3.7286	0.000145
2	-0.276208	-3.0881	0.001241
3	-0.188974	-2.1128	0.018304
4	-0.176062	-1.9684	0.025615
5	-0.249526	-2.7898	0.00305
6	0.047388	0.5298	0.29859
7	-0.206223	-2.3056	0.011389
8	-0.051287	-0.5734	0.283699
9	-0.068638	-0.7674	0.222147
10	-0.108997	-1.2186	0.11264
11	0.095834	1.0715	0.143014
12	0.11916	1.3322	0.092601
13	0.013374	0.1495	0.440692
14	-0.065752	-0.7351	0.231818
15	-0.097644	-1.0917	0.138533
16	-0.114018	-1.2748	0.102379
17	-0.054333	-0.6075	0.272322
18	0.192845	2.1561	0.016497
19	0.072745	0.8133	0.208791
20	-0.042113	-0.4708	0.31929
21	-0.061354	-0.686	0.247004

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.333501 & -3.7286 & 0.000145 \tabularnewline
2 & -0.276208 & -3.0881 & 0.001241 \tabularnewline
3 & -0.188974 & -2.1128 & 0.018304 \tabularnewline
4 & -0.176062 & -1.9684 & 0.025615 \tabularnewline
5 & -0.249526 & -2.7898 & 0.00305 \tabularnewline
6 & 0.047388 & 0.5298 & 0.29859 \tabularnewline
7 & -0.206223 & -2.3056 & 0.011389 \tabularnewline
8 & -0.051287 & -0.5734 & 0.283699 \tabularnewline
9 & -0.068638 & -0.7674 & 0.222147 \tabularnewline
10 & -0.108997 & -1.2186 & 0.11264 \tabularnewline
11 & 0.095834 & 1.0715 & 0.143014 \tabularnewline
12 & 0.11916 & 1.3322 & 0.092601 \tabularnewline
13 & 0.013374 & 0.1495 & 0.440692 \tabularnewline
14 & -0.065752 & -0.7351 & 0.231818 \tabularnewline
15 & -0.097644 & -1.0917 & 0.138533 \tabularnewline
16 & -0.114018 & -1.2748 & 0.102379 \tabularnewline
17 & -0.054333 & -0.6075 & 0.272322 \tabularnewline
18 & 0.192845 & 2.1561 & 0.016497 \tabularnewline
19 & 0.072745 & 0.8133 & 0.208791 \tabularnewline
20 & -0.042113 & -0.4708 & 0.31929 \tabularnewline
21 & -0.061354 & -0.686 & 0.247004 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299086&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]-0.333501[/C][C]-3.7286[/C][C]0.000145[/C][/ROW]
[ROW][C]2[/C][C]-0.276208[/C][C]-3.0881[/C][C]0.001241[/C][/ROW]
[ROW][C]3[/C][C]-0.188974[/C][C]-2.1128[/C][C]0.018304[/C][/ROW]
[ROW][C]4[/C][C]-0.176062[/C][C]-1.9684[/C][C]0.025615[/C][/ROW]
[ROW][C]5[/C][C]-0.249526[/C][C]-2.7898[/C][C]0.00305[/C][/ROW]
[ROW][C]6[/C][C]0.047388[/C][C]0.5298[/C][C]0.29859[/C][/ROW]
[ROW][C]7[/C][C]-0.206223[/C][C]-2.3056[/C][C]0.011389[/C][/ROW]
[ROW][C]8[/C][C]-0.051287[/C][C]-0.5734[/C][C]0.283699[/C][/ROW]
[ROW][C]9[/C][C]-0.068638[/C][C]-0.7674[/C][C]0.222147[/C][/ROW]
[ROW][C]10[/C][C]-0.108997[/C][C]-1.2186[/C][C]0.11264[/C][/ROW]
[ROW][C]11[/C][C]0.095834[/C][C]1.0715[/C][C]0.143014[/C][/ROW]
[ROW][C]12[/C][C]0.11916[/C][C]1.3322[/C][C]0.092601[/C][/ROW]
[ROW][C]13[/C][C]0.013374[/C][C]0.1495[/C][C]0.440692[/C][/ROW]
[ROW][C]14[/C][C]-0.065752[/C][C]-0.7351[/C][C]0.231818[/C][/ROW]
[ROW][C]15[/C][C]-0.097644[/C][C]-1.0917[/C][C]0.138533[/C][/ROW]
[ROW][C]16[/C][C]-0.114018[/C][C]-1.2748[/C][C]0.102379[/C][/ROW]
[ROW][C]17[/C][C]-0.054333[/C][C]-0.6075[/C][C]0.272322[/C][/ROW]
[ROW][C]18[/C][C]0.192845[/C][C]2.1561[/C][C]0.016497[/C][/ROW]
[ROW][C]19[/C][C]0.072745[/C][C]0.8133[/C][C]0.208791[/C][/ROW]
[ROW][C]20[/C][C]-0.042113[/C][C]-0.4708[/C][C]0.31929[/C][/ROW]
[ROW][C]21[/C][C]-0.061354[/C][C]-0.686[/C][C]0.247004[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299086&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299086&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	-0.333501	-3.7286	0.000145
2	-0.276208	-3.0881	0.001241
3	-0.188974	-2.1128	0.018304
4	-0.176062	-1.9684	0.025615
5	-0.249526	-2.7898	0.00305
6	0.047388	0.5298	0.29859
7	-0.206223	-2.3056	0.011389
8	-0.051287	-0.5734	0.283699
9	-0.068638	-0.7674	0.222147
10	-0.108997	-1.2186	0.11264
11	0.095834	1.0715	0.143014
12	0.11916	1.3322	0.092601
13	0.013374	0.1495	0.440692
14	-0.065752	-0.7351	0.231818
15	-0.097644	-1.0917	0.138533
16	-0.114018	-1.2748	0.102379
17	-0.054333	-0.6075	0.272322
18	0.192845	2.1561	0.016497
19	0.072745	0.8133	0.208791
20	-0.042113	-0.4708	0.31929
21	-0.061354	-0.686	0.247004

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

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Figure 3

PNG link

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Parameters (Session):

par1 = 1 ; par2 = 1 ; par3 = 1 ; par4 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; 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 <- '1'
par3 <- '1'
par2 <- '0.0'
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