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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 14 Dec 2016 17:41:08 +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/14/t148173384710u547tv7wzjfmo.htm/, Retrieved Fri, 01 Nov 2024 03:47:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299618, Retrieved Fri, 01 Nov 2024 03:47:41 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-12-14 16:41:08] [1a4fa2544711480e714211476e711237] [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=299618&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=299618&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299618&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	-0.53227	-5.5058	0
2	0.058745	0.6077	0.272351
3	0.034921	0.3612	0.359323
4	-0.047883	-0.4953	0.310701
5	0.086272	0.8924	0.18709
6	-0.230567	-2.385	0.009419
7	0.178628	1.8477	0.033701
8	-0.041365	-0.4279	0.334798
9	-0.14969	-1.5484	0.062239
10	0.247416	2.5593	0.005943
11	-0.188697	-1.9519	0.026782
12	0.224365	2.3208	0.011095
13	-0.208364	-2.1553	0.016689
14	0.122179	1.2638	0.104518
15	-0.008055	-0.0833	0.466874
16	-0.115984	-1.1997	0.116443
17	0.181998	1.8826	0.031235
18	-0.122369	-1.2658	0.104168
19	-0.025689	-0.2657	0.39548
20	0.071799	0.7427	0.229648

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.53227 & -5.5058 & 0 \tabularnewline
2 & 0.058745 & 0.6077 & 0.272351 \tabularnewline
3 & 0.034921 & 0.3612 & 0.359323 \tabularnewline
4 & -0.047883 & -0.4953 & 0.310701 \tabularnewline
5 & 0.086272 & 0.8924 & 0.18709 \tabularnewline
6 & -0.230567 & -2.385 & 0.009419 \tabularnewline
7 & 0.178628 & 1.8477 & 0.033701 \tabularnewline
8 & -0.041365 & -0.4279 & 0.334798 \tabularnewline
9 & -0.14969 & -1.5484 & 0.062239 \tabularnewline
10 & 0.247416 & 2.5593 & 0.005943 \tabularnewline
11 & -0.188697 & -1.9519 & 0.026782 \tabularnewline
12 & 0.224365 & 2.3208 & 0.011095 \tabularnewline
13 & -0.208364 & -2.1553 & 0.016689 \tabularnewline
14 & 0.122179 & 1.2638 & 0.104518 \tabularnewline
15 & -0.008055 & -0.0833 & 0.466874 \tabularnewline
16 & -0.115984 & -1.1997 & 0.116443 \tabularnewline
17 & 0.181998 & 1.8826 & 0.031235 \tabularnewline
18 & -0.122369 & -1.2658 & 0.104168 \tabularnewline
19 & -0.025689 & -0.2657 & 0.39548 \tabularnewline
20 & 0.071799 & 0.7427 & 0.229648 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299618&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]-0.53227[/C][C]-5.5058[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.058745[/C][C]0.6077[/C][C]0.272351[/C][/ROW]
[ROW][C]3[/C][C]0.034921[/C][C]0.3612[/C][C]0.359323[/C][/ROW]
[ROW][C]4[/C][C]-0.047883[/C][C]-0.4953[/C][C]0.310701[/C][/ROW]
[ROW][C]5[/C][C]0.086272[/C][C]0.8924[/C][C]0.18709[/C][/ROW]
[ROW][C]6[/C][C]-0.230567[/C][C]-2.385[/C][C]0.009419[/C][/ROW]
[ROW][C]7[/C][C]0.178628[/C][C]1.8477[/C][C]0.033701[/C][/ROW]
[ROW][C]8[/C][C]-0.041365[/C][C]-0.4279[/C][C]0.334798[/C][/ROW]
[ROW][C]9[/C][C]-0.14969[/C][C]-1.5484[/C][C]0.062239[/C][/ROW]
[ROW][C]10[/C][C]0.247416[/C][C]2.5593[/C][C]0.005943[/C][/ROW]
[ROW][C]11[/C][C]-0.188697[/C][C]-1.9519[/C][C]0.026782[/C][/ROW]
[ROW][C]12[/C][C]0.224365[/C][C]2.3208[/C][C]0.011095[/C][/ROW]
[ROW][C]13[/C][C]-0.208364[/C][C]-2.1553[/C][C]0.016689[/C][/ROW]
[ROW][C]14[/C][C]0.122179[/C][C]1.2638[/C][C]0.104518[/C][/ROW]
[ROW][C]15[/C][C]-0.008055[/C][C]-0.0833[/C][C]0.466874[/C][/ROW]
[ROW][C]16[/C][C]-0.115984[/C][C]-1.1997[/C][C]0.116443[/C][/ROW]
[ROW][C]17[/C][C]0.181998[/C][C]1.8826[/C][C]0.031235[/C][/ROW]
[ROW][C]18[/C][C]-0.122369[/C][C]-1.2658[/C][C]0.104168[/C][/ROW]
[ROW][C]19[/C][C]-0.025689[/C][C]-0.2657[/C][C]0.39548[/C][/ROW]
[ROW][C]20[/C][C]0.071799[/C][C]0.7427[/C][C]0.229648[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299618&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299618&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	-0.53227	-5.5058	0
2	0.058745	0.6077	0.272351
3	0.034921	0.3612	0.359323
4	-0.047883	-0.4953	0.310701
5	0.086272	0.8924	0.18709
6	-0.230567	-2.385	0.009419
7	0.178628	1.8477	0.033701
8	-0.041365	-0.4279	0.334798
9	-0.14969	-1.5484	0.062239
10	0.247416	2.5593	0.005943
11	-0.188697	-1.9519	0.026782
12	0.224365	2.3208	0.011095
13	-0.208364	-2.1553	0.016689
14	0.122179	1.2638	0.104518
15	-0.008055	-0.0833	0.466874
16	-0.115984	-1.1997	0.116443
17	0.181998	1.8826	0.031235
18	-0.122369	-1.2658	0.104168
19	-0.025689	-0.2657	0.39548
20	0.071799	0.7427	0.229648

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.53227	-5.5058	0
2	-0.31334	-3.2412	0.000793
3	-0.14048	-1.4531	0.074556
4	-0.114481	-1.1842	0.119478
5	0.029192	0.302	0.381633
6	-0.25393	-2.6267	0.004944
7	-0.143743	-1.4869	0.069993
8	-0.0867	-0.8968	0.185912
9	-0.298623	-3.089	0.00128
10	-0.045093	-0.4664	0.320923
11	-0.142246	-1.4714	0.072058
12	0.093564	0.9678	0.167655
13	-0.061866	-0.64	0.261786
14	0.010157	0.1051	0.458262
15	-0.036059	-0.373	0.354945
16	-0.074826	-0.774	0.220317
17	0.076127	0.7875	0.216376
18	0.107569	1.1127	0.134166
19	-0.023462	-0.2427	0.404356
20	0.022127	0.2289	0.409699

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.53227 & -5.5058 & 0 \tabularnewline
2 & -0.31334 & -3.2412 & 0.000793 \tabularnewline
3 & -0.14048 & -1.4531 & 0.074556 \tabularnewline
4 & -0.114481 & -1.1842 & 0.119478 \tabularnewline
5 & 0.029192 & 0.302 & 0.381633 \tabularnewline
6 & -0.25393 & -2.6267 & 0.004944 \tabularnewline
7 & -0.143743 & -1.4869 & 0.069993 \tabularnewline
8 & -0.0867 & -0.8968 & 0.185912 \tabularnewline
9 & -0.298623 & -3.089 & 0.00128 \tabularnewline
10 & -0.045093 & -0.4664 & 0.320923 \tabularnewline
11 & -0.142246 & -1.4714 & 0.072058 \tabularnewline
12 & 0.093564 & 0.9678 & 0.167655 \tabularnewline
13 & -0.061866 & -0.64 & 0.261786 \tabularnewline
14 & 0.010157 & 0.1051 & 0.458262 \tabularnewline
15 & -0.036059 & -0.373 & 0.354945 \tabularnewline
16 & -0.074826 & -0.774 & 0.220317 \tabularnewline
17 & 0.076127 & 0.7875 & 0.216376 \tabularnewline
18 & 0.107569 & 1.1127 & 0.134166 \tabularnewline
19 & -0.023462 & -0.2427 & 0.404356 \tabularnewline
20 & 0.022127 & 0.2289 & 0.409699 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299618&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]-0.53227[/C][C]-5.5058[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.31334[/C][C]-3.2412[/C][C]0.000793[/C][/ROW]
[ROW][C]3[/C][C]-0.14048[/C][C]-1.4531[/C][C]0.074556[/C][/ROW]
[ROW][C]4[/C][C]-0.114481[/C][C]-1.1842[/C][C]0.119478[/C][/ROW]
[ROW][C]5[/C][C]0.029192[/C][C]0.302[/C][C]0.381633[/C][/ROW]
[ROW][C]6[/C][C]-0.25393[/C][C]-2.6267[/C][C]0.004944[/C][/ROW]
[ROW][C]7[/C][C]-0.143743[/C][C]-1.4869[/C][C]0.069993[/C][/ROW]
[ROW][C]8[/C][C]-0.0867[/C][C]-0.8968[/C][C]0.185912[/C][/ROW]
[ROW][C]9[/C][C]-0.298623[/C][C]-3.089[/C][C]0.00128[/C][/ROW]
[ROW][C]10[/C][C]-0.045093[/C][C]-0.4664[/C][C]0.320923[/C][/ROW]
[ROW][C]11[/C][C]-0.142246[/C][C]-1.4714[/C][C]0.072058[/C][/ROW]
[ROW][C]12[/C][C]0.093564[/C][C]0.9678[/C][C]0.167655[/C][/ROW]
[ROW][C]13[/C][C]-0.061866[/C][C]-0.64[/C][C]0.261786[/C][/ROW]
[ROW][C]14[/C][C]0.010157[/C][C]0.1051[/C][C]0.458262[/C][/ROW]
[ROW][C]15[/C][C]-0.036059[/C][C]-0.373[/C][C]0.354945[/C][/ROW]
[ROW][C]16[/C][C]-0.074826[/C][C]-0.774[/C][C]0.220317[/C][/ROW]
[ROW][C]17[/C][C]0.076127[/C][C]0.7875[/C][C]0.216376[/C][/ROW]
[ROW][C]18[/C][C]0.107569[/C][C]1.1127[/C][C]0.134166[/C][/ROW]
[ROW][C]19[/C][C]-0.023462[/C][C]-0.2427[/C][C]0.404356[/C][/ROW]
[ROW][C]20[/C][C]0.022127[/C][C]0.2289[/C][C]0.409699[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299618&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299618&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	-0.53227	-5.5058	0
2	-0.31334	-3.2412	0.000793
3	-0.14048	-1.4531	0.074556
4	-0.114481	-1.1842	0.119478
5	0.029192	0.302	0.381633
6	-0.25393	-2.6267	0.004944
7	-0.143743	-1.4869	0.069993
8	-0.0867	-0.8968	0.185912
9	-0.298623	-3.089	0.00128
10	-0.045093	-0.4664	0.320923
11	-0.142246	-1.4714	0.072058
12	0.093564	0.9678	0.167655
13	-0.061866	-0.64	0.261786
14	0.010157	0.1051	0.458262
15	-0.036059	-0.373	0.354945
16	-0.074826	-0.774	0.220317
17	0.076127	0.7875	0.216376
18	0.107569	1.1127	0.134166
19	-0.023462	-0.2427	0.404356
20	0.022127	0.2289	0.409699

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 = 0 ; 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 <- '0'
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,'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