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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 21:12:19 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/16/t1481919160g0c51xffk09hkrj.htm/, Retrieved Fri, 03 May 2024 03:31:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300533, Retrieved Fri, 03 May 2024 03:31:22 +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] [N2099 - r0481974] [2016-12-16 20:12:19] [ee2f08b6fcfe19fae25bd9410e008f6d] [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=300533&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=300533&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300533&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	0.306701	3.4427	0.000391
2	0.178054	1.9987	0.023899
3	-0.056299	-0.632	0.264279
4	0.023931	0.2686	0.39433
5	0.008704	0.0977	0.46116
6	0.043219	0.4851	0.314212
7	0.0223	0.2503	0.401377
8	-0.011544	-0.1296	0.44855
9	-0.031479	-0.3534	0.362208
10	0.047303	0.531	0.298185
11	0.325939	3.6587	0.000186
12	0.443305	4.9761	1e-06
13	0.359111	4.031	4.8e-05
14	0.086016	0.9655	0.168065
15	-0.060821	-0.6827	0.24802
16	-0.065219	-0.7321	0.23274
17	0.054842	0.6156	0.269634
18	0.015083	0.1693	0.432915
19	-0.060332	-0.6772	0.249754
20	0.006781	0.0761	0.469722
21	-0.057221	-0.6423	0.260922

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.306701 & 3.4427 & 0.000391 \tabularnewline
2 & 0.178054 & 1.9987 & 0.023899 \tabularnewline
3 & -0.056299 & -0.632 & 0.264279 \tabularnewline
4 & 0.023931 & 0.2686 & 0.39433 \tabularnewline
5 & 0.008704 & 0.0977 & 0.46116 \tabularnewline
6 & 0.043219 & 0.4851 & 0.314212 \tabularnewline
7 & 0.0223 & 0.2503 & 0.401377 \tabularnewline
8 & -0.011544 & -0.1296 & 0.44855 \tabularnewline
9 & -0.031479 & -0.3534 & 0.362208 \tabularnewline
10 & 0.047303 & 0.531 & 0.298185 \tabularnewline
11 & 0.325939 & 3.6587 & 0.000186 \tabularnewline
12 & 0.443305 & 4.9761 & 1e-06 \tabularnewline
13 & 0.359111 & 4.031 & 4.8e-05 \tabularnewline
14 & 0.086016 & 0.9655 & 0.168065 \tabularnewline
15 & -0.060821 & -0.6827 & 0.24802 \tabularnewline
16 & -0.065219 & -0.7321 & 0.23274 \tabularnewline
17 & 0.054842 & 0.6156 & 0.269634 \tabularnewline
18 & 0.015083 & 0.1693 & 0.432915 \tabularnewline
19 & -0.060332 & -0.6772 & 0.249754 \tabularnewline
20 & 0.006781 & 0.0761 & 0.469722 \tabularnewline
21 & -0.057221 & -0.6423 & 0.260922 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300533&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]0.306701[/C][C]3.4427[/C][C]0.000391[/C][/ROW]
[ROW][C]2[/C][C]0.178054[/C][C]1.9987[/C][C]0.023899[/C][/ROW]
[ROW][C]3[/C][C]-0.056299[/C][C]-0.632[/C][C]0.264279[/C][/ROW]
[ROW][C]4[/C][C]0.023931[/C][C]0.2686[/C][C]0.39433[/C][/ROW]
[ROW][C]5[/C][C]0.008704[/C][C]0.0977[/C][C]0.46116[/C][/ROW]
[ROW][C]6[/C][C]0.043219[/C][C]0.4851[/C][C]0.314212[/C][/ROW]
[ROW][C]7[/C][C]0.0223[/C][C]0.2503[/C][C]0.401377[/C][/ROW]
[ROW][C]8[/C][C]-0.011544[/C][C]-0.1296[/C][C]0.44855[/C][/ROW]
[ROW][C]9[/C][C]-0.031479[/C][C]-0.3534[/C][C]0.362208[/C][/ROW]
[ROW][C]10[/C][C]0.047303[/C][C]0.531[/C][C]0.298185[/C][/ROW]
[ROW][C]11[/C][C]0.325939[/C][C]3.6587[/C][C]0.000186[/C][/ROW]
[ROW][C]12[/C][C]0.443305[/C][C]4.9761[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.359111[/C][C]4.031[/C][C]4.8e-05[/C][/ROW]
[ROW][C]14[/C][C]0.086016[/C][C]0.9655[/C][C]0.168065[/C][/ROW]
[ROW][C]15[/C][C]-0.060821[/C][C]-0.6827[/C][C]0.24802[/C][/ROW]
[ROW][C]16[/C][C]-0.065219[/C][C]-0.7321[/C][C]0.23274[/C][/ROW]
[ROW][C]17[/C][C]0.054842[/C][C]0.6156[/C][C]0.269634[/C][/ROW]
[ROW][C]18[/C][C]0.015083[/C][C]0.1693[/C][C]0.432915[/C][/ROW]
[ROW][C]19[/C][C]-0.060332[/C][C]-0.6772[/C][C]0.249754[/C][/ROW]
[ROW][C]20[/C][C]0.006781[/C][C]0.0761[/C][C]0.469722[/C][/ROW]
[ROW][C]21[/C][C]-0.057221[/C][C]-0.6423[/C][C]0.260922[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300533&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300533&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	0.306701	3.4427	0.000391
2	0.178054	1.9987	0.023899
3	-0.056299	-0.632	0.264279
4	0.023931	0.2686	0.39433
5	0.008704	0.0977	0.46116
6	0.043219	0.4851	0.314212
7	0.0223	0.2503	0.401377
8	-0.011544	-0.1296	0.44855
9	-0.031479	-0.3534	0.362208
10	0.047303	0.531	0.298185
11	0.325939	3.6587	0.000186
12	0.443305	4.9761	1e-06
13	0.359111	4.031	4.8e-05
14	0.086016	0.9655	0.168065
15	-0.060821	-0.6827	0.24802
16	-0.065219	-0.7321	0.23274
17	0.054842	0.6156	0.269634
18	0.015083	0.1693	0.432915
19	-0.060332	-0.6772	0.249754
20	0.006781	0.0761	0.469722
21	-0.057221	-0.6423	0.260922

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.306701	3.4427	0.000391
2	0.09271	1.0407	0.150011
3	-0.149508	-1.6782	0.047891
4	0.07097	0.7966	0.213582
5	0.019493	0.2188	0.413575
6	0.011731	0.1317	0.447724
7	0.010765	0.1208	0.452007
8	-0.031862	-0.3576	0.360604
9	-0.01996	-0.2241	0.41154
10	0.081238	0.9119	0.181782
11	0.336985	3.7826	0.000119
12	0.308594	3.464	0.000364
13	0.142546	1.6001	0.056043
14	-0.078027	-0.8759	0.191389
15	-0.119808	-1.3448	0.090546
16	-0.037975	-0.4263	0.33532
17	0.091055	1.0221	0.154349
18	-0.032475	-0.3645	0.358037
19	-0.137919	-1.5481	0.062049
20	0.092756	1.0412	0.149891
21	-0.017891	-0.2008	0.420579

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.306701 & 3.4427 & 0.000391 \tabularnewline
2 & 0.09271 & 1.0407 & 0.150011 \tabularnewline
3 & -0.149508 & -1.6782 & 0.047891 \tabularnewline
4 & 0.07097 & 0.7966 & 0.213582 \tabularnewline
5 & 0.019493 & 0.2188 & 0.413575 \tabularnewline
6 & 0.011731 & 0.1317 & 0.447724 \tabularnewline
7 & 0.010765 & 0.1208 & 0.452007 \tabularnewline
8 & -0.031862 & -0.3576 & 0.360604 \tabularnewline
9 & -0.01996 & -0.2241 & 0.41154 \tabularnewline
10 & 0.081238 & 0.9119 & 0.181782 \tabularnewline
11 & 0.336985 & 3.7826 & 0.000119 \tabularnewline
12 & 0.308594 & 3.464 & 0.000364 \tabularnewline
13 & 0.142546 & 1.6001 & 0.056043 \tabularnewline
14 & -0.078027 & -0.8759 & 0.191389 \tabularnewline
15 & -0.119808 & -1.3448 & 0.090546 \tabularnewline
16 & -0.037975 & -0.4263 & 0.33532 \tabularnewline
17 & 0.091055 & 1.0221 & 0.154349 \tabularnewline
18 & -0.032475 & -0.3645 & 0.358037 \tabularnewline
19 & -0.137919 & -1.5481 & 0.062049 \tabularnewline
20 & 0.092756 & 1.0412 & 0.149891 \tabularnewline
21 & -0.017891 & -0.2008 & 0.420579 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300533&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]0.306701[/C][C]3.4427[/C][C]0.000391[/C][/ROW]
[ROW][C]2[/C][C]0.09271[/C][C]1.0407[/C][C]0.150011[/C][/ROW]
[ROW][C]3[/C][C]-0.149508[/C][C]-1.6782[/C][C]0.047891[/C][/ROW]
[ROW][C]4[/C][C]0.07097[/C][C]0.7966[/C][C]0.213582[/C][/ROW]
[ROW][C]5[/C][C]0.019493[/C][C]0.2188[/C][C]0.413575[/C][/ROW]
[ROW][C]6[/C][C]0.011731[/C][C]0.1317[/C][C]0.447724[/C][/ROW]
[ROW][C]7[/C][C]0.010765[/C][C]0.1208[/C][C]0.452007[/C][/ROW]
[ROW][C]8[/C][C]-0.031862[/C][C]-0.3576[/C][C]0.360604[/C][/ROW]
[ROW][C]9[/C][C]-0.01996[/C][C]-0.2241[/C][C]0.41154[/C][/ROW]
[ROW][C]10[/C][C]0.081238[/C][C]0.9119[/C][C]0.181782[/C][/ROW]
[ROW][C]11[/C][C]0.336985[/C][C]3.7826[/C][C]0.000119[/C][/ROW]
[ROW][C]12[/C][C]0.308594[/C][C]3.464[/C][C]0.000364[/C][/ROW]
[ROW][C]13[/C][C]0.142546[/C][C]1.6001[/C][C]0.056043[/C][/ROW]
[ROW][C]14[/C][C]-0.078027[/C][C]-0.8759[/C][C]0.191389[/C][/ROW]
[ROW][C]15[/C][C]-0.119808[/C][C]-1.3448[/C][C]0.090546[/C][/ROW]
[ROW][C]16[/C][C]-0.037975[/C][C]-0.4263[/C][C]0.33532[/C][/ROW]
[ROW][C]17[/C][C]0.091055[/C][C]1.0221[/C][C]0.154349[/C][/ROW]
[ROW][C]18[/C][C]-0.032475[/C][C]-0.3645[/C][C]0.358037[/C][/ROW]
[ROW][C]19[/C][C]-0.137919[/C][C]-1.5481[/C][C]0.062049[/C][/ROW]
[ROW][C]20[/C][C]0.092756[/C][C]1.0412[/C][C]0.149891[/C][/ROW]
[ROW][C]21[/C][C]-0.017891[/C][C]-0.2008[/C][C]0.420579[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300533&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300533&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	0.306701	3.4427	0.000391
2	0.09271	1.0407	0.150011
3	-0.149508	-1.6782	0.047891
4	0.07097	0.7966	0.213582
5	0.019493	0.2188	0.413575
6	0.011731	0.1317	0.447724
7	0.010765	0.1208	0.452007
8	-0.031862	-0.3576	0.360604
9	-0.01996	-0.2241	0.41154
10	0.081238	0.9119	0.181782
11	0.336985	3.7826	0.000119
12	0.308594	3.464	0.000364
13	0.142546	1.6001	0.056043
14	-0.078027	-0.8759	0.191389
15	-0.119808	-1.3448	0.090546
16	-0.037975	-0.4263	0.33532
17	0.091055	1.0221	0.154349
18	-0.032475	-0.3645	0.358037
19	-0.137919	-1.5481	0.062049
20	0.092756	1.0412	0.149891
21	-0.017891	-0.2008	0.420579

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 = 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):

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