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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 11 Dec 2016 17:37:02 +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/11/t1481474306jh0o9d9b5da25q4.htm/, Retrieved Thu, 02 May 2024 04:01:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298825, Retrieved Thu, 02 May 2024 04:01:26 +0000

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-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2016-12-11 16:37:02] [10299735033611e1e2dae6371997f8c9] [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=298825&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=298825&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298825&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	0.696456	7.5011	0
2	0.604544	6.5111	0
3	0.658224	7.0893	0
4	0.569366	6.1323	0
5	0.577092	6.2155	0
6	0.745406	8.0283	0
7	0.526301	5.6684	0
8	0.477608	5.144	1e-06
9	0.515165	5.5485	0
10	0.415283	4.4727	9e-06
11	0.461397	4.9694	1e-06
12	0.66442	7.156	0
13	0.405444	4.3668	1.4e-05
14	0.343988	3.7049	0.000163
15	0.402875	4.3391	1.5e-05
16	0.334732	3.6052	0.000231
17	0.359435	3.8712	9e-05
18	0.525714	5.6621	0
19	0.328838	3.5417	0.000287
20	0.302339	3.2563	0.00074

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.696456 & 7.5011 & 0 \tabularnewline
2 & 0.604544 & 6.5111 & 0 \tabularnewline
3 & 0.658224 & 7.0893 & 0 \tabularnewline
4 & 0.569366 & 6.1323 & 0 \tabularnewline
5 & 0.577092 & 6.2155 & 0 \tabularnewline
6 & 0.745406 & 8.0283 & 0 \tabularnewline
7 & 0.526301 & 5.6684 & 0 \tabularnewline
8 & 0.477608 & 5.144 & 1e-06 \tabularnewline
9 & 0.515165 & 5.5485 & 0 \tabularnewline
10 & 0.415283 & 4.4727 & 9e-06 \tabularnewline
11 & 0.461397 & 4.9694 & 1e-06 \tabularnewline
12 & 0.66442 & 7.156 & 0 \tabularnewline
13 & 0.405444 & 4.3668 & 1.4e-05 \tabularnewline
14 & 0.343988 & 3.7049 & 0.000163 \tabularnewline
15 & 0.402875 & 4.3391 & 1.5e-05 \tabularnewline
16 & 0.334732 & 3.6052 & 0.000231 \tabularnewline
17 & 0.359435 & 3.8712 & 9e-05 \tabularnewline
18 & 0.525714 & 5.6621 & 0 \tabularnewline
19 & 0.328838 & 3.5417 & 0.000287 \tabularnewline
20 & 0.302339 & 3.2563 & 0.00074 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298825&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]0.696456[/C][C]7.5011[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.604544[/C][C]6.5111[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.658224[/C][C]7.0893[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.569366[/C][C]6.1323[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.577092[/C][C]6.2155[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.745406[/C][C]8.0283[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.526301[/C][C]5.6684[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.477608[/C][C]5.144[/C][C]1e-06[/C][/ROW]
[ROW][C]9[/C][C]0.515165[/C][C]5.5485[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.415283[/C][C]4.4727[/C][C]9e-06[/C][/ROW]
[ROW][C]11[/C][C]0.461397[/C][C]4.9694[/C][C]1e-06[/C][/ROW]
[ROW][C]12[/C][C]0.66442[/C][C]7.156[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.405444[/C][C]4.3668[/C][C]1.4e-05[/C][/ROW]
[ROW][C]14[/C][C]0.343988[/C][C]3.7049[/C][C]0.000163[/C][/ROW]
[ROW][C]15[/C][C]0.402875[/C][C]4.3391[/C][C]1.5e-05[/C][/ROW]
[ROW][C]16[/C][C]0.334732[/C][C]3.6052[/C][C]0.000231[/C][/ROW]
[ROW][C]17[/C][C]0.359435[/C][C]3.8712[/C][C]9e-05[/C][/ROW]
[ROW][C]18[/C][C]0.525714[/C][C]5.6621[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.328838[/C][C]3.5417[/C][C]0.000287[/C][/ROW]
[ROW][C]20[/C][C]0.302339[/C][C]3.2563[/C][C]0.00074[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298825&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298825&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	0.696456	7.5011	0
2	0.604544	6.5111	0
3	0.658224	7.0893	0
4	0.569366	6.1323	0
5	0.577092	6.2155	0
6	0.745406	8.0283	0
7	0.526301	5.6684	0
8	0.477608	5.144	1e-06
9	0.515165	5.5485	0
10	0.415283	4.4727	9e-06
11	0.461397	4.9694	1e-06
12	0.66442	7.156	0
13	0.405444	4.3668	1.4e-05
14	0.343988	3.7049	0.000163
15	0.402875	4.3391	1.5e-05
16	0.334732	3.6052	0.000231
17	0.359435	3.8712	9e-05
18	0.525714	5.6621	0
19	0.328838	3.5417	0.000287
20	0.302339	3.2563	0.00074

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.696456	7.5011	0
2	0.232048	2.4992	0.006923
3	0.355641	3.8304	0.000104
4	-0.00315	-0.0339	0.486497
5	0.182397	1.9645	0.025933
6	0.465364	5.0121	1e-06
7	-0.378898	-4.0809	4.1e-05
8	0.036418	0.3922	0.347802
9	-0.094696	-1.0199	0.154948
10	-0.068754	-0.7405	0.230246
11	0.206011	2.2188	0.014223
12	0.33637	3.6228	0.000217
13	-0.418986	-4.5126	8e-06
14	-0.046976	-0.5059	0.306928
15	0.007412	0.0798	0.468255
16	0.108758	1.1714	0.121928
17	0.016507	0.1778	0.429599
18	0.073952	0.7965	0.213688
19	-0.017445	-0.1879	0.425646
20	0.016364	0.1762	0.430203

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.696456 & 7.5011 & 0 \tabularnewline
2 & 0.232048 & 2.4992 & 0.006923 \tabularnewline
3 & 0.355641 & 3.8304 & 0.000104 \tabularnewline
4 & -0.00315 & -0.0339 & 0.486497 \tabularnewline
5 & 0.182397 & 1.9645 & 0.025933 \tabularnewline
6 & 0.465364 & 5.0121 & 1e-06 \tabularnewline
7 & -0.378898 & -4.0809 & 4.1e-05 \tabularnewline
8 & 0.036418 & 0.3922 & 0.347802 \tabularnewline
9 & -0.094696 & -1.0199 & 0.154948 \tabularnewline
10 & -0.068754 & -0.7405 & 0.230246 \tabularnewline
11 & 0.206011 & 2.2188 & 0.014223 \tabularnewline
12 & 0.33637 & 3.6228 & 0.000217 \tabularnewline
13 & -0.418986 & -4.5126 & 8e-06 \tabularnewline
14 & -0.046976 & -0.5059 & 0.306928 \tabularnewline
15 & 0.007412 & 0.0798 & 0.468255 \tabularnewline
16 & 0.108758 & 1.1714 & 0.121928 \tabularnewline
17 & 0.016507 & 0.1778 & 0.429599 \tabularnewline
18 & 0.073952 & 0.7965 & 0.213688 \tabularnewline
19 & -0.017445 & -0.1879 & 0.425646 \tabularnewline
20 & 0.016364 & 0.1762 & 0.430203 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298825&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]0.696456[/C][C]7.5011[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.232048[/C][C]2.4992[/C][C]0.006923[/C][/ROW]
[ROW][C]3[/C][C]0.355641[/C][C]3.8304[/C][C]0.000104[/C][/ROW]
[ROW][C]4[/C][C]-0.00315[/C][C]-0.0339[/C][C]0.486497[/C][/ROW]
[ROW][C]5[/C][C]0.182397[/C][C]1.9645[/C][C]0.025933[/C][/ROW]
[ROW][C]6[/C][C]0.465364[/C][C]5.0121[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]-0.378898[/C][C]-4.0809[/C][C]4.1e-05[/C][/ROW]
[ROW][C]8[/C][C]0.036418[/C][C]0.3922[/C][C]0.347802[/C][/ROW]
[ROW][C]9[/C][C]-0.094696[/C][C]-1.0199[/C][C]0.154948[/C][/ROW]
[ROW][C]10[/C][C]-0.068754[/C][C]-0.7405[/C][C]0.230246[/C][/ROW]
[ROW][C]11[/C][C]0.206011[/C][C]2.2188[/C][C]0.014223[/C][/ROW]
[ROW][C]12[/C][C]0.33637[/C][C]3.6228[/C][C]0.000217[/C][/ROW]
[ROW][C]13[/C][C]-0.418986[/C][C]-4.5126[/C][C]8e-06[/C][/ROW]
[ROW][C]14[/C][C]-0.046976[/C][C]-0.5059[/C][C]0.306928[/C][/ROW]
[ROW][C]15[/C][C]0.007412[/C][C]0.0798[/C][C]0.468255[/C][/ROW]
[ROW][C]16[/C][C]0.108758[/C][C]1.1714[/C][C]0.121928[/C][/ROW]
[ROW][C]17[/C][C]0.016507[/C][C]0.1778[/C][C]0.429599[/C][/ROW]
[ROW][C]18[/C][C]0.073952[/C][C]0.7965[/C][C]0.213688[/C][/ROW]
[ROW][C]19[/C][C]-0.017445[/C][C]-0.1879[/C][C]0.425646[/C][/ROW]
[ROW][C]20[/C][C]0.016364[/C][C]0.1762[/C][C]0.430203[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298825&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298825&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	0.696456	7.5011	0
2	0.232048	2.4992	0.006923
3	0.355641	3.8304	0.000104
4	-0.00315	-0.0339	0.486497
5	0.182397	1.9645	0.025933
6	0.465364	5.0121	1e-06
7	-0.378898	-4.0809	4.1e-05
8	0.036418	0.3922	0.347802
9	-0.094696	-1.0199	0.154948
10	-0.068754	-0.7405	0.230246
11	0.206011	2.2188	0.014223
12	0.33637	3.6228	0.000217
13	-0.418986	-4.5126	8e-06
14	-0.046976	-0.5059	0.306928
15	0.007412	0.0798	0.468255
16	0.108758	1.1714	0.121928
17	0.016507	0.1778	0.429599
18	0.073952	0.7965	0.213688
19	-0.017445	-0.1879	0.425646
20	0.016364	0.1762	0.430203

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):

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '6'
par4 <- '1'
par3 <- '1'
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