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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 06 Dec 2016 20:33:37 +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/06/t1481052925ml2uz9mot47nxu4.htm/, Retrieved Sat, 04 May 2024 16:12:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297911, Retrieved Sat, 04 May 2024 16:12:24 +0000

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-       [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2016-12-06 19:33:37] [aed32bb2e1132335210cb15bafce0db8] [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=297911&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=297911&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297911&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	0.880723	9.4857	0
2	0.832677	8.9682	0
3	0.788415	8.4915	0
4	0.697042	7.5074	0
5	0.67718	7.2935	0
6	0.635984	6.8498	0
7	0.589615	6.3503	0
8	0.548012	5.9023	0
9	0.537812	5.7924	0
10	0.482211	5.1936	0
11	0.44079	4.7475	3e-06
12	0.409847	4.4142	1.1e-05
13	0.337315	3.633	0.000209
14	0.315942	3.4028	0.000458
15	0.28874	3.1098	0.001178
16	0.238546	2.5692	0.00573
17	0.225963	2.4337	0.008235
18	0.199474	2.1484	0.016881
19	0.180649	1.9456	0.027058
20	0.173736	1.8712	0.031919

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.880723 & 9.4857 & 0 \tabularnewline
2 & 0.832677 & 8.9682 & 0 \tabularnewline
3 & 0.788415 & 8.4915 & 0 \tabularnewline
4 & 0.697042 & 7.5074 & 0 \tabularnewline
5 & 0.67718 & 7.2935 & 0 \tabularnewline
6 & 0.635984 & 6.8498 & 0 \tabularnewline
7 & 0.589615 & 6.3503 & 0 \tabularnewline
8 & 0.548012 & 5.9023 & 0 \tabularnewline
9 & 0.537812 & 5.7924 & 0 \tabularnewline
10 & 0.482211 & 5.1936 & 0 \tabularnewline
11 & 0.44079 & 4.7475 & 3e-06 \tabularnewline
12 & 0.409847 & 4.4142 & 1.1e-05 \tabularnewline
13 & 0.337315 & 3.633 & 0.000209 \tabularnewline
14 & 0.315942 & 3.4028 & 0.000458 \tabularnewline
15 & 0.28874 & 3.1098 & 0.001178 \tabularnewline
16 & 0.238546 & 2.5692 & 0.00573 \tabularnewline
17 & 0.225963 & 2.4337 & 0.008235 \tabularnewline
18 & 0.199474 & 2.1484 & 0.016881 \tabularnewline
19 & 0.180649 & 1.9456 & 0.027058 \tabularnewline
20 & 0.173736 & 1.8712 & 0.031919 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297911&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]0.880723[/C][C]9.4857[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.832677[/C][C]8.9682[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.788415[/C][C]8.4915[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.697042[/C][C]7.5074[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.67718[/C][C]7.2935[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.635984[/C][C]6.8498[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.589615[/C][C]6.3503[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.548012[/C][C]5.9023[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.537812[/C][C]5.7924[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.482211[/C][C]5.1936[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.44079[/C][C]4.7475[/C][C]3e-06[/C][/ROW]
[ROW][C]12[/C][C]0.409847[/C][C]4.4142[/C][C]1.1e-05[/C][/ROW]
[ROW][C]13[/C][C]0.337315[/C][C]3.633[/C][C]0.000209[/C][/ROW]
[ROW][C]14[/C][C]0.315942[/C][C]3.4028[/C][C]0.000458[/C][/ROW]
[ROW][C]15[/C][C]0.28874[/C][C]3.1098[/C][C]0.001178[/C][/ROW]
[ROW][C]16[/C][C]0.238546[/C][C]2.5692[/C][C]0.00573[/C][/ROW]
[ROW][C]17[/C][C]0.225963[/C][C]2.4337[/C][C]0.008235[/C][/ROW]
[ROW][C]18[/C][C]0.199474[/C][C]2.1484[/C][C]0.016881[/C][/ROW]
[ROW][C]19[/C][C]0.180649[/C][C]1.9456[/C][C]0.027058[/C][/ROW]
[ROW][C]20[/C][C]0.173736[/C][C]1.8712[/C][C]0.031919[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297911&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297911&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	0.880723	9.4857	0
2	0.832677	8.9682	0
3	0.788415	8.4915	0
4	0.697042	7.5074	0
5	0.67718	7.2935	0
6	0.635984	6.8498	0
7	0.589615	6.3503	0
8	0.548012	5.9023	0
9	0.537812	5.7924	0
10	0.482211	5.1936	0
11	0.44079	4.7475	3e-06
12	0.409847	4.4142	1.1e-05
13	0.337315	3.633	0.000209
14	0.315942	3.4028	0.000458
15	0.28874	3.1098	0.001178
16	0.238546	2.5692	0.00573
17	0.225963	2.4337	0.008235
18	0.199474	2.1484	0.016881
19	0.180649	1.9456	0.027058
20	0.173736	1.8712	0.031919

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.880723	9.4857	0
2	0.25411	2.7368	0.00359
3	0.083918	0.9038	0.183982
4	-0.209586	-2.2573	0.01293
5	0.180258	1.9414	0.027315
6	0.022868	0.2463	0.402945
7	-0.01284	-0.1383	0.445125
8	-0.10642	-1.1462	0.12704
9	0.199891	2.1529	0.016699
10	-0.158023	-1.702	0.045721
11	-0.043024	-0.4634	0.321978
12	-0.047182	-0.5082	0.306151
13	-0.05791	-0.6237	0.267023
14	0.03596	0.3873	0.34962
15	0.039009	0.4201	0.33758
16	-0.088366	-0.9517	0.171606
17	0.053198	0.573	0.283889
18	-0.008324	-0.0897	0.464357
19	0.07718	0.8313	0.203768
20	-0.013765	-0.1483	0.441199

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.880723 & 9.4857 & 0 \tabularnewline
2 & 0.25411 & 2.7368 & 0.00359 \tabularnewline
3 & 0.083918 & 0.9038 & 0.183982 \tabularnewline
4 & -0.209586 & -2.2573 & 0.01293 \tabularnewline
5 & 0.180258 & 1.9414 & 0.027315 \tabularnewline
6 & 0.022868 & 0.2463 & 0.402945 \tabularnewline
7 & -0.01284 & -0.1383 & 0.445125 \tabularnewline
8 & -0.10642 & -1.1462 & 0.12704 \tabularnewline
9 & 0.199891 & 2.1529 & 0.016699 \tabularnewline
10 & -0.158023 & -1.702 & 0.045721 \tabularnewline
11 & -0.043024 & -0.4634 & 0.321978 \tabularnewline
12 & -0.047182 & -0.5082 & 0.306151 \tabularnewline
13 & -0.05791 & -0.6237 & 0.267023 \tabularnewline
14 & 0.03596 & 0.3873 & 0.34962 \tabularnewline
15 & 0.039009 & 0.4201 & 0.33758 \tabularnewline
16 & -0.088366 & -0.9517 & 0.171606 \tabularnewline
17 & 0.053198 & 0.573 & 0.283889 \tabularnewline
18 & -0.008324 & -0.0897 & 0.464357 \tabularnewline
19 & 0.07718 & 0.8313 & 0.203768 \tabularnewline
20 & -0.013765 & -0.1483 & 0.441199 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297911&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]0.880723[/C][C]9.4857[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.25411[/C][C]2.7368[/C][C]0.00359[/C][/ROW]
[ROW][C]3[/C][C]0.083918[/C][C]0.9038[/C][C]0.183982[/C][/ROW]
[ROW][C]4[/C][C]-0.209586[/C][C]-2.2573[/C][C]0.01293[/C][/ROW]
[ROW][C]5[/C][C]0.180258[/C][C]1.9414[/C][C]0.027315[/C][/ROW]
[ROW][C]6[/C][C]0.022868[/C][C]0.2463[/C][C]0.402945[/C][/ROW]
[ROW][C]7[/C][C]-0.01284[/C][C]-0.1383[/C][C]0.445125[/C][/ROW]
[ROW][C]8[/C][C]-0.10642[/C][C]-1.1462[/C][C]0.12704[/C][/ROW]
[ROW][C]9[/C][C]0.199891[/C][C]2.1529[/C][C]0.016699[/C][/ROW]
[ROW][C]10[/C][C]-0.158023[/C][C]-1.702[/C][C]0.045721[/C][/ROW]
[ROW][C]11[/C][C]-0.043024[/C][C]-0.4634[/C][C]0.321978[/C][/ROW]
[ROW][C]12[/C][C]-0.047182[/C][C]-0.5082[/C][C]0.306151[/C][/ROW]
[ROW][C]13[/C][C]-0.05791[/C][C]-0.6237[/C][C]0.267023[/C][/ROW]
[ROW][C]14[/C][C]0.03596[/C][C]0.3873[/C][C]0.34962[/C][/ROW]
[ROW][C]15[/C][C]0.039009[/C][C]0.4201[/C][C]0.33758[/C][/ROW]
[ROW][C]16[/C][C]-0.088366[/C][C]-0.9517[/C][C]0.171606[/C][/ROW]
[ROW][C]17[/C][C]0.053198[/C][C]0.573[/C][C]0.283889[/C][/ROW]
[ROW][C]18[/C][C]-0.008324[/C][C]-0.0897[/C][C]0.464357[/C][/ROW]
[ROW][C]19[/C][C]0.07718[/C][C]0.8313[/C][C]0.203768[/C][/ROW]
[ROW][C]20[/C][C]-0.013765[/C][C]-0.1483[/C][C]0.441199[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297911&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297911&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	0.880723	9.4857	0
2	0.25411	2.7368	0.00359
3	0.083918	0.9038	0.183982
4	-0.209586	-2.2573	0.01293
5	0.180258	1.9414	0.027315
6	0.022868	0.2463	0.402945
7	-0.01284	-0.1383	0.445125
8	-0.10642	-1.1462	0.12704
9	0.199891	2.1529	0.016699
10	-0.158023	-1.702	0.045721
11	-0.043024	-0.4634	0.321978
12	-0.047182	-0.5082	0.306151
13	-0.05791	-0.6237	0.267023
14	0.03596	0.3873	0.34962
15	0.039009	0.4201	0.33758
16	-0.088366	-0.9517	0.171606
17	0.053198	0.573	0.283889
18	-0.008324	-0.0897	0.464357
19	0.07718	0.8313	0.203768
20	-0.013765	-0.1483	0.441199

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

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Figure 3

PNG link

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Parameters (Session):

par2 = grey ; par3 = FALSE ; par4 = 5-point Likert ;

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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code