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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 15 Nov 2011 06:47:59 -0500

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/2011/Nov/15/t1321357832o36z8cyequxl5my.htm/, Retrieved Thu, 25 Apr 2024 02:27:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=142776, Retrieved Thu, 25 Apr 2024 02:27:37 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W11

Estimated Impact

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

-       [(Partial) Autocorrelation Function] [inschrijvingen ni...] [2011-11-15 11:47:59] [bd8cebb9d7961275d2f6ed94788b7e5f] [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	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142776&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142776&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142776&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.302855	3.6216	0.000203
2	-0.102148	-1.2215	0.111952
3	-0.241273	-2.8852	0.002259
4	-0.300402	-3.5923	0.000225
5	-0.094073	-1.1249	0.131248
6	-0.078443	-0.938	0.174904
7	-0.092362	-1.1045	0.135618
8	-0.294802	-3.5253	0.000284
9	-0.191778	-2.2933	0.011643
10	-0.104917	-1.2546	0.105831
11	0.282931	3.3834	0.000462
12	0.829178	9.9155	0
13	0.284501	3.4021	0.000434
14	-0.105752	-1.2646	0.104035
15	-0.222131	-2.6563	0.004399
16	-0.231076	-2.7633	0.003238
17	-0.062279	-0.7447	0.228823
18	-0.066185	-0.7915	0.214994
19	-0.0904	-1.081	0.140753
20	-0.29711	-3.5529	0.000258
21	-0.162732	-1.946	0.026808

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.302855 & 3.6216 & 0.000203 \tabularnewline
2 & -0.102148 & -1.2215 & 0.111952 \tabularnewline
3 & -0.241273 & -2.8852 & 0.002259 \tabularnewline
4 & -0.300402 & -3.5923 & 0.000225 \tabularnewline
5 & -0.094073 & -1.1249 & 0.131248 \tabularnewline
6 & -0.078443 & -0.938 & 0.174904 \tabularnewline
7 & -0.092362 & -1.1045 & 0.135618 \tabularnewline
8 & -0.294802 & -3.5253 & 0.000284 \tabularnewline
9 & -0.191778 & -2.2933 & 0.011643 \tabularnewline
10 & -0.104917 & -1.2546 & 0.105831 \tabularnewline
11 & 0.282931 & 3.3834 & 0.000462 \tabularnewline
12 & 0.829178 & 9.9155 & 0 \tabularnewline
13 & 0.284501 & 3.4021 & 0.000434 \tabularnewline
14 & -0.105752 & -1.2646 & 0.104035 \tabularnewline
15 & -0.222131 & -2.6563 & 0.004399 \tabularnewline
16 & -0.231076 & -2.7633 & 0.003238 \tabularnewline
17 & -0.062279 & -0.7447 & 0.228823 \tabularnewline
18 & -0.066185 & -0.7915 & 0.214994 \tabularnewline
19 & -0.0904 & -1.081 & 0.140753 \tabularnewline
20 & -0.29711 & -3.5529 & 0.000258 \tabularnewline
21 & -0.162732 & -1.946 & 0.026808 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142776&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]0.302855[/C][C]3.6216[/C][C]0.000203[/C][/ROW]
[ROW][C]2[/C][C]-0.102148[/C][C]-1.2215[/C][C]0.111952[/C][/ROW]
[ROW][C]3[/C][C]-0.241273[/C][C]-2.8852[/C][C]0.002259[/C][/ROW]
[ROW][C]4[/C][C]-0.300402[/C][C]-3.5923[/C][C]0.000225[/C][/ROW]
[ROW][C]5[/C][C]-0.094073[/C][C]-1.1249[/C][C]0.131248[/C][/ROW]
[ROW][C]6[/C][C]-0.078443[/C][C]-0.938[/C][C]0.174904[/C][/ROW]
[ROW][C]7[/C][C]-0.092362[/C][C]-1.1045[/C][C]0.135618[/C][/ROW]
[ROW][C]8[/C][C]-0.294802[/C][C]-3.5253[/C][C]0.000284[/C][/ROW]
[ROW][C]9[/C][C]-0.191778[/C][C]-2.2933[/C][C]0.011643[/C][/ROW]
[ROW][C]10[/C][C]-0.104917[/C][C]-1.2546[/C][C]0.105831[/C][/ROW]
[ROW][C]11[/C][C]0.282931[/C][C]3.3834[/C][C]0.000462[/C][/ROW]
[ROW][C]12[/C][C]0.829178[/C][C]9.9155[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.284501[/C][C]3.4021[/C][C]0.000434[/C][/ROW]
[ROW][C]14[/C][C]-0.105752[/C][C]-1.2646[/C][C]0.104035[/C][/ROW]
[ROW][C]15[/C][C]-0.222131[/C][C]-2.6563[/C][C]0.004399[/C][/ROW]
[ROW][C]16[/C][C]-0.231076[/C][C]-2.7633[/C][C]0.003238[/C][/ROW]
[ROW][C]17[/C][C]-0.062279[/C][C]-0.7447[/C][C]0.228823[/C][/ROW]
[ROW][C]18[/C][C]-0.066185[/C][C]-0.7915[/C][C]0.214994[/C][/ROW]
[ROW][C]19[/C][C]-0.0904[/C][C]-1.081[/C][C]0.140753[/C][/ROW]
[ROW][C]20[/C][C]-0.29711[/C][C]-3.5529[/C][C]0.000258[/C][/ROW]
[ROW][C]21[/C][C]-0.162732[/C][C]-1.946[/C][C]0.026808[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142776&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142776&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	0.302855	3.6216	0.000203
2	-0.102148	-1.2215	0.111952
3	-0.241273	-2.8852	0.002259
4	-0.300402	-3.5923	0.000225
5	-0.094073	-1.1249	0.131248
6	-0.078443	-0.938	0.174904
7	-0.092362	-1.1045	0.135618
8	-0.294802	-3.5253	0.000284
9	-0.191778	-2.2933	0.011643
10	-0.104917	-1.2546	0.105831
11	0.282931	3.3834	0.000462
12	0.829178	9.9155	0
13	0.284501	3.4021	0.000434
14	-0.105752	-1.2646	0.104035
15	-0.222131	-2.6563	0.004399
16	-0.231076	-2.7633	0.003238
17	-0.062279	-0.7447	0.228823
18	-0.066185	-0.7915	0.214994
19	-0.0904	-1.081	0.140753
20	-0.29711	-3.5529	0.000258
21	-0.162732	-1.946	0.026808

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.302855	3.6216	0.000203
2	-0.213446	-2.5524	0.005873
3	-0.160447	-1.9187	0.02851
4	-0.22163	-2.6503	0.004474
5	0.010084	0.1206	0.452095
6	-0.190643	-2.2798	0.012051
7	-0.153657	-1.8375	0.034108
8	-0.454732	-5.4378	0
9	-0.233751	-2.7953	0.002949
10	-0.547297	-6.5447	0
11	-0.130043	-1.5551	0.061067
12	0.571287	6.8316	0
13	-0.149281	-1.7851	0.038179
14	-0.171815	-2.0546	0.020869
15	0.067207	0.8037	0.211457
16	0.062464	0.747	0.228158
17	0.007638	0.0913	0.463678
18	-0.079945	-0.956	0.170343
19	0.037143	0.4442	0.328795
20	-0.094677	-1.1322	0.129729
21	-0.004683	-0.056	0.477707

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.302855 & 3.6216 & 0.000203 \tabularnewline
2 & -0.213446 & -2.5524 & 0.005873 \tabularnewline
3 & -0.160447 & -1.9187 & 0.02851 \tabularnewline
4 & -0.22163 & -2.6503 & 0.004474 \tabularnewline
5 & 0.010084 & 0.1206 & 0.452095 \tabularnewline
6 & -0.190643 & -2.2798 & 0.012051 \tabularnewline
7 & -0.153657 & -1.8375 & 0.034108 \tabularnewline
8 & -0.454732 & -5.4378 & 0 \tabularnewline
9 & -0.233751 & -2.7953 & 0.002949 \tabularnewline
10 & -0.547297 & -6.5447 & 0 \tabularnewline
11 & -0.130043 & -1.5551 & 0.061067 \tabularnewline
12 & 0.571287 & 6.8316 & 0 \tabularnewline
13 & -0.149281 & -1.7851 & 0.038179 \tabularnewline
14 & -0.171815 & -2.0546 & 0.020869 \tabularnewline
15 & 0.067207 & 0.8037 & 0.211457 \tabularnewline
16 & 0.062464 & 0.747 & 0.228158 \tabularnewline
17 & 0.007638 & 0.0913 & 0.463678 \tabularnewline
18 & -0.079945 & -0.956 & 0.170343 \tabularnewline
19 & 0.037143 & 0.4442 & 0.328795 \tabularnewline
20 & -0.094677 & -1.1322 & 0.129729 \tabularnewline
21 & -0.004683 & -0.056 & 0.477707 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142776&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]0.302855[/C][C]3.6216[/C][C]0.000203[/C][/ROW]
[ROW][C]2[/C][C]-0.213446[/C][C]-2.5524[/C][C]0.005873[/C][/ROW]
[ROW][C]3[/C][C]-0.160447[/C][C]-1.9187[/C][C]0.02851[/C][/ROW]
[ROW][C]4[/C][C]-0.22163[/C][C]-2.6503[/C][C]0.004474[/C][/ROW]
[ROW][C]5[/C][C]0.010084[/C][C]0.1206[/C][C]0.452095[/C][/ROW]
[ROW][C]6[/C][C]-0.190643[/C][C]-2.2798[/C][C]0.012051[/C][/ROW]
[ROW][C]7[/C][C]-0.153657[/C][C]-1.8375[/C][C]0.034108[/C][/ROW]
[ROW][C]8[/C][C]-0.454732[/C][C]-5.4378[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]-0.233751[/C][C]-2.7953[/C][C]0.002949[/C][/ROW]
[ROW][C]10[/C][C]-0.547297[/C][C]-6.5447[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]-0.130043[/C][C]-1.5551[/C][C]0.061067[/C][/ROW]
[ROW][C]12[/C][C]0.571287[/C][C]6.8316[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.149281[/C][C]-1.7851[/C][C]0.038179[/C][/ROW]
[ROW][C]14[/C][C]-0.171815[/C][C]-2.0546[/C][C]0.020869[/C][/ROW]
[ROW][C]15[/C][C]0.067207[/C][C]0.8037[/C][C]0.211457[/C][/ROW]
[ROW][C]16[/C][C]0.062464[/C][C]0.747[/C][C]0.228158[/C][/ROW]
[ROW][C]17[/C][C]0.007638[/C][C]0.0913[/C][C]0.463678[/C][/ROW]
[ROW][C]18[/C][C]-0.079945[/C][C]-0.956[/C][C]0.170343[/C][/ROW]
[ROW][C]19[/C][C]0.037143[/C][C]0.4442[/C][C]0.328795[/C][/ROW]
[ROW][C]20[/C][C]-0.094677[/C][C]-1.1322[/C][C]0.129729[/C][/ROW]
[ROW][C]21[/C][C]-0.004683[/C][C]-0.056[/C][C]0.477707[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142776&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142776&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	0.302855	3.6216	0.000203
2	-0.213446	-2.5524	0.005873
3	-0.160447	-1.9187	0.02851
4	-0.22163	-2.6503	0.004474
5	0.010084	0.1206	0.452095
6	-0.190643	-2.2798	0.012051
7	-0.153657	-1.8375	0.034108
8	-0.454732	-5.4378	0
9	-0.233751	-2.7953	0.002949
10	-0.547297	-6.5447	0
11	-0.130043	-1.5551	0.061067
12	0.571287	6.8316	0
13	-0.149281	-1.7851	0.038179
14	-0.171815	-2.0546	0.020869
15	0.067207	0.8037	0.211457
16	0.062464	0.747	0.228158
17	0.007638	0.0913	0.463678
18	-0.079945	-0.956	0.170343
19	0.037143	0.4442	0.328795
20	-0.094677	-1.1322	0.129729
21	-0.004683	-0.056	0.477707

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)
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