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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 19 Dec 2016 20:39:03 +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/t14821763731nr8c8zlvw7eio4.htm/, Retrieved Fri, 17 May 2024 16:27:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301470, Retrieved Fri, 17 May 2024 16:27:28 +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] [N2044 Variance re...] [2016-12-19 19:39:03] [2e11ca31a00cf8de75c33c1af2d59434] [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=301470&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=301470&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301470&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	0.500811	5.0827	1e-06
2	0.446878	4.5353	8e-06
3	0.378057	3.8369	0.000108
4	0.221287	2.2458	0.013425
5	0.301685	3.0618	0.001403
6	0.244816	2.4846	0.00729
7	0.153639	1.5593	0.061001
8	0.23263	2.3609	0.010055
9	0.077631	0.7879	0.216293
10	0.111227	1.1288	0.130796
11	-0.000653	-0.0066	0.497362
12	-0.226068	-2.2943	0.0119
13	-0.011735	-0.1191	0.452714
14	-0.066882	-0.6788	0.249402
15	0.024097	0.2446	0.403644
16	0.117915	1.1967	0.117084
17	-0.038643	-0.3922	0.347867
18	-0.010483	-0.1064	0.457741
19	-0.031192	-0.3166	0.376109
20	-0.136798	-1.3883	0.084014

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.500811 & 5.0827 & 1e-06 \tabularnewline
2 & 0.446878 & 4.5353 & 8e-06 \tabularnewline
3 & 0.378057 & 3.8369 & 0.000108 \tabularnewline
4 & 0.221287 & 2.2458 & 0.013425 \tabularnewline
5 & 0.301685 & 3.0618 & 0.001403 \tabularnewline
6 & 0.244816 & 2.4846 & 0.00729 \tabularnewline
7 & 0.153639 & 1.5593 & 0.061001 \tabularnewline
8 & 0.23263 & 2.3609 & 0.010055 \tabularnewline
9 & 0.077631 & 0.7879 & 0.216293 \tabularnewline
10 & 0.111227 & 1.1288 & 0.130796 \tabularnewline
11 & -0.000653 & -0.0066 & 0.497362 \tabularnewline
12 & -0.226068 & -2.2943 & 0.0119 \tabularnewline
13 & -0.011735 & -0.1191 & 0.452714 \tabularnewline
14 & -0.066882 & -0.6788 & 0.249402 \tabularnewline
15 & 0.024097 & 0.2446 & 0.403644 \tabularnewline
16 & 0.117915 & 1.1967 & 0.117084 \tabularnewline
17 & -0.038643 & -0.3922 & 0.347867 \tabularnewline
18 & -0.010483 & -0.1064 & 0.457741 \tabularnewline
19 & -0.031192 & -0.3166 & 0.376109 \tabularnewline
20 & -0.136798 & -1.3883 & 0.084014 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301470&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]0.500811[/C][C]5.0827[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.446878[/C][C]4.5353[/C][C]8e-06[/C][/ROW]
[ROW][C]3[/C][C]0.378057[/C][C]3.8369[/C][C]0.000108[/C][/ROW]
[ROW][C]4[/C][C]0.221287[/C][C]2.2458[/C][C]0.013425[/C][/ROW]
[ROW][C]5[/C][C]0.301685[/C][C]3.0618[/C][C]0.001403[/C][/ROW]
[ROW][C]6[/C][C]0.244816[/C][C]2.4846[/C][C]0.00729[/C][/ROW]
[ROW][C]7[/C][C]0.153639[/C][C]1.5593[/C][C]0.061001[/C][/ROW]
[ROW][C]8[/C][C]0.23263[/C][C]2.3609[/C][C]0.010055[/C][/ROW]
[ROW][C]9[/C][C]0.077631[/C][C]0.7879[/C][C]0.216293[/C][/ROW]
[ROW][C]10[/C][C]0.111227[/C][C]1.1288[/C][C]0.130796[/C][/ROW]
[ROW][C]11[/C][C]-0.000653[/C][C]-0.0066[/C][C]0.497362[/C][/ROW]
[ROW][C]12[/C][C]-0.226068[/C][C]-2.2943[/C][C]0.0119[/C][/ROW]
[ROW][C]13[/C][C]-0.011735[/C][C]-0.1191[/C][C]0.452714[/C][/ROW]
[ROW][C]14[/C][C]-0.066882[/C][C]-0.6788[/C][C]0.249402[/C][/ROW]
[ROW][C]15[/C][C]0.024097[/C][C]0.2446[/C][C]0.403644[/C][/ROW]
[ROW][C]16[/C][C]0.117915[/C][C]1.1967[/C][C]0.117084[/C][/ROW]
[ROW][C]17[/C][C]-0.038643[/C][C]-0.3922[/C][C]0.347867[/C][/ROW]
[ROW][C]18[/C][C]-0.010483[/C][C]-0.1064[/C][C]0.457741[/C][/ROW]
[ROW][C]19[/C][C]-0.031192[/C][C]-0.3166[/C][C]0.376109[/C][/ROW]
[ROW][C]20[/C][C]-0.136798[/C][C]-1.3883[/C][C]0.084014[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301470&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301470&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	0.500811	5.0827	1e-06
2	0.446878	4.5353	8e-06
3	0.378057	3.8369	0.000108
4	0.221287	2.2458	0.013425
5	0.301685	3.0618	0.001403
6	0.244816	2.4846	0.00729
7	0.153639	1.5593	0.061001
8	0.23263	2.3609	0.010055
9	0.077631	0.7879	0.216293
10	0.111227	1.1288	0.130796
11	-0.000653	-0.0066	0.497362
12	-0.226068	-2.2943	0.0119
13	-0.011735	-0.1191	0.452714
14	-0.066882	-0.6788	0.249402
15	0.024097	0.2446	0.403644
16	0.117915	1.1967	0.117084
17	-0.038643	-0.3922	0.347867
18	-0.010483	-0.1064	0.457741
19	-0.031192	-0.3166	0.376109
20	-0.136798	-1.3883	0.084014

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.500811	5.0827	1e-06
2	0.261705	2.656	0.004582
3	0.117157	1.189	0.118584
4	-0.09178	-0.9315	0.176896
5	0.166787	1.6927	0.046767
6	0.04507	0.4574	0.32417
7	-0.079599	-0.8078	0.210522
8	0.106187	1.0777	0.141847
9	-0.113539	-1.1523	0.125933
10	0.029576	0.3002	0.382329
11	-0.162245	-1.6466	0.051343
12	-0.307038	-3.1161	0.001187
13	0.233856	2.3734	0.00974
14	0.05159	0.5236	0.300846
15	0.138158	1.4021	0.081939
16	0.076189	0.7732	0.220577
17	-0.080372	-0.8157	0.208281
18	-0.0478	-0.4851	0.314312
19	-0.053342	-0.5414	0.294713
20	-0.079401	-0.8058	0.211097

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.500811 & 5.0827 & 1e-06 \tabularnewline
2 & 0.261705 & 2.656 & 0.004582 \tabularnewline
3 & 0.117157 & 1.189 & 0.118584 \tabularnewline
4 & -0.09178 & -0.9315 & 0.176896 \tabularnewline
5 & 0.166787 & 1.6927 & 0.046767 \tabularnewline
6 & 0.04507 & 0.4574 & 0.32417 \tabularnewline
7 & -0.079599 & -0.8078 & 0.210522 \tabularnewline
8 & 0.106187 & 1.0777 & 0.141847 \tabularnewline
9 & -0.113539 & -1.1523 & 0.125933 \tabularnewline
10 & 0.029576 & 0.3002 & 0.382329 \tabularnewline
11 & -0.162245 & -1.6466 & 0.051343 \tabularnewline
12 & -0.307038 & -3.1161 & 0.001187 \tabularnewline
13 & 0.233856 & 2.3734 & 0.00974 \tabularnewline
14 & 0.05159 & 0.5236 & 0.300846 \tabularnewline
15 & 0.138158 & 1.4021 & 0.081939 \tabularnewline
16 & 0.076189 & 0.7732 & 0.220577 \tabularnewline
17 & -0.080372 & -0.8157 & 0.208281 \tabularnewline
18 & -0.0478 & -0.4851 & 0.314312 \tabularnewline
19 & -0.053342 & -0.5414 & 0.294713 \tabularnewline
20 & -0.079401 & -0.8058 & 0.211097 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301470&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]0.500811[/C][C]5.0827[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.261705[/C][C]2.656[/C][C]0.004582[/C][/ROW]
[ROW][C]3[/C][C]0.117157[/C][C]1.189[/C][C]0.118584[/C][/ROW]
[ROW][C]4[/C][C]-0.09178[/C][C]-0.9315[/C][C]0.176896[/C][/ROW]
[ROW][C]5[/C][C]0.166787[/C][C]1.6927[/C][C]0.046767[/C][/ROW]
[ROW][C]6[/C][C]0.04507[/C][C]0.4574[/C][C]0.32417[/C][/ROW]
[ROW][C]7[/C][C]-0.079599[/C][C]-0.8078[/C][C]0.210522[/C][/ROW]
[ROW][C]8[/C][C]0.106187[/C][C]1.0777[/C][C]0.141847[/C][/ROW]
[ROW][C]9[/C][C]-0.113539[/C][C]-1.1523[/C][C]0.125933[/C][/ROW]
[ROW][C]10[/C][C]0.029576[/C][C]0.3002[/C][C]0.382329[/C][/ROW]
[ROW][C]11[/C][C]-0.162245[/C][C]-1.6466[/C][C]0.051343[/C][/ROW]
[ROW][C]12[/C][C]-0.307038[/C][C]-3.1161[/C][C]0.001187[/C][/ROW]
[ROW][C]13[/C][C]0.233856[/C][C]2.3734[/C][C]0.00974[/C][/ROW]
[ROW][C]14[/C][C]0.05159[/C][C]0.5236[/C][C]0.300846[/C][/ROW]
[ROW][C]15[/C][C]0.138158[/C][C]1.4021[/C][C]0.081939[/C][/ROW]
[ROW][C]16[/C][C]0.076189[/C][C]0.7732[/C][C]0.220577[/C][/ROW]
[ROW][C]17[/C][C]-0.080372[/C][C]-0.8157[/C][C]0.208281[/C][/ROW]
[ROW][C]18[/C][C]-0.0478[/C][C]-0.4851[/C][C]0.314312[/C][/ROW]
[ROW][C]19[/C][C]-0.053342[/C][C]-0.5414[/C][C]0.294713[/C][/ROW]
[ROW][C]20[/C][C]-0.079401[/C][C]-0.8058[/C][C]0.211097[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301470&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301470&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	0.500811	5.0827	1e-06
2	0.261705	2.656	0.004582
3	0.117157	1.189	0.118584
4	-0.09178	-0.9315	0.176896
5	0.166787	1.6927	0.046767
6	0.04507	0.4574	0.32417
7	-0.079599	-0.8078	0.210522
8	0.106187	1.0777	0.141847
9	-0.113539	-1.1523	0.125933
10	0.029576	0.3002	0.382329
11	-0.162245	-1.6466	0.051343
12	-0.307038	-3.1161	0.001187
13	0.233856	2.3734	0.00974
14	0.05159	0.5236	0.300846
15	0.138158	1.4021	0.081939
16	0.076189	0.7732	0.220577
17	-0.080372	-0.8157	0.208281
18	-0.0478	-0.4851	0.314312
19	-0.053342	-0.5414	0.294713
20	-0.079401	-0.8058	0.211097

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):

par1 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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