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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 19 Dec 2016 17:26:05 +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/19/t148216512137f58789tbtuqao.htm/, Retrieved Fri, 17 May 2024 19:57:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301409, Retrieved Fri, 17 May 2024 19:57:52 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-12-19 16:26:05] [361c8dad91b3f1ef2e651cd04783c23b] [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=301409&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=301409&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301409&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	0.708208	7.9496	0
2	0.651788	7.3163	0
3	0.611495	6.864	0
4	0.547978	6.151	0
5	0.59052	6.6286	0
6	0.493971	5.5448	0
7	0.487293	5.4698	0
8	0.427248	4.7958	2e-06
9	0.410154	4.604	5e-06
10	0.407287	4.5718	6e-06
11	0.392752	4.4086	1.1e-05
12	0.480489	5.3935	0
13	0.379651	4.2616	2e-05
14	0.429191	4.8177	2e-06
15	0.352888	3.9612	6.2e-05
16	0.278708	3.1285	0.001092
17	0.391456	4.3941	1.2e-05
18	0.32881	3.6909	0.000166
19	0.280625	3.15	0.00102
20	0.239516	2.6886	0.004073
21	0.225259	2.5285	0.006345

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.708208 & 7.9496 & 0 \tabularnewline
2 & 0.651788 & 7.3163 & 0 \tabularnewline
3 & 0.611495 & 6.864 & 0 \tabularnewline
4 & 0.547978 & 6.151 & 0 \tabularnewline
5 & 0.59052 & 6.6286 & 0 \tabularnewline
6 & 0.493971 & 5.5448 & 0 \tabularnewline
7 & 0.487293 & 5.4698 & 0 \tabularnewline
8 & 0.427248 & 4.7958 & 2e-06 \tabularnewline
9 & 0.410154 & 4.604 & 5e-06 \tabularnewline
10 & 0.407287 & 4.5718 & 6e-06 \tabularnewline
11 & 0.392752 & 4.4086 & 1.1e-05 \tabularnewline
12 & 0.480489 & 5.3935 & 0 \tabularnewline
13 & 0.379651 & 4.2616 & 2e-05 \tabularnewline
14 & 0.429191 & 4.8177 & 2e-06 \tabularnewline
15 & 0.352888 & 3.9612 & 6.2e-05 \tabularnewline
16 & 0.278708 & 3.1285 & 0.001092 \tabularnewline
17 & 0.391456 & 4.3941 & 1.2e-05 \tabularnewline
18 & 0.32881 & 3.6909 & 0.000166 \tabularnewline
19 & 0.280625 & 3.15 & 0.00102 \tabularnewline
20 & 0.239516 & 2.6886 & 0.004073 \tabularnewline
21 & 0.225259 & 2.5285 & 0.006345 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301409&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]0.708208[/C][C]7.9496[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.651788[/C][C]7.3163[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.611495[/C][C]6.864[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.547978[/C][C]6.151[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.59052[/C][C]6.6286[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.493971[/C][C]5.5448[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.487293[/C][C]5.4698[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.427248[/C][C]4.7958[/C][C]2e-06[/C][/ROW]
[ROW][C]9[/C][C]0.410154[/C][C]4.604[/C][C]5e-06[/C][/ROW]
[ROW][C]10[/C][C]0.407287[/C][C]4.5718[/C][C]6e-06[/C][/ROW]
[ROW][C]11[/C][C]0.392752[/C][C]4.4086[/C][C]1.1e-05[/C][/ROW]
[ROW][C]12[/C][C]0.480489[/C][C]5.3935[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.379651[/C][C]4.2616[/C][C]2e-05[/C][/ROW]
[ROW][C]14[/C][C]0.429191[/C][C]4.8177[/C][C]2e-06[/C][/ROW]
[ROW][C]15[/C][C]0.352888[/C][C]3.9612[/C][C]6.2e-05[/C][/ROW]
[ROW][C]16[/C][C]0.278708[/C][C]3.1285[/C][C]0.001092[/C][/ROW]
[ROW][C]17[/C][C]0.391456[/C][C]4.3941[/C][C]1.2e-05[/C][/ROW]
[ROW][C]18[/C][C]0.32881[/C][C]3.6909[/C][C]0.000166[/C][/ROW]
[ROW][C]19[/C][C]0.280625[/C][C]3.15[/C][C]0.00102[/C][/ROW]
[ROW][C]20[/C][C]0.239516[/C][C]2.6886[/C][C]0.004073[/C][/ROW]
[ROW][C]21[/C][C]0.225259[/C][C]2.5285[/C][C]0.006345[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301409&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301409&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	0.708208	7.9496	0
2	0.651788	7.3163	0
3	0.611495	6.864	0
4	0.547978	6.151	0
5	0.59052	6.6286	0
6	0.493971	5.5448	0
7	0.487293	5.4698	0
8	0.427248	4.7958	2e-06
9	0.410154	4.604	5e-06
10	0.407287	4.5718	6e-06
11	0.392752	4.4086	1.1e-05
12	0.480489	5.3935	0
13	0.379651	4.2616	2e-05
14	0.429191	4.8177	2e-06
15	0.352888	3.9612	6.2e-05
16	0.278708	3.1285	0.001092
17	0.391456	4.3941	1.2e-05
18	0.32881	3.6909	0.000166
19	0.280625	3.15	0.00102
20	0.239516	2.6886	0.004073
21	0.225259	2.5285	0.006345

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.708208	7.9496	0
2	0.3014	3.3832	0.000478
3	0.166754	1.8718	0.031776
4	0.034956	0.3924	0.347719
5	0.221917	2.491	0.007019
6	-0.091209	-1.0238	0.153942
7	0.055577	0.6238	0.266928
8	-0.073225	-0.8219	0.20633
9	0.055704	0.6253	0.26646
10	0.008319	0.0934	0.462875
11	0.081802	0.9182	0.180129
12	0.232929	2.6146	0.005011
13	-0.138379	-1.5533	0.06143
14	0.138948	1.5597	0.060671
15	-0.179724	-2.0174	0.022889
16	-0.115573	-1.2973	0.098449
17	0.192103	2.1563	0.016478
18	0.00582	0.0653	0.474008
19	-0.189054	-2.1221	0.017892
20	0.009976	0.112	0.455508
21	0.068315	0.7668	0.222307

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.708208 & 7.9496 & 0 \tabularnewline
2 & 0.3014 & 3.3832 & 0.000478 \tabularnewline
3 & 0.166754 & 1.8718 & 0.031776 \tabularnewline
4 & 0.034956 & 0.3924 & 0.347719 \tabularnewline
5 & 0.221917 & 2.491 & 0.007019 \tabularnewline
6 & -0.091209 & -1.0238 & 0.153942 \tabularnewline
7 & 0.055577 & 0.6238 & 0.266928 \tabularnewline
8 & -0.073225 & -0.8219 & 0.20633 \tabularnewline
9 & 0.055704 & 0.6253 & 0.26646 \tabularnewline
10 & 0.008319 & 0.0934 & 0.462875 \tabularnewline
11 & 0.081802 & 0.9182 & 0.180129 \tabularnewline
12 & 0.232929 & 2.6146 & 0.005011 \tabularnewline
13 & -0.138379 & -1.5533 & 0.06143 \tabularnewline
14 & 0.138948 & 1.5597 & 0.060671 \tabularnewline
15 & -0.179724 & -2.0174 & 0.022889 \tabularnewline
16 & -0.115573 & -1.2973 & 0.098449 \tabularnewline
17 & 0.192103 & 2.1563 & 0.016478 \tabularnewline
18 & 0.00582 & 0.0653 & 0.474008 \tabularnewline
19 & -0.189054 & -2.1221 & 0.017892 \tabularnewline
20 & 0.009976 & 0.112 & 0.455508 \tabularnewline
21 & 0.068315 & 0.7668 & 0.222307 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301409&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]0.708208[/C][C]7.9496[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.3014[/C][C]3.3832[/C][C]0.000478[/C][/ROW]
[ROW][C]3[/C][C]0.166754[/C][C]1.8718[/C][C]0.031776[/C][/ROW]
[ROW][C]4[/C][C]0.034956[/C][C]0.3924[/C][C]0.347719[/C][/ROW]
[ROW][C]5[/C][C]0.221917[/C][C]2.491[/C][C]0.007019[/C][/ROW]
[ROW][C]6[/C][C]-0.091209[/C][C]-1.0238[/C][C]0.153942[/C][/ROW]
[ROW][C]7[/C][C]0.055577[/C][C]0.6238[/C][C]0.266928[/C][/ROW]
[ROW][C]8[/C][C]-0.073225[/C][C]-0.8219[/C][C]0.20633[/C][/ROW]
[ROW][C]9[/C][C]0.055704[/C][C]0.6253[/C][C]0.26646[/C][/ROW]
[ROW][C]10[/C][C]0.008319[/C][C]0.0934[/C][C]0.462875[/C][/ROW]
[ROW][C]11[/C][C]0.081802[/C][C]0.9182[/C][C]0.180129[/C][/ROW]
[ROW][C]12[/C][C]0.232929[/C][C]2.6146[/C][C]0.005011[/C][/ROW]
[ROW][C]13[/C][C]-0.138379[/C][C]-1.5533[/C][C]0.06143[/C][/ROW]
[ROW][C]14[/C][C]0.138948[/C][C]1.5597[/C][C]0.060671[/C][/ROW]
[ROW][C]15[/C][C]-0.179724[/C][C]-2.0174[/C][C]0.022889[/C][/ROW]
[ROW][C]16[/C][C]-0.115573[/C][C]-1.2973[/C][C]0.098449[/C][/ROW]
[ROW][C]17[/C][C]0.192103[/C][C]2.1563[/C][C]0.016478[/C][/ROW]
[ROW][C]18[/C][C]0.00582[/C][C]0.0653[/C][C]0.474008[/C][/ROW]
[ROW][C]19[/C][C]-0.189054[/C][C]-2.1221[/C][C]0.017892[/C][/ROW]
[ROW][C]20[/C][C]0.009976[/C][C]0.112[/C][C]0.455508[/C][/ROW]
[ROW][C]21[/C][C]0.068315[/C][C]0.7668[/C][C]0.222307[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301409&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301409&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	0.708208	7.9496	0
2	0.3014	3.3832	0.000478
3	0.166754	1.8718	0.031776
4	0.034956	0.3924	0.347719
5	0.221917	2.491	0.007019
6	-0.091209	-1.0238	0.153942
7	0.055577	0.6238	0.266928
8	-0.073225	-0.8219	0.20633
9	0.055704	0.6253	0.26646
10	0.008319	0.0934	0.462875
11	0.081802	0.9182	0.180129
12	0.232929	2.6146	0.005011
13	-0.138379	-1.5533	0.06143
14	0.138948	1.5597	0.060671
15	-0.179724	-2.0174	0.022889
16	-0.115573	-1.2973	0.098449
17	0.192103	2.1563	0.016478
18	0.00582	0.0653	0.474008
19	-0.189054	-2.1221	0.017892
20	0.009976	0.112	0.455508
21	0.068315	0.7668	0.222307

Figure 1

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Postscript link

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Figure 2

PNG link

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Figure 3

PNG link

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Parameters (Session):

par4 = 12 ;

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 <- '12'
par4 <- '0'
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