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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 22 Jan 2016 10:44:23 +0000

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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/Jan/22/t14534595366qn7cspoear1iqf.htm/, Retrieved Tue, 07 May 2024 16:22:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=291562, Retrieved Tue, 07 May 2024 16:22:44 +0000

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Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Multiple Regression] [] [2016-01-22 10:31:33] [9532f32b74e28ad25b08dafeb45359b0]
- RMPD    [(Partial) Autocorrelation Function] [] [2016-01-22 10:44:23] [367ad10dbc749ecaa08cb2fc99c565b9] [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	'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=291562&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=291562&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=291562&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	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.274454	-2.1081	0.019639
2	-0.365156	-2.8048	0.003403
3	0.13745	1.0558	0.147689
4	0.048913	0.3757	0.35424
5	-0.077648	-0.5964	0.276587
6	0.028569	0.2194	0.413531
7	0.036997	0.2842	0.388633
8	-0.092297	-0.7089	0.240575
9	-0.102703	-0.7889	0.216672
10	0.365164	2.8049	0.003403
11	0.135194	1.0384	0.151651
12	-0.617126	-4.7402	7e-06
13	0.210258	1.615	0.055821
14	0.183264	1.4077	0.082236
15	-0.167875	-1.2895	0.101133
16	0.041857	0.3215	0.37448
17	0.061973	0.476	0.317907
18	-0.031662	-0.2432	0.404346

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.274454 & -2.1081 & 0.019639 \tabularnewline
2 & -0.365156 & -2.8048 & 0.003403 \tabularnewline
3 & 0.13745 & 1.0558 & 0.147689 \tabularnewline
4 & 0.048913 & 0.3757 & 0.35424 \tabularnewline
5 & -0.077648 & -0.5964 & 0.276587 \tabularnewline
6 & 0.028569 & 0.2194 & 0.413531 \tabularnewline
7 & 0.036997 & 0.2842 & 0.388633 \tabularnewline
8 & -0.092297 & -0.7089 & 0.240575 \tabularnewline
9 & -0.102703 & -0.7889 & 0.216672 \tabularnewline
10 & 0.365164 & 2.8049 & 0.003403 \tabularnewline
11 & 0.135194 & 1.0384 & 0.151651 \tabularnewline
12 & -0.617126 & -4.7402 & 7e-06 \tabularnewline
13 & 0.210258 & 1.615 & 0.055821 \tabularnewline
14 & 0.183264 & 1.4077 & 0.082236 \tabularnewline
15 & -0.167875 & -1.2895 & 0.101133 \tabularnewline
16 & 0.041857 & 0.3215 & 0.37448 \tabularnewline
17 & 0.061973 & 0.476 & 0.317907 \tabularnewline
18 & -0.031662 & -0.2432 & 0.404346 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=291562&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]-0.274454[/C][C]-2.1081[/C][C]0.019639[/C][/ROW]
[ROW][C]2[/C][C]-0.365156[/C][C]-2.8048[/C][C]0.003403[/C][/ROW]
[ROW][C]3[/C][C]0.13745[/C][C]1.0558[/C][C]0.147689[/C][/ROW]
[ROW][C]4[/C][C]0.048913[/C][C]0.3757[/C][C]0.35424[/C][/ROW]
[ROW][C]5[/C][C]-0.077648[/C][C]-0.5964[/C][C]0.276587[/C][/ROW]
[ROW][C]6[/C][C]0.028569[/C][C]0.2194[/C][C]0.413531[/C][/ROW]
[ROW][C]7[/C][C]0.036997[/C][C]0.2842[/C][C]0.388633[/C][/ROW]
[ROW][C]8[/C][C]-0.092297[/C][C]-0.7089[/C][C]0.240575[/C][/ROW]
[ROW][C]9[/C][C]-0.102703[/C][C]-0.7889[/C][C]0.216672[/C][/ROW]
[ROW][C]10[/C][C]0.365164[/C][C]2.8049[/C][C]0.003403[/C][/ROW]
[ROW][C]11[/C][C]0.135194[/C][C]1.0384[/C][C]0.151651[/C][/ROW]
[ROW][C]12[/C][C]-0.617126[/C][C]-4.7402[/C][C]7e-06[/C][/ROW]
[ROW][C]13[/C][C]0.210258[/C][C]1.615[/C][C]0.055821[/C][/ROW]
[ROW][C]14[/C][C]0.183264[/C][C]1.4077[/C][C]0.082236[/C][/ROW]
[ROW][C]15[/C][C]-0.167875[/C][C]-1.2895[/C][C]0.101133[/C][/ROW]
[ROW][C]16[/C][C]0.041857[/C][C]0.3215[/C][C]0.37448[/C][/ROW]
[ROW][C]17[/C][C]0.061973[/C][C]0.476[/C][C]0.317907[/C][/ROW]
[ROW][C]18[/C][C]-0.031662[/C][C]-0.2432[/C][C]0.404346[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=291562&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=291562&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	-0.274454	-2.1081	0.019639
2	-0.365156	-2.8048	0.003403
3	0.13745	1.0558	0.147689
4	0.048913	0.3757	0.35424
5	-0.077648	-0.5964	0.276587
6	0.028569	0.2194	0.413531
7	0.036997	0.2842	0.388633
8	-0.092297	-0.7089	0.240575
9	-0.102703	-0.7889	0.216672
10	0.365164	2.8049	0.003403
11	0.135194	1.0384	0.151651
12	-0.617126	-4.7402	7e-06
13	0.210258	1.615	0.055821
14	0.183264	1.4077	0.082236
15	-0.167875	-1.2895	0.101133
16	0.041857	0.3215	0.37448
17	0.061973	0.476	0.317907
18	-0.031662	-0.2432	0.404346

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.274454	-2.1081	0.019639
2	-0.476363	-3.659	0.000271
3	-0.197594	-1.5177	0.06721
4	-0.203612	-1.564	0.061586
5	-0.18887	-1.4507	0.076075
6	-0.134915	-1.0363	0.152144
7	-0.097413	-0.7482	0.228643
8	-0.187628	-1.4412	0.077408
9	-0.362758	-2.7864	0.003579
10	0.100188	0.7696	0.222317
11	0.426592	3.2767	0.000881
12	-0.213395	-1.6391	0.053255
13	0.092186	0.7081	0.240838
14	-0.049171	-0.3777	0.353509
15	-0.07942	-0.61	0.272091
16	0.004638	0.0356	0.48585
17	-0.027445	-0.2108	0.416882
18	0.089242	0.6855	0.247862

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.274454 & -2.1081 & 0.019639 \tabularnewline
2 & -0.476363 & -3.659 & 0.000271 \tabularnewline
3 & -0.197594 & -1.5177 & 0.06721 \tabularnewline
4 & -0.203612 & -1.564 & 0.061586 \tabularnewline
5 & -0.18887 & -1.4507 & 0.076075 \tabularnewline
6 & -0.134915 & -1.0363 & 0.152144 \tabularnewline
7 & -0.097413 & -0.7482 & 0.228643 \tabularnewline
8 & -0.187628 & -1.4412 & 0.077408 \tabularnewline
9 & -0.362758 & -2.7864 & 0.003579 \tabularnewline
10 & 0.100188 & 0.7696 & 0.222317 \tabularnewline
11 & 0.426592 & 3.2767 & 0.000881 \tabularnewline
12 & -0.213395 & -1.6391 & 0.053255 \tabularnewline
13 & 0.092186 & 0.7081 & 0.240838 \tabularnewline
14 & -0.049171 & -0.3777 & 0.353509 \tabularnewline
15 & -0.07942 & -0.61 & 0.272091 \tabularnewline
16 & 0.004638 & 0.0356 & 0.48585 \tabularnewline
17 & -0.027445 & -0.2108 & 0.416882 \tabularnewline
18 & 0.089242 & 0.6855 & 0.247862 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=291562&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]-0.274454[/C][C]-2.1081[/C][C]0.019639[/C][/ROW]
[ROW][C]2[/C][C]-0.476363[/C][C]-3.659[/C][C]0.000271[/C][/ROW]
[ROW][C]3[/C][C]-0.197594[/C][C]-1.5177[/C][C]0.06721[/C][/ROW]
[ROW][C]4[/C][C]-0.203612[/C][C]-1.564[/C][C]0.061586[/C][/ROW]
[ROW][C]5[/C][C]-0.18887[/C][C]-1.4507[/C][C]0.076075[/C][/ROW]
[ROW][C]6[/C][C]-0.134915[/C][C]-1.0363[/C][C]0.152144[/C][/ROW]
[ROW][C]7[/C][C]-0.097413[/C][C]-0.7482[/C][C]0.228643[/C][/ROW]
[ROW][C]8[/C][C]-0.187628[/C][C]-1.4412[/C][C]0.077408[/C][/ROW]
[ROW][C]9[/C][C]-0.362758[/C][C]-2.7864[/C][C]0.003579[/C][/ROW]
[ROW][C]10[/C][C]0.100188[/C][C]0.7696[/C][C]0.222317[/C][/ROW]
[ROW][C]11[/C][C]0.426592[/C][C]3.2767[/C][C]0.000881[/C][/ROW]
[ROW][C]12[/C][C]-0.213395[/C][C]-1.6391[/C][C]0.053255[/C][/ROW]
[ROW][C]13[/C][C]0.092186[/C][C]0.7081[/C][C]0.240838[/C][/ROW]
[ROW][C]14[/C][C]-0.049171[/C][C]-0.3777[/C][C]0.353509[/C][/ROW]
[ROW][C]15[/C][C]-0.07942[/C][C]-0.61[/C][C]0.272091[/C][/ROW]
[ROW][C]16[/C][C]0.004638[/C][C]0.0356[/C][C]0.48585[/C][/ROW]
[ROW][C]17[/C][C]-0.027445[/C][C]-0.2108[/C][C]0.416882[/C][/ROW]
[ROW][C]18[/C][C]0.089242[/C][C]0.6855[/C][C]0.247862[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=291562&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=291562&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	-0.274454	-2.1081	0.019639
2	-0.476363	-3.659	0.000271
3	-0.197594	-1.5177	0.06721
4	-0.203612	-1.564	0.061586
5	-0.18887	-1.4507	0.076075
6	-0.134915	-1.0363	0.152144
7	-0.097413	-0.7482	0.228643
8	-0.187628	-1.4412	0.077408
9	-0.362758	-2.7864	0.003579
10	0.100188	0.7696	0.222317
11	0.426592	3.2767	0.000881
12	-0.213395	-1.6391	0.053255
13	0.092186	0.7081	0.240838
14	-0.049171	-0.3777	0.353509
15	-0.07942	-0.61	0.272091
16	0.004638	0.0356	0.48585
17	-0.027445	-0.2108	0.416882
18	0.089242	0.6855	0.247862

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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 <- '1'
par3 <- '0'
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,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),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,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code