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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 01 Feb 2018 11:31:53 +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/2018/Feb/01/t1517481124bag91mfwrt2tn57.htm/, Retrieved Sun, 28 Apr 2024 23:13:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=314745, Retrieved Sun, 28 Apr 2024 23:13:51 +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] [] [2018-02-01 10:31:53] [767bae2faba658f23149559b7968621e] [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	2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=314745&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=314745&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=314745&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	2 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.809501	11.7865	0
2	0.742182	10.8063	0
3	0.813647	11.8469	0
4	0.743185	10.8209	0
5	0.766736	11.1638	0
6	0.812171	11.8254	0
7	0.709738	10.3339	0
8	0.684183	9.9619	0
9	0.701122	10.2085	0
10	0.607301	8.8424	0
11	0.668915	9.7395	0
12	0.770662	11.221	0
13	0.625612	9.109	0
14	0.573819	8.3549	0
15	0.617067	8.9846	0
16	0.572154	8.3307	0
17	0.597303	8.6969	0
18	0.631336	9.1924	0
19	0.547494	7.9716	0
20	0.536636	7.8135	0
21	0.540541	7.8704	0
22	0.464956	6.7699	0
23	0.532609	7.7549	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.809501 & 11.7865 & 0 \tabularnewline
2 & 0.742182 & 10.8063 & 0 \tabularnewline
3 & 0.813647 & 11.8469 & 0 \tabularnewline
4 & 0.743185 & 10.8209 & 0 \tabularnewline
5 & 0.766736 & 11.1638 & 0 \tabularnewline
6 & 0.812171 & 11.8254 & 0 \tabularnewline
7 & 0.709738 & 10.3339 & 0 \tabularnewline
8 & 0.684183 & 9.9619 & 0 \tabularnewline
9 & 0.701122 & 10.2085 & 0 \tabularnewline
10 & 0.607301 & 8.8424 & 0 \tabularnewline
11 & 0.668915 & 9.7395 & 0 \tabularnewline
12 & 0.770662 & 11.221 & 0 \tabularnewline
13 & 0.625612 & 9.109 & 0 \tabularnewline
14 & 0.573819 & 8.3549 & 0 \tabularnewline
15 & 0.617067 & 8.9846 & 0 \tabularnewline
16 & 0.572154 & 8.3307 & 0 \tabularnewline
17 & 0.597303 & 8.6969 & 0 \tabularnewline
18 & 0.631336 & 9.1924 & 0 \tabularnewline
19 & 0.547494 & 7.9716 & 0 \tabularnewline
20 & 0.536636 & 7.8135 & 0 \tabularnewline
21 & 0.540541 & 7.8704 & 0 \tabularnewline
22 & 0.464956 & 6.7699 & 0 \tabularnewline
23 & 0.532609 & 7.7549 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=314745&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]0.809501[/C][C]11.7865[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.742182[/C][C]10.8063[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.813647[/C][C]11.8469[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.743185[/C][C]10.8209[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.766736[/C][C]11.1638[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.812171[/C][C]11.8254[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.709738[/C][C]10.3339[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.684183[/C][C]9.9619[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.701122[/C][C]10.2085[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.607301[/C][C]8.8424[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.668915[/C][C]9.7395[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.770662[/C][C]11.221[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.625612[/C][C]9.109[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.573819[/C][C]8.3549[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.617067[/C][C]8.9846[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.572154[/C][C]8.3307[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.597303[/C][C]8.6969[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.631336[/C][C]9.1924[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.547494[/C][C]7.9716[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.536636[/C][C]7.8135[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.540541[/C][C]7.8704[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.464956[/C][C]6.7699[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.532609[/C][C]7.7549[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=314745&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=314745&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	0.809501	11.7865	0
2	0.742182	10.8063	0
3	0.813647	11.8469	0
4	0.743185	10.8209	0
5	0.766736	11.1638	0
6	0.812171	11.8254	0
7	0.709738	10.3339	0
8	0.684183	9.9619	0
9	0.701122	10.2085	0
10	0.607301	8.8424	0
11	0.668915	9.7395	0
12	0.770662	11.221	0
13	0.625612	9.109	0
14	0.573819	8.3549	0
15	0.617067	8.9846	0
16	0.572154	8.3307	0
17	0.597303	8.6969	0
18	0.631336	9.1924	0
19	0.547494	7.9716	0
20	0.536636	7.8135	0
21	0.540541	7.8704	0
22	0.464956	6.7699	0
23	0.532609	7.7549	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.809501	11.7865	0
2	0.252069	3.6702	0.000153
3	0.496402	7.2277	0
4	-0.055444	-0.8073	0.210204
5	0.361379	5.2618	0
6	0.142928	2.0811	0.019315
7	-0.123052	-1.7917	0.037307
8	-0.080821	-1.1768	0.120304
9	-0.085211	-1.2407	0.108045
10	-0.268446	-3.9086	6.2e-05
11	0.269931	3.9303	5.7e-05
12	0.418349	6.0913	0
13	-0.188647	-2.7467	0.003268
14	-0.206703	-3.0096	0.001466
15	-0.081361	-1.1846	0.118744
16	0.090347	1.3155	0.094886
17	-0.055473	-0.8077	0.210083
18	0.054666	0.7959	0.213477
19	0.045688	0.6652	0.253312
20	0.037498	0.546	0.292826
21	-0.049524	-0.7211	0.235827
22	-0.027974	-0.4073	0.342097
23	0.059429	0.8653	0.193928

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.809501 & 11.7865 & 0 \tabularnewline
2 & 0.252069 & 3.6702 & 0.000153 \tabularnewline
3 & 0.496402 & 7.2277 & 0 \tabularnewline
4 & -0.055444 & -0.8073 & 0.210204 \tabularnewline
5 & 0.361379 & 5.2618 & 0 \tabularnewline
6 & 0.142928 & 2.0811 & 0.019315 \tabularnewline
7 & -0.123052 & -1.7917 & 0.037307 \tabularnewline
8 & -0.080821 & -1.1768 & 0.120304 \tabularnewline
9 & -0.085211 & -1.2407 & 0.108045 \tabularnewline
10 & -0.268446 & -3.9086 & 6.2e-05 \tabularnewline
11 & 0.269931 & 3.9303 & 5.7e-05 \tabularnewline
12 & 0.418349 & 6.0913 & 0 \tabularnewline
13 & -0.188647 & -2.7467 & 0.003268 \tabularnewline
14 & -0.206703 & -3.0096 & 0.001466 \tabularnewline
15 & -0.081361 & -1.1846 & 0.118744 \tabularnewline
16 & 0.090347 & 1.3155 & 0.094886 \tabularnewline
17 & -0.055473 & -0.8077 & 0.210083 \tabularnewline
18 & 0.054666 & 0.7959 & 0.213477 \tabularnewline
19 & 0.045688 & 0.6652 & 0.253312 \tabularnewline
20 & 0.037498 & 0.546 & 0.292826 \tabularnewline
21 & -0.049524 & -0.7211 & 0.235827 \tabularnewline
22 & -0.027974 & -0.4073 & 0.342097 \tabularnewline
23 & 0.059429 & 0.8653 & 0.193928 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=314745&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]0.809501[/C][C]11.7865[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.252069[/C][C]3.6702[/C][C]0.000153[/C][/ROW]
[ROW][C]3[/C][C]0.496402[/C][C]7.2277[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.055444[/C][C]-0.8073[/C][C]0.210204[/C][/ROW]
[ROW][C]5[/C][C]0.361379[/C][C]5.2618[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.142928[/C][C]2.0811[/C][C]0.019315[/C][/ROW]
[ROW][C]7[/C][C]-0.123052[/C][C]-1.7917[/C][C]0.037307[/C][/ROW]
[ROW][C]8[/C][C]-0.080821[/C][C]-1.1768[/C][C]0.120304[/C][/ROW]
[ROW][C]9[/C][C]-0.085211[/C][C]-1.2407[/C][C]0.108045[/C][/ROW]
[ROW][C]10[/C][C]-0.268446[/C][C]-3.9086[/C][C]6.2e-05[/C][/ROW]
[ROW][C]11[/C][C]0.269931[/C][C]3.9303[/C][C]5.7e-05[/C][/ROW]
[ROW][C]12[/C][C]0.418349[/C][C]6.0913[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.188647[/C][C]-2.7467[/C][C]0.003268[/C][/ROW]
[ROW][C]14[/C][C]-0.206703[/C][C]-3.0096[/C][C]0.001466[/C][/ROW]
[ROW][C]15[/C][C]-0.081361[/C][C]-1.1846[/C][C]0.118744[/C][/ROW]
[ROW][C]16[/C][C]0.090347[/C][C]1.3155[/C][C]0.094886[/C][/ROW]
[ROW][C]17[/C][C]-0.055473[/C][C]-0.8077[/C][C]0.210083[/C][/ROW]
[ROW][C]18[/C][C]0.054666[/C][C]0.7959[/C][C]0.213477[/C][/ROW]
[ROW][C]19[/C][C]0.045688[/C][C]0.6652[/C][C]0.253312[/C][/ROW]
[ROW][C]20[/C][C]0.037498[/C][C]0.546[/C][C]0.292826[/C][/ROW]
[ROW][C]21[/C][C]-0.049524[/C][C]-0.7211[/C][C]0.235827[/C][/ROW]
[ROW][C]22[/C][C]-0.027974[/C][C]-0.4073[/C][C]0.342097[/C][/ROW]
[ROW][C]23[/C][C]0.059429[/C][C]0.8653[/C][C]0.193928[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=314745&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=314745&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	0.809501	11.7865	0
2	0.252069	3.6702	0.000153
3	0.496402	7.2277	0
4	-0.055444	-0.8073	0.210204
5	0.361379	5.2618	0
6	0.142928	2.0811	0.019315
7	-0.123052	-1.7917	0.037307
8	-0.080821	-1.1768	0.120304
9	-0.085211	-1.2407	0.108045
10	-0.268446	-3.9086	6.2e-05
11	0.269931	3.9303	5.7e-05
12	0.418349	6.0913	0
13	-0.188647	-2.7467	0.003268
14	-0.206703	-3.0096	0.001466
15	-0.081361	-1.1846	0.118744
16	0.090347	1.3155	0.094886
17	-0.055473	-0.8077	0.210083
18	0.054666	0.7959	0.213477
19	0.045688	0.6652	0.253312
20	0.037498	0.546	0.292826
21	-0.049524	-0.7211	0.235827
22	-0.027974	-0.4073	0.342097
23	0.059429	0.8653	0.193928

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

Postscript link

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Parameters (Session):

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