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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 12 Mar 2016 15:07:32 +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/Mar/12/t1457795343uet18my1exik633.htm/, Retrieved Sun, 05 May 2024 20:04:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293923, Retrieved Sun, 05 May 2024 20:04:35 +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] [consumptieprijsin...] [2016-03-12 15:07:32] [567a9be58124adae7ccc8a0c8709ba48] [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	'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293923&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293923&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293923&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.216148	2.3579	0.010005
2	0.071792	0.7832	0.217545
3	-0.170872	-1.864	0.032394
4	-0.101322	-1.1053	0.135631
5	-0.00388	-0.0423	0.483156
6	0.028083	0.3064	0.379935
7	-0.004599	-0.0502	0.480035
8	-0.138259	-1.5082	0.067074
9	-0.17469	-1.9056	0.029555
10	-0.032569	-0.3553	0.361503
11	0.174849	1.9074	0.029441
12	0.343116	3.743	0.000141
13	0.273176	2.98	0.001748
14	-0.077126	-0.8413	0.200922
15	-0.145584	-1.5881	0.057455
16	-0.20418	-2.2273	0.013903
17	-0.120085	-1.31	0.096365
18	-0.034696	-0.3785	0.352869
19	-0.032425	-0.3537	0.362088
20	-0.087098	-0.9501	0.171986

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.216148 & 2.3579 & 0.010005 \tabularnewline
2 & 0.071792 & 0.7832 & 0.217545 \tabularnewline
3 & -0.170872 & -1.864 & 0.032394 \tabularnewline
4 & -0.101322 & -1.1053 & 0.135631 \tabularnewline
5 & -0.00388 & -0.0423 & 0.483156 \tabularnewline
6 & 0.028083 & 0.3064 & 0.379935 \tabularnewline
7 & -0.004599 & -0.0502 & 0.480035 \tabularnewline
8 & -0.138259 & -1.5082 & 0.067074 \tabularnewline
9 & -0.17469 & -1.9056 & 0.029555 \tabularnewline
10 & -0.032569 & -0.3553 & 0.361503 \tabularnewline
11 & 0.174849 & 1.9074 & 0.029441 \tabularnewline
12 & 0.343116 & 3.743 & 0.000141 \tabularnewline
13 & 0.273176 & 2.98 & 0.001748 \tabularnewline
14 & -0.077126 & -0.8413 & 0.200922 \tabularnewline
15 & -0.145584 & -1.5881 & 0.057455 \tabularnewline
16 & -0.20418 & -2.2273 & 0.013903 \tabularnewline
17 & -0.120085 & -1.31 & 0.096365 \tabularnewline
18 & -0.034696 & -0.3785 & 0.352869 \tabularnewline
19 & -0.032425 & -0.3537 & 0.362088 \tabularnewline
20 & -0.087098 & -0.9501 & 0.171986 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293923&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]0.216148[/C][C]2.3579[/C][C]0.010005[/C][/ROW]
[ROW][C]2[/C][C]0.071792[/C][C]0.7832[/C][C]0.217545[/C][/ROW]
[ROW][C]3[/C][C]-0.170872[/C][C]-1.864[/C][C]0.032394[/C][/ROW]
[ROW][C]4[/C][C]-0.101322[/C][C]-1.1053[/C][C]0.135631[/C][/ROW]
[ROW][C]5[/C][C]-0.00388[/C][C]-0.0423[/C][C]0.483156[/C][/ROW]
[ROW][C]6[/C][C]0.028083[/C][C]0.3064[/C][C]0.379935[/C][/ROW]
[ROW][C]7[/C][C]-0.004599[/C][C]-0.0502[/C][C]0.480035[/C][/ROW]
[ROW][C]8[/C][C]-0.138259[/C][C]-1.5082[/C][C]0.067074[/C][/ROW]
[ROW][C]9[/C][C]-0.17469[/C][C]-1.9056[/C][C]0.029555[/C][/ROW]
[ROW][C]10[/C][C]-0.032569[/C][C]-0.3553[/C][C]0.361503[/C][/ROW]
[ROW][C]11[/C][C]0.174849[/C][C]1.9074[/C][C]0.029441[/C][/ROW]
[ROW][C]12[/C][C]0.343116[/C][C]3.743[/C][C]0.000141[/C][/ROW]
[ROW][C]13[/C][C]0.273176[/C][C]2.98[/C][C]0.001748[/C][/ROW]
[ROW][C]14[/C][C]-0.077126[/C][C]-0.8413[/C][C]0.200922[/C][/ROW]
[ROW][C]15[/C][C]-0.145584[/C][C]-1.5881[/C][C]0.057455[/C][/ROW]
[ROW][C]16[/C][C]-0.20418[/C][C]-2.2273[/C][C]0.013903[/C][/ROW]
[ROW][C]17[/C][C]-0.120085[/C][C]-1.31[/C][C]0.096365[/C][/ROW]
[ROW][C]18[/C][C]-0.034696[/C][C]-0.3785[/C][C]0.352869[/C][/ROW]
[ROW][C]19[/C][C]-0.032425[/C][C]-0.3537[/C][C]0.362088[/C][/ROW]
[ROW][C]20[/C][C]-0.087098[/C][C]-0.9501[/C][C]0.171986[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293923&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293923&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	0.216148	2.3579	0.010005
2	0.071792	0.7832	0.217545
3	-0.170872	-1.864	0.032394
4	-0.101322	-1.1053	0.135631
5	-0.00388	-0.0423	0.483156
6	0.028083	0.3064	0.379935
7	-0.004599	-0.0502	0.480035
8	-0.138259	-1.5082	0.067074
9	-0.17469	-1.9056	0.029555
10	-0.032569	-0.3553	0.361503
11	0.174849	1.9074	0.029441
12	0.343116	3.743	0.000141
13	0.273176	2.98	0.001748
14	-0.077126	-0.8413	0.200922
15	-0.145584	-1.5881	0.057455
16	-0.20418	-2.2273	0.013903
17	-0.120085	-1.31	0.096365
18	-0.034696	-0.3785	0.352869
19	-0.032425	-0.3537	0.362088
20	-0.087098	-0.9501	0.171986

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.216148	2.3579	0.010005
2	0.026301	0.2869	0.387342
3	-0.201199	-2.1948	0.015059
4	-0.02833	-0.309	0.378915
5	0.054301	0.5924	0.277369
6	-0.006308	-0.0688	0.472628
7	-0.043765	-0.4774	0.316969
8	-0.138541	-1.5113	0.066681
9	-0.116699	-1.273	0.102743
10	0.050439	0.5502	0.291597
11	0.168205	1.8349	0.034509
12	0.242704	2.6476	0.004603
13	0.155214	1.6932	0.046518
14	-0.17414	-1.8996	0.02995
15	-0.069093	-0.7537	0.226254
16	-0.10438	-1.1387	0.128567
17	-0.140207	-1.5295	0.064401
18	-0.045823	-0.4999	0.309044
19	-0.006858	-0.0748	0.470246
20	-0.002197	-0.024	0.490459

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.216148 & 2.3579 & 0.010005 \tabularnewline
2 & 0.026301 & 0.2869 & 0.387342 \tabularnewline
3 & -0.201199 & -2.1948 & 0.015059 \tabularnewline
4 & -0.02833 & -0.309 & 0.378915 \tabularnewline
5 & 0.054301 & 0.5924 & 0.277369 \tabularnewline
6 & -0.006308 & -0.0688 & 0.472628 \tabularnewline
7 & -0.043765 & -0.4774 & 0.316969 \tabularnewline
8 & -0.138541 & -1.5113 & 0.066681 \tabularnewline
9 & -0.116699 & -1.273 & 0.102743 \tabularnewline
10 & 0.050439 & 0.5502 & 0.291597 \tabularnewline
11 & 0.168205 & 1.8349 & 0.034509 \tabularnewline
12 & 0.242704 & 2.6476 & 0.004603 \tabularnewline
13 & 0.155214 & 1.6932 & 0.046518 \tabularnewline
14 & -0.17414 & -1.8996 & 0.02995 \tabularnewline
15 & -0.069093 & -0.7537 & 0.226254 \tabularnewline
16 & -0.10438 & -1.1387 & 0.128567 \tabularnewline
17 & -0.140207 & -1.5295 & 0.064401 \tabularnewline
18 & -0.045823 & -0.4999 & 0.309044 \tabularnewline
19 & -0.006858 & -0.0748 & 0.470246 \tabularnewline
20 & -0.002197 & -0.024 & 0.490459 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293923&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]0.216148[/C][C]2.3579[/C][C]0.010005[/C][/ROW]
[ROW][C]2[/C][C]0.026301[/C][C]0.2869[/C][C]0.387342[/C][/ROW]
[ROW][C]3[/C][C]-0.201199[/C][C]-2.1948[/C][C]0.015059[/C][/ROW]
[ROW][C]4[/C][C]-0.02833[/C][C]-0.309[/C][C]0.378915[/C][/ROW]
[ROW][C]5[/C][C]0.054301[/C][C]0.5924[/C][C]0.277369[/C][/ROW]
[ROW][C]6[/C][C]-0.006308[/C][C]-0.0688[/C][C]0.472628[/C][/ROW]
[ROW][C]7[/C][C]-0.043765[/C][C]-0.4774[/C][C]0.316969[/C][/ROW]
[ROW][C]8[/C][C]-0.138541[/C][C]-1.5113[/C][C]0.066681[/C][/ROW]
[ROW][C]9[/C][C]-0.116699[/C][C]-1.273[/C][C]0.102743[/C][/ROW]
[ROW][C]10[/C][C]0.050439[/C][C]0.5502[/C][C]0.291597[/C][/ROW]
[ROW][C]11[/C][C]0.168205[/C][C]1.8349[/C][C]0.034509[/C][/ROW]
[ROW][C]12[/C][C]0.242704[/C][C]2.6476[/C][C]0.004603[/C][/ROW]
[ROW][C]13[/C][C]0.155214[/C][C]1.6932[/C][C]0.046518[/C][/ROW]
[ROW][C]14[/C][C]-0.17414[/C][C]-1.8996[/C][C]0.02995[/C][/ROW]
[ROW][C]15[/C][C]-0.069093[/C][C]-0.7537[/C][C]0.226254[/C][/ROW]
[ROW][C]16[/C][C]-0.10438[/C][C]-1.1387[/C][C]0.128567[/C][/ROW]
[ROW][C]17[/C][C]-0.140207[/C][C]-1.5295[/C][C]0.064401[/C][/ROW]
[ROW][C]18[/C][C]-0.045823[/C][C]-0.4999[/C][C]0.309044[/C][/ROW]
[ROW][C]19[/C][C]-0.006858[/C][C]-0.0748[/C][C]0.470246[/C][/ROW]
[ROW][C]20[/C][C]-0.002197[/C][C]-0.024[/C][C]0.490459[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293923&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293923&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	0.216148	2.3579	0.010005
2	0.026301	0.2869	0.387342
3	-0.201199	-2.1948	0.015059
4	-0.02833	-0.309	0.378915
5	0.054301	0.5924	0.277369
6	-0.006308	-0.0688	0.472628
7	-0.043765	-0.4774	0.316969
8	-0.138541	-1.5113	0.066681
9	-0.116699	-1.273	0.102743
10	0.050439	0.5502	0.291597
11	0.168205	1.8349	0.034509
12	0.242704	2.6476	0.004603
13	0.155214	1.6932	0.046518
14	-0.17414	-1.8996	0.02995
15	-0.069093	-0.7537	0.226254
16	-0.10438	-1.1387	0.128567
17	-0.140207	-1.5295	0.064401
18	-0.045823	-0.4999	0.309044
19	-0.006858	-0.0748	0.470246
20	-0.002197	-0.024	0.490459

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):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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,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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code