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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 14 Dec 2016 14:30:20 +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/14/t1481722519vo3yio6iwav5glt.htm/, Retrieved Fri, 03 May 2024 18:40:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299418, Retrieved Fri, 03 May 2024 18:40:56 +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] [] [2016-12-14 13:30:20] [2802fcbee976b89d2ab84425d3d65dcf] [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=299418&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=299418&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299418&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	0.927713	10.4136	0
2	0.900306	10.1059	0
3	0.857858	9.6294	0
4	0.822159	9.2287	0
5	0.801095	8.9923	0
6	0.762021	8.5537	0
7	0.743567	8.3465	0
8	0.707999	7.9473	0
9	0.684624	7.6849	0
10	0.663722	7.4503	0
11	0.634049	7.1172	0
12	0.62302	6.9934	0
13	0.587769	6.5977	0
14	0.579919	6.5096	0
15	0.553319	6.211	0
16	0.534558	6.0004	0
17	0.521216	5.8506	0
18	0.488092	5.4788	0
19	0.477128	5.3558	0
20	0.449846	5.0495	1e-06
21	0.431438	4.8429	2e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.927713 & 10.4136 & 0 \tabularnewline
2 & 0.900306 & 10.1059 & 0 \tabularnewline
3 & 0.857858 & 9.6294 & 0 \tabularnewline
4 & 0.822159 & 9.2287 & 0 \tabularnewline
5 & 0.801095 & 8.9923 & 0 \tabularnewline
6 & 0.762021 & 8.5537 & 0 \tabularnewline
7 & 0.743567 & 8.3465 & 0 \tabularnewline
8 & 0.707999 & 7.9473 & 0 \tabularnewline
9 & 0.684624 & 7.6849 & 0 \tabularnewline
10 & 0.663722 & 7.4503 & 0 \tabularnewline
11 & 0.634049 & 7.1172 & 0 \tabularnewline
12 & 0.62302 & 6.9934 & 0 \tabularnewline
13 & 0.587769 & 6.5977 & 0 \tabularnewline
14 & 0.579919 & 6.5096 & 0 \tabularnewline
15 & 0.553319 & 6.211 & 0 \tabularnewline
16 & 0.534558 & 6.0004 & 0 \tabularnewline
17 & 0.521216 & 5.8506 & 0 \tabularnewline
18 & 0.488092 & 5.4788 & 0 \tabularnewline
19 & 0.477128 & 5.3558 & 0 \tabularnewline
20 & 0.449846 & 5.0495 & 1e-06 \tabularnewline
21 & 0.431438 & 4.8429 & 2e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299418&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]0.927713[/C][C]10.4136[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.900306[/C][C]10.1059[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.857858[/C][C]9.6294[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.822159[/C][C]9.2287[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.801095[/C][C]8.9923[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.762021[/C][C]8.5537[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.743567[/C][C]8.3465[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.707999[/C][C]7.9473[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.684624[/C][C]7.6849[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.663722[/C][C]7.4503[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.634049[/C][C]7.1172[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.62302[/C][C]6.9934[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.587769[/C][C]6.5977[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.579919[/C][C]6.5096[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.553319[/C][C]6.211[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.534558[/C][C]6.0004[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.521216[/C][C]5.8506[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.488092[/C][C]5.4788[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.477128[/C][C]5.3558[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.449846[/C][C]5.0495[/C][C]1e-06[/C][/ROW]
[ROW][C]21[/C][C]0.431438[/C][C]4.8429[/C][C]2e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299418&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299418&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	0.927713	10.4136	0
2	0.900306	10.1059	0
3	0.857858	9.6294	0
4	0.822159	9.2287	0
5	0.801095	8.9923	0
6	0.762021	8.5537	0
7	0.743567	8.3465	0
8	0.707999	7.9473	0
9	0.684624	7.6849	0
10	0.663722	7.4503	0
11	0.634049	7.1172	0
12	0.62302	6.9934	0
13	0.587769	6.5977	0
14	0.579919	6.5096	0
15	0.553319	6.211	0
16	0.534558	6.0004	0
17	0.521216	5.8506	0
18	0.488092	5.4788	0
19	0.477128	5.3558	0
20	0.449846	5.0495	1e-06
21	0.431438	4.8429	2e-06

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.927713	10.4136	0
2	0.284567	3.1943	0.000886
3	-0.028788	-0.3231	0.373563
4	-0.007315	-0.0821	0.467346
5	0.115016	1.2911	0.099525
6	-0.082368	-0.9246	0.178476
7	0.067562	0.7584	0.224821
8	-0.056304	-0.632	0.264263
9	0.020288	0.2277	0.410111
10	0.039723	0.4459	0.328219
11	-0.043394	-0.4871	0.313516
12	0.072018	0.8084	0.210191
13	-0.095744	-1.0747	0.142276
14	0.096388	1.082	0.14067
15	-0.04918	-0.552	0.290949
16	0.000759	0.0085	0.496608
17	0.024895	0.2794	0.390179
18	-0.090252	-1.0131	0.156484
19	0.033036	0.3708	0.355694
20	-0.014924	-0.1675	0.433616
21	-0.024051	-0.27	0.393812

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.927713 & 10.4136 & 0 \tabularnewline
2 & 0.284567 & 3.1943 & 0.000886 \tabularnewline
3 & -0.028788 & -0.3231 & 0.373563 \tabularnewline
4 & -0.007315 & -0.0821 & 0.467346 \tabularnewline
5 & 0.115016 & 1.2911 & 0.099525 \tabularnewline
6 & -0.082368 & -0.9246 & 0.178476 \tabularnewline
7 & 0.067562 & 0.7584 & 0.224821 \tabularnewline
8 & -0.056304 & -0.632 & 0.264263 \tabularnewline
9 & 0.020288 & 0.2277 & 0.410111 \tabularnewline
10 & 0.039723 & 0.4459 & 0.328219 \tabularnewline
11 & -0.043394 & -0.4871 & 0.313516 \tabularnewline
12 & 0.072018 & 0.8084 & 0.210191 \tabularnewline
13 & -0.095744 & -1.0747 & 0.142276 \tabularnewline
14 & 0.096388 & 1.082 & 0.14067 \tabularnewline
15 & -0.04918 & -0.552 & 0.290949 \tabularnewline
16 & 0.000759 & 0.0085 & 0.496608 \tabularnewline
17 & 0.024895 & 0.2794 & 0.390179 \tabularnewline
18 & -0.090252 & -1.0131 & 0.156484 \tabularnewline
19 & 0.033036 & 0.3708 & 0.355694 \tabularnewline
20 & -0.014924 & -0.1675 & 0.433616 \tabularnewline
21 & -0.024051 & -0.27 & 0.393812 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299418&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]0.927713[/C][C]10.4136[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.284567[/C][C]3.1943[/C][C]0.000886[/C][/ROW]
[ROW][C]3[/C][C]-0.028788[/C][C]-0.3231[/C][C]0.373563[/C][/ROW]
[ROW][C]4[/C][C]-0.007315[/C][C]-0.0821[/C][C]0.467346[/C][/ROW]
[ROW][C]5[/C][C]0.115016[/C][C]1.2911[/C][C]0.099525[/C][/ROW]
[ROW][C]6[/C][C]-0.082368[/C][C]-0.9246[/C][C]0.178476[/C][/ROW]
[ROW][C]7[/C][C]0.067562[/C][C]0.7584[/C][C]0.224821[/C][/ROW]
[ROW][C]8[/C][C]-0.056304[/C][C]-0.632[/C][C]0.264263[/C][/ROW]
[ROW][C]9[/C][C]0.020288[/C][C]0.2277[/C][C]0.410111[/C][/ROW]
[ROW][C]10[/C][C]0.039723[/C][C]0.4459[/C][C]0.328219[/C][/ROW]
[ROW][C]11[/C][C]-0.043394[/C][C]-0.4871[/C][C]0.313516[/C][/ROW]
[ROW][C]12[/C][C]0.072018[/C][C]0.8084[/C][C]0.210191[/C][/ROW]
[ROW][C]13[/C][C]-0.095744[/C][C]-1.0747[/C][C]0.142276[/C][/ROW]
[ROW][C]14[/C][C]0.096388[/C][C]1.082[/C][C]0.14067[/C][/ROW]
[ROW][C]15[/C][C]-0.04918[/C][C]-0.552[/C][C]0.290949[/C][/ROW]
[ROW][C]16[/C][C]0.000759[/C][C]0.0085[/C][C]0.496608[/C][/ROW]
[ROW][C]17[/C][C]0.024895[/C][C]0.2794[/C][C]0.390179[/C][/ROW]
[ROW][C]18[/C][C]-0.090252[/C][C]-1.0131[/C][C]0.156484[/C][/ROW]
[ROW][C]19[/C][C]0.033036[/C][C]0.3708[/C][C]0.355694[/C][/ROW]
[ROW][C]20[/C][C]-0.014924[/C][C]-0.1675[/C][C]0.433616[/C][/ROW]
[ROW][C]21[/C][C]-0.024051[/C][C]-0.27[/C][C]0.393812[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299418&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299418&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	0.927713	10.4136	0
2	0.284567	3.1943	0.000886
3	-0.028788	-0.3231	0.373563
4	-0.007315	-0.0821	0.467346
5	0.115016	1.2911	0.099525
6	-0.082368	-0.9246	0.178476
7	0.067562	0.7584	0.224821
8	-0.056304	-0.632	0.264263
9	0.020288	0.2277	0.410111
10	0.039723	0.4459	0.328219
11	-0.043394	-0.4871	0.313516
12	0.072018	0.8084	0.210191
13	-0.095744	-1.0747	0.142276
14	0.096388	1.082	0.14067
15	-0.04918	-0.552	0.290949
16	0.000759	0.0085	0.496608
17	0.024895	0.2794	0.390179
18	-0.090252	-1.0131	0.156484
19	0.033036	0.3708	0.355694
20	-0.014924	-0.1675	0.433616
21	-0.024051	-0.27	0.393812

Figure 1

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Postscript link

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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 = 6 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 6 ; 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