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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Dec 2016 15:21:26 +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/23/t1482502928r30e9snsss9av9m.htm/, Retrieved Tue, 07 May 2024 19:34:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302965, Retrieved Tue, 07 May 2024 19:34:11 +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] [ACF N2671] [2016-12-23 14:21:26] [11b61e09f442d73f657668491c17a736] [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=302965&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=302965&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302965&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	-0.218072	-2.2239	0.014158
2	0.006175	0.063	0.474956
3	0.126048	1.2854	0.100746
4	-0.049889	-0.5088	0.305995
5	0.233494	2.3812	0.009538
6	-0.019659	-0.2005	0.420747
7	-0.045879	-0.4679	0.320426
8	-0.046774	-0.477	0.31718
9	-0.121796	-1.2421	0.108501
10	0.09752	0.9945	0.161141
11	0.039162	0.3994	0.345217
12	-0.263576	-2.688	0.004186
13	0.061028	0.6224	0.267532
14	-0.062313	-0.6355	0.263258
15	0.089633	0.9141	0.181393
16	0.053307	0.5436	0.29393
17	-0.084048	-0.8571	0.196673
18	0.019816	0.2021	0.420121
19	-0.101408	-1.0342	0.151729
20	0.223872	2.2831	0.012231

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.218072 & -2.2239 & 0.014158 \tabularnewline
2 & 0.006175 & 0.063 & 0.474956 \tabularnewline
3 & 0.126048 & 1.2854 & 0.100746 \tabularnewline
4 & -0.049889 & -0.5088 & 0.305995 \tabularnewline
5 & 0.233494 & 2.3812 & 0.009538 \tabularnewline
6 & -0.019659 & -0.2005 & 0.420747 \tabularnewline
7 & -0.045879 & -0.4679 & 0.320426 \tabularnewline
8 & -0.046774 & -0.477 & 0.31718 \tabularnewline
9 & -0.121796 & -1.2421 & 0.108501 \tabularnewline
10 & 0.09752 & 0.9945 & 0.161141 \tabularnewline
11 & 0.039162 & 0.3994 & 0.345217 \tabularnewline
12 & -0.263576 & -2.688 & 0.004186 \tabularnewline
13 & 0.061028 & 0.6224 & 0.267532 \tabularnewline
14 & -0.062313 & -0.6355 & 0.263258 \tabularnewline
15 & 0.089633 & 0.9141 & 0.181393 \tabularnewline
16 & 0.053307 & 0.5436 & 0.29393 \tabularnewline
17 & -0.084048 & -0.8571 & 0.196673 \tabularnewline
18 & 0.019816 & 0.2021 & 0.420121 \tabularnewline
19 & -0.101408 & -1.0342 & 0.151729 \tabularnewline
20 & 0.223872 & 2.2831 & 0.012231 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302965&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]-0.218072[/C][C]-2.2239[/C][C]0.014158[/C][/ROW]
[ROW][C]2[/C][C]0.006175[/C][C]0.063[/C][C]0.474956[/C][/ROW]
[ROW][C]3[/C][C]0.126048[/C][C]1.2854[/C][C]0.100746[/C][/ROW]
[ROW][C]4[/C][C]-0.049889[/C][C]-0.5088[/C][C]0.305995[/C][/ROW]
[ROW][C]5[/C][C]0.233494[/C][C]2.3812[/C][C]0.009538[/C][/ROW]
[ROW][C]6[/C][C]-0.019659[/C][C]-0.2005[/C][C]0.420747[/C][/ROW]
[ROW][C]7[/C][C]-0.045879[/C][C]-0.4679[/C][C]0.320426[/C][/ROW]
[ROW][C]8[/C][C]-0.046774[/C][C]-0.477[/C][C]0.31718[/C][/ROW]
[ROW][C]9[/C][C]-0.121796[/C][C]-1.2421[/C][C]0.108501[/C][/ROW]
[ROW][C]10[/C][C]0.09752[/C][C]0.9945[/C][C]0.161141[/C][/ROW]
[ROW][C]11[/C][C]0.039162[/C][C]0.3994[/C][C]0.345217[/C][/ROW]
[ROW][C]12[/C][C]-0.263576[/C][C]-2.688[/C][C]0.004186[/C][/ROW]
[ROW][C]13[/C][C]0.061028[/C][C]0.6224[/C][C]0.267532[/C][/ROW]
[ROW][C]14[/C][C]-0.062313[/C][C]-0.6355[/C][C]0.263258[/C][/ROW]
[ROW][C]15[/C][C]0.089633[/C][C]0.9141[/C][C]0.181393[/C][/ROW]
[ROW][C]16[/C][C]0.053307[/C][C]0.5436[/C][C]0.29393[/C][/ROW]
[ROW][C]17[/C][C]-0.084048[/C][C]-0.8571[/C][C]0.196673[/C][/ROW]
[ROW][C]18[/C][C]0.019816[/C][C]0.2021[/C][C]0.420121[/C][/ROW]
[ROW][C]19[/C][C]-0.101408[/C][C]-1.0342[/C][C]0.151729[/C][/ROW]
[ROW][C]20[/C][C]0.223872[/C][C]2.2831[/C][C]0.012231[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302965&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302965&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	-0.218072	-2.2239	0.014158
2	0.006175	0.063	0.474956
3	0.126048	1.2854	0.100746
4	-0.049889	-0.5088	0.305995
5	0.233494	2.3812	0.009538
6	-0.019659	-0.2005	0.420747
7	-0.045879	-0.4679	0.320426
8	-0.046774	-0.477	0.31718
9	-0.121796	-1.2421	0.108501
10	0.09752	0.9945	0.161141
11	0.039162	0.3994	0.345217
12	-0.263576	-2.688	0.004186
13	0.061028	0.6224	0.267532
14	-0.062313	-0.6355	0.263258
15	0.089633	0.9141	0.181393
16	0.053307	0.5436	0.29393
17	-0.084048	-0.8571	0.196673
18	0.019816	0.2021	0.420121
19	-0.101408	-1.0342	0.151729
20	0.223872	2.2831	0.012231

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.218072	-2.2239	0.014158
2	-0.043447	-0.4431	0.329317
3	0.124104	1.2656	0.104239
4	0.005631	0.0574	0.477159
5	0.240109	2.4486	0.008006
6	0.075025	0.7651	0.22297
7	-0.029875	-0.3047	0.380615
8	-0.140069	-1.4284	0.078082
9	-0.202057	-2.0606	0.020919
10	-0.029129	-0.2971	0.383506
11	0.088501	0.9025	0.184428
12	-0.187514	-1.9123	0.029296
13	0.002294	0.0234	0.490692
14	-0.00218	-0.0222	0.491155
15	0.137581	1.4031	0.081789
16	0.082342	0.8397	0.201493
17	0.045029	0.4592	0.323522
18	-0.023184	-0.2364	0.406782
19	-0.148208	-1.5114	0.066856
20	0.103294	1.0534	0.1473

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.218072 & -2.2239 & 0.014158 \tabularnewline
2 & -0.043447 & -0.4431 & 0.329317 \tabularnewline
3 & 0.124104 & 1.2656 & 0.104239 \tabularnewline
4 & 0.005631 & 0.0574 & 0.477159 \tabularnewline
5 & 0.240109 & 2.4486 & 0.008006 \tabularnewline
6 & 0.075025 & 0.7651 & 0.22297 \tabularnewline
7 & -0.029875 & -0.3047 & 0.380615 \tabularnewline
8 & -0.140069 & -1.4284 & 0.078082 \tabularnewline
9 & -0.202057 & -2.0606 & 0.020919 \tabularnewline
10 & -0.029129 & -0.2971 & 0.383506 \tabularnewline
11 & 0.088501 & 0.9025 & 0.184428 \tabularnewline
12 & -0.187514 & -1.9123 & 0.029296 \tabularnewline
13 & 0.002294 & 0.0234 & 0.490692 \tabularnewline
14 & -0.00218 & -0.0222 & 0.491155 \tabularnewline
15 & 0.137581 & 1.4031 & 0.081789 \tabularnewline
16 & 0.082342 & 0.8397 & 0.201493 \tabularnewline
17 & 0.045029 & 0.4592 & 0.323522 \tabularnewline
18 & -0.023184 & -0.2364 & 0.406782 \tabularnewline
19 & -0.148208 & -1.5114 & 0.066856 \tabularnewline
20 & 0.103294 & 1.0534 & 0.1473 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302965&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]-0.218072[/C][C]-2.2239[/C][C]0.014158[/C][/ROW]
[ROW][C]2[/C][C]-0.043447[/C][C]-0.4431[/C][C]0.329317[/C][/ROW]
[ROW][C]3[/C][C]0.124104[/C][C]1.2656[/C][C]0.104239[/C][/ROW]
[ROW][C]4[/C][C]0.005631[/C][C]0.0574[/C][C]0.477159[/C][/ROW]
[ROW][C]5[/C][C]0.240109[/C][C]2.4486[/C][C]0.008006[/C][/ROW]
[ROW][C]6[/C][C]0.075025[/C][C]0.7651[/C][C]0.22297[/C][/ROW]
[ROW][C]7[/C][C]-0.029875[/C][C]-0.3047[/C][C]0.380615[/C][/ROW]
[ROW][C]8[/C][C]-0.140069[/C][C]-1.4284[/C][C]0.078082[/C][/ROW]
[ROW][C]9[/C][C]-0.202057[/C][C]-2.0606[/C][C]0.020919[/C][/ROW]
[ROW][C]10[/C][C]-0.029129[/C][C]-0.2971[/C][C]0.383506[/C][/ROW]
[ROW][C]11[/C][C]0.088501[/C][C]0.9025[/C][C]0.184428[/C][/ROW]
[ROW][C]12[/C][C]-0.187514[/C][C]-1.9123[/C][C]0.029296[/C][/ROW]
[ROW][C]13[/C][C]0.002294[/C][C]0.0234[/C][C]0.490692[/C][/ROW]
[ROW][C]14[/C][C]-0.00218[/C][C]-0.0222[/C][C]0.491155[/C][/ROW]
[ROW][C]15[/C][C]0.137581[/C][C]1.4031[/C][C]0.081789[/C][/ROW]
[ROW][C]16[/C][C]0.082342[/C][C]0.8397[/C][C]0.201493[/C][/ROW]
[ROW][C]17[/C][C]0.045029[/C][C]0.4592[/C][C]0.323522[/C][/ROW]
[ROW][C]18[/C][C]-0.023184[/C][C]-0.2364[/C][C]0.406782[/C][/ROW]
[ROW][C]19[/C][C]-0.148208[/C][C]-1.5114[/C][C]0.066856[/C][/ROW]
[ROW][C]20[/C][C]0.103294[/C][C]1.0534[/C][C]0.1473[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302965&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302965&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	-0.218072	-2.2239	0.014158
2	-0.043447	-0.4431	0.329317
3	0.124104	1.2656	0.104239
4	0.005631	0.0574	0.477159
5	0.240109	2.4486	0.008006
6	0.075025	0.7651	0.22297
7	-0.029875	-0.3047	0.380615
8	-0.140069	-1.4284	0.078082
9	-0.202057	-2.0606	0.020919
10	-0.029129	-0.2971	0.383506
11	0.088501	0.9025	0.184428
12	-0.187514	-1.9123	0.029296
13	0.002294	0.0234	0.490692
14	-0.00218	-0.0222	0.491155
15	0.137581	1.4031	0.081789
16	0.082342	0.8397	0.201493
17	0.045029	0.4592	0.323522
18	-0.023184	-0.2364	0.406782
19	-0.148208	-1.5114	0.066856
20	0.103294	1.0534	0.1473

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

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Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = Default ; par2 = -0.9 ; par3 = 1 ; par4 = 1 ; 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