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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 13 Aug 2014 15:56:04 +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/2014/Aug/13/t14079417862cvledw1tqk3a6d.htm/, Retrieved Thu, 16 May 2024 04:52:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235529, Retrieved Thu, 16 May 2024 04:52:14 +0000

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-       [(Partial) Autocorrelation Function] [] [2014-08-13 14:56:04] [b3e3d38149b35cb70244b37a39776b3a] [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 Maurice George Kendall' @ kendall.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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235529&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235529&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235529&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 Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.149707	-1.5558	0.061341
2	0.11797	1.226	0.111437
3	-0.019229	-0.1998	0.420992
4	-0.121648	-1.2642	0.104439
5	0.163684	1.7011	0.045905
6	-0.34097	-3.5435	0.000292
7	0.174541	1.8139	0.036236
8	-0.141041	-1.4657	0.072812
9	-0.004108	-0.0427	0.483015
10	0.137236	1.4262	0.078348
11	-0.087482	-0.9091	0.18265
12	0.444665	4.6211	5e-06
13	-0.158056	-1.6426	0.051691
14	0.120018	1.2473	0.107499
15	-0.010195	-0.1059	0.457911
16	-0.139715	-1.452	0.074706
17	0.175755	1.8265	0.035268
18	-0.346346	-3.5993	0.000242
19	0.160987	1.673	0.048608
20	-0.114112	-1.1859	0.119134

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.149707 & -1.5558 & 0.061341 \tabularnewline
2 & 0.11797 & 1.226 & 0.111437 \tabularnewline
3 & -0.019229 & -0.1998 & 0.420992 \tabularnewline
4 & -0.121648 & -1.2642 & 0.104439 \tabularnewline
5 & 0.163684 & 1.7011 & 0.045905 \tabularnewline
6 & -0.34097 & -3.5435 & 0.000292 \tabularnewline
7 & 0.174541 & 1.8139 & 0.036236 \tabularnewline
8 & -0.141041 & -1.4657 & 0.072812 \tabularnewline
9 & -0.004108 & -0.0427 & 0.483015 \tabularnewline
10 & 0.137236 & 1.4262 & 0.078348 \tabularnewline
11 & -0.087482 & -0.9091 & 0.18265 \tabularnewline
12 & 0.444665 & 4.6211 & 5e-06 \tabularnewline
13 & -0.158056 & -1.6426 & 0.051691 \tabularnewline
14 & 0.120018 & 1.2473 & 0.107499 \tabularnewline
15 & -0.010195 & -0.1059 & 0.457911 \tabularnewline
16 & -0.139715 & -1.452 & 0.074706 \tabularnewline
17 & 0.175755 & 1.8265 & 0.035268 \tabularnewline
18 & -0.346346 & -3.5993 & 0.000242 \tabularnewline
19 & 0.160987 & 1.673 & 0.048608 \tabularnewline
20 & -0.114112 & -1.1859 & 0.119134 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235529&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]-0.149707[/C][C]-1.5558[/C][C]0.061341[/C][/ROW]
[ROW][C]2[/C][C]0.11797[/C][C]1.226[/C][C]0.111437[/C][/ROW]
[ROW][C]3[/C][C]-0.019229[/C][C]-0.1998[/C][C]0.420992[/C][/ROW]
[ROW][C]4[/C][C]-0.121648[/C][C]-1.2642[/C][C]0.104439[/C][/ROW]
[ROW][C]5[/C][C]0.163684[/C][C]1.7011[/C][C]0.045905[/C][/ROW]
[ROW][C]6[/C][C]-0.34097[/C][C]-3.5435[/C][C]0.000292[/C][/ROW]
[ROW][C]7[/C][C]0.174541[/C][C]1.8139[/C][C]0.036236[/C][/ROW]
[ROW][C]8[/C][C]-0.141041[/C][C]-1.4657[/C][C]0.072812[/C][/ROW]
[ROW][C]9[/C][C]-0.004108[/C][C]-0.0427[/C][C]0.483015[/C][/ROW]
[ROW][C]10[/C][C]0.137236[/C][C]1.4262[/C][C]0.078348[/C][/ROW]
[ROW][C]11[/C][C]-0.087482[/C][C]-0.9091[/C][C]0.18265[/C][/ROW]
[ROW][C]12[/C][C]0.444665[/C][C]4.6211[/C][C]5e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.158056[/C][C]-1.6426[/C][C]0.051691[/C][/ROW]
[ROW][C]14[/C][C]0.120018[/C][C]1.2473[/C][C]0.107499[/C][/ROW]
[ROW][C]15[/C][C]-0.010195[/C][C]-0.1059[/C][C]0.457911[/C][/ROW]
[ROW][C]16[/C][C]-0.139715[/C][C]-1.452[/C][C]0.074706[/C][/ROW]
[ROW][C]17[/C][C]0.175755[/C][C]1.8265[/C][C]0.035268[/C][/ROW]
[ROW][C]18[/C][C]-0.346346[/C][C]-3.5993[/C][C]0.000242[/C][/ROW]
[ROW][C]19[/C][C]0.160987[/C][C]1.673[/C][C]0.048608[/C][/ROW]
[ROW][C]20[/C][C]-0.114112[/C][C]-1.1859[/C][C]0.119134[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235529&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235529&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	-0.149707	-1.5558	0.061341
2	0.11797	1.226	0.111437
3	-0.019229	-0.1998	0.420992
4	-0.121648	-1.2642	0.104439
5	0.163684	1.7011	0.045905
6	-0.34097	-3.5435	0.000292
7	0.174541	1.8139	0.036236
8	-0.141041	-1.4657	0.072812
9	-0.004108	-0.0427	0.483015
10	0.137236	1.4262	0.078348
11	-0.087482	-0.9091	0.18265
12	0.444665	4.6211	5e-06
13	-0.158056	-1.6426	0.051691
14	0.120018	1.2473	0.107499
15	-0.010195	-0.1059	0.457911
16	-0.139715	-1.452	0.074706
17	0.175755	1.8265	0.035268
18	-0.346346	-3.5993	0.000242
19	0.160987	1.673	0.048608
20	-0.114112	-1.1859	0.119134

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.149707	-1.5558	0.061341
2	0.097748	1.0158	0.15599
3	0.01171	0.1217	0.451682
4	-0.138654	-1.4409	0.076249
5	0.136466	1.4182	0.079506
6	-0.294019	-3.0555	0.001415
7	0.087594	0.9103	0.182345
8	-0.078616	-0.817	0.207863
9	-0.028582	-0.297	0.383508
10	0.089841	0.9337	0.176283
11	0.028706	0.2983	0.383014
12	0.338754	3.5204	0.000316
13	-0.018656	-0.1939	0.423319
14	0.024555	0.2552	0.399532
15	0.014901	0.1549	0.43861
16	-0.063614	-0.6611	0.254979
17	0.076384	0.7938	0.214524
18	-0.139997	-1.4549	0.0743
19	0.012674	0.1317	0.44773
20	0.004297	0.0447	0.482232

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.149707 & -1.5558 & 0.061341 \tabularnewline
2 & 0.097748 & 1.0158 & 0.15599 \tabularnewline
3 & 0.01171 & 0.1217 & 0.451682 \tabularnewline
4 & -0.138654 & -1.4409 & 0.076249 \tabularnewline
5 & 0.136466 & 1.4182 & 0.079506 \tabularnewline
6 & -0.294019 & -3.0555 & 0.001415 \tabularnewline
7 & 0.087594 & 0.9103 & 0.182345 \tabularnewline
8 & -0.078616 & -0.817 & 0.207863 \tabularnewline
9 & -0.028582 & -0.297 & 0.383508 \tabularnewline
10 & 0.089841 & 0.9337 & 0.176283 \tabularnewline
11 & 0.028706 & 0.2983 & 0.383014 \tabularnewline
12 & 0.338754 & 3.5204 & 0.000316 \tabularnewline
13 & -0.018656 & -0.1939 & 0.423319 \tabularnewline
14 & 0.024555 & 0.2552 & 0.399532 \tabularnewline
15 & 0.014901 & 0.1549 & 0.43861 \tabularnewline
16 & -0.063614 & -0.6611 & 0.254979 \tabularnewline
17 & 0.076384 & 0.7938 & 0.214524 \tabularnewline
18 & -0.139997 & -1.4549 & 0.0743 \tabularnewline
19 & 0.012674 & 0.1317 & 0.44773 \tabularnewline
20 & 0.004297 & 0.0447 & 0.482232 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235529&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]-0.149707[/C][C]-1.5558[/C][C]0.061341[/C][/ROW]
[ROW][C]2[/C][C]0.097748[/C][C]1.0158[/C][C]0.15599[/C][/ROW]
[ROW][C]3[/C][C]0.01171[/C][C]0.1217[/C][C]0.451682[/C][/ROW]
[ROW][C]4[/C][C]-0.138654[/C][C]-1.4409[/C][C]0.076249[/C][/ROW]
[ROW][C]5[/C][C]0.136466[/C][C]1.4182[/C][C]0.079506[/C][/ROW]
[ROW][C]6[/C][C]-0.294019[/C][C]-3.0555[/C][C]0.001415[/C][/ROW]
[ROW][C]7[/C][C]0.087594[/C][C]0.9103[/C][C]0.182345[/C][/ROW]
[ROW][C]8[/C][C]-0.078616[/C][C]-0.817[/C][C]0.207863[/C][/ROW]
[ROW][C]9[/C][C]-0.028582[/C][C]-0.297[/C][C]0.383508[/C][/ROW]
[ROW][C]10[/C][C]0.089841[/C][C]0.9337[/C][C]0.176283[/C][/ROW]
[ROW][C]11[/C][C]0.028706[/C][C]0.2983[/C][C]0.383014[/C][/ROW]
[ROW][C]12[/C][C]0.338754[/C][C]3.5204[/C][C]0.000316[/C][/ROW]
[ROW][C]13[/C][C]-0.018656[/C][C]-0.1939[/C][C]0.423319[/C][/ROW]
[ROW][C]14[/C][C]0.024555[/C][C]0.2552[/C][C]0.399532[/C][/ROW]
[ROW][C]15[/C][C]0.014901[/C][C]0.1549[/C][C]0.43861[/C][/ROW]
[ROW][C]16[/C][C]-0.063614[/C][C]-0.6611[/C][C]0.254979[/C][/ROW]
[ROW][C]17[/C][C]0.076384[/C][C]0.7938[/C][C]0.214524[/C][/ROW]
[ROW][C]18[/C][C]-0.139997[/C][C]-1.4549[/C][C]0.0743[/C][/ROW]
[ROW][C]19[/C][C]0.012674[/C][C]0.1317[/C][C]0.44773[/C][/ROW]
[ROW][C]20[/C][C]0.004297[/C][C]0.0447[/C][C]0.482232[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235529&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235529&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	-0.149707	-1.5558	0.061341
2	0.097748	1.0158	0.15599
3	0.01171	0.1217	0.451682
4	-0.138654	-1.4409	0.076249
5	0.136466	1.4182	0.079506
6	-0.294019	-3.0555	0.001415
7	0.087594	0.9103	0.182345
8	-0.078616	-0.817	0.207863
9	-0.028582	-0.297	0.383508
10	0.089841	0.9337	0.176283
11	0.028706	0.2983	0.383014
12	0.338754	3.5204	0.000316
13	-0.018656	-0.1939	0.423319
14	0.024555	0.2552	0.399532
15	0.014901	0.1549	0.43861
16	-0.063614	-0.6611	0.254979
17	0.076384	0.7938	0.214524
18	-0.139997	-1.4549	0.0743
19	0.012674	0.1317	0.44773
20	0.004297	0.0447	0.482232

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 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = 48 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = 48 ;

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)
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