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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 08 Dec 2008 14:58:33 -0700

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/2008/Dec/08/t1228773630ayfrg2x2l2achjs.htm/, Retrieved Thu, 16 May 2024 12:10:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31093, Retrieved Thu, 16 May 2024 12:10:24 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

168

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

F     [Law of Averages] [Random Walk Simul...] [2008-11-25 17:50:19] [b98453cac15ba1066b407e146608df68]
F       [Law of Averages] [Non Stationary Ti...] [2008-11-30 21:33:42] [82d201ca7b4e7cd2c6f885d29b5b6937]
F RMPD    [(Partial) Autocorrelation Function] [(P) ACF] [2008-12-08 21:03:21] [82d201ca7b4e7cd2c6f885d29b5b6937]
F   P         [(Partial) Autocorrelation Function] [acf] [2008-12-08 21:58:33] [00a0a665d7a07edd2e460056b0c0c354] [Current]

Feedback Forum

2008-12-15 21:55:06 [Inge Meelberghs] [reply] 
Dit zijn de gegevens die ik moet invullen: 
Lags = 60 
d = 0 
D = 0 
Λ = 1 
Seasonal period = 12 
 
Zoals vermeld had ik de lags dus beter op 60 gezet doordat je dan een beter beeld krijgt van de LT-trend en het seizonaliteitspatroon. Uit de ACF kunnen we duidelijk een LT-trend en seizonaliteit waarnemen. Deze gaan we proberen uit te zuiveren door d = 0 en D = 1 in te vullen. We moeten dus 1 keer seizonaal differentiëren om de reeks stationair te maken. Dit doen we in stap 3. 
2008-12-15 22:39:27 [Inge Meelberghs] [reply] 
Op mijn voorgaande uitleg moet ik even terugkomen door een gemaakte typfout. Er is in dit geval in mijn tijdreeks namelijk geen sprake van een lange termijn trend. Dit zien we ook in de grafiek. Enkel seizonaliteit is hier te bespeuren. Hierdoor moeten we ook enkel 1 keer seizonaal differentiëren en is d = 0.

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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' @ 193.190.124.10:1001

\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' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31093&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' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31093&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31093&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' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.576789	4.5049	1.5e-05
2	0.452923	3.5374	0.000389
3	0.543069	4.2415	3.8e-05
4	0.504518	3.9404	0.000106
5	0.424712	3.3171	0.000768
6	0.449427	3.5101	0.000424
7	0.29371	2.2939	0.012626
8	0.379082	2.9607	0.002184
9	0.314034	2.4527	0.008527
10	0.165544	1.2929	0.100454
11	0.243936	1.9052	0.030735
12	0.445199	3.4771	0.00047
13	0.193111	1.5082	0.068327
14	0.103016	0.8046	0.212094
15	0.1347	1.052	0.148466
16	0.164569	1.2853	0.101768
17	0.113004	0.8826	0.190462

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.576789 & 4.5049 & 1.5e-05 \tabularnewline
2 & 0.452923 & 3.5374 & 0.000389 \tabularnewline
3 & 0.543069 & 4.2415 & 3.8e-05 \tabularnewline
4 & 0.504518 & 3.9404 & 0.000106 \tabularnewline
5 & 0.424712 & 3.3171 & 0.000768 \tabularnewline
6 & 0.449427 & 3.5101 & 0.000424 \tabularnewline
7 & 0.29371 & 2.2939 & 0.012626 \tabularnewline
8 & 0.379082 & 2.9607 & 0.002184 \tabularnewline
9 & 0.314034 & 2.4527 & 0.008527 \tabularnewline
10 & 0.165544 & 1.2929 & 0.100454 \tabularnewline
11 & 0.243936 & 1.9052 & 0.030735 \tabularnewline
12 & 0.445199 & 3.4771 & 0.00047 \tabularnewline
13 & 0.193111 & 1.5082 & 0.068327 \tabularnewline
14 & 0.103016 & 0.8046 & 0.212094 \tabularnewline
15 & 0.1347 & 1.052 & 0.148466 \tabularnewline
16 & 0.164569 & 1.2853 & 0.101768 \tabularnewline
17 & 0.113004 & 0.8826 & 0.190462 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31093&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]0.576789[/C][C]4.5049[/C][C]1.5e-05[/C][/ROW]
[ROW][C]2[/C][C]0.452923[/C][C]3.5374[/C][C]0.000389[/C][/ROW]
[ROW][C]3[/C][C]0.543069[/C][C]4.2415[/C][C]3.8e-05[/C][/ROW]
[ROW][C]4[/C][C]0.504518[/C][C]3.9404[/C][C]0.000106[/C][/ROW]
[ROW][C]5[/C][C]0.424712[/C][C]3.3171[/C][C]0.000768[/C][/ROW]
[ROW][C]6[/C][C]0.449427[/C][C]3.5101[/C][C]0.000424[/C][/ROW]
[ROW][C]7[/C][C]0.29371[/C][C]2.2939[/C][C]0.012626[/C][/ROW]
[ROW][C]8[/C][C]0.379082[/C][C]2.9607[/C][C]0.002184[/C][/ROW]
[ROW][C]9[/C][C]0.314034[/C][C]2.4527[/C][C]0.008527[/C][/ROW]
[ROW][C]10[/C][C]0.165544[/C][C]1.2929[/C][C]0.100454[/C][/ROW]
[ROW][C]11[/C][C]0.243936[/C][C]1.9052[/C][C]0.030735[/C][/ROW]
[ROW][C]12[/C][C]0.445199[/C][C]3.4771[/C][C]0.00047[/C][/ROW]
[ROW][C]13[/C][C]0.193111[/C][C]1.5082[/C][C]0.068327[/C][/ROW]
[ROW][C]14[/C][C]0.103016[/C][C]0.8046[/C][C]0.212094[/C][/ROW]
[ROW][C]15[/C][C]0.1347[/C][C]1.052[/C][C]0.148466[/C][/ROW]
[ROW][C]16[/C][C]0.164569[/C][C]1.2853[/C][C]0.101768[/C][/ROW]
[ROW][C]17[/C][C]0.113004[/C][C]0.8826[/C][C]0.190462[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31093&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31093&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	0.576789	4.5049	1.5e-05
2	0.452923	3.5374	0.000389
3	0.543069	4.2415	3.8e-05
4	0.504518	3.9404	0.000106
5	0.424712	3.3171	0.000768
6	0.449427	3.5101	0.000424
7	0.29371	2.2939	0.012626
8	0.379082	2.9607	0.002184
9	0.314034	2.4527	0.008527
10	0.165544	1.2929	0.100454
11	0.243936	1.9052	0.030735
12	0.445199	3.4771	0.00047
13	0.193111	1.5082	0.068327
14	0.103016	0.8046	0.212094
15	0.1347	1.052	0.148466
16	0.164569	1.2853	0.101768
17	0.113004	0.8826	0.190462

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.576789	4.5049	1.5e-05
2	0.180181	1.4073	0.082213
3	0.348443	2.7214	0.00423
4	0.130198	1.0169	0.156614
5	0.044282	0.3459	0.365321
6	0.107264	0.8378	0.202719
7	-0.217128	-1.6958	0.047509
8	0.199537	1.5584	0.062152
9	-0.149358	-1.1665	0.123972
10	-0.128289	-1.002	0.160158
11	0.128295	1.002	0.160147
12	0.350836	2.7401	0.004022
13	-0.220308	-1.7207	0.045191
14	-0.185603	-1.4496	0.076145
15	-0.081376	-0.6356	0.263719
16	0.072958	0.5698	0.285447
17	-0.058324	-0.4555	0.325176

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.576789 & 4.5049 & 1.5e-05 \tabularnewline
2 & 0.180181 & 1.4073 & 0.082213 \tabularnewline
3 & 0.348443 & 2.7214 & 0.00423 \tabularnewline
4 & 0.130198 & 1.0169 & 0.156614 \tabularnewline
5 & 0.044282 & 0.3459 & 0.365321 \tabularnewline
6 & 0.107264 & 0.8378 & 0.202719 \tabularnewline
7 & -0.217128 & -1.6958 & 0.047509 \tabularnewline
8 & 0.199537 & 1.5584 & 0.062152 \tabularnewline
9 & -0.149358 & -1.1665 & 0.123972 \tabularnewline
10 & -0.128289 & -1.002 & 0.160158 \tabularnewline
11 & 0.128295 & 1.002 & 0.160147 \tabularnewline
12 & 0.350836 & 2.7401 & 0.004022 \tabularnewline
13 & -0.220308 & -1.7207 & 0.045191 \tabularnewline
14 & -0.185603 & -1.4496 & 0.076145 \tabularnewline
15 & -0.081376 & -0.6356 & 0.263719 \tabularnewline
16 & 0.072958 & 0.5698 & 0.285447 \tabularnewline
17 & -0.058324 & -0.4555 & 0.325176 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31093&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]0.576789[/C][C]4.5049[/C][C]1.5e-05[/C][/ROW]
[ROW][C]2[/C][C]0.180181[/C][C]1.4073[/C][C]0.082213[/C][/ROW]
[ROW][C]3[/C][C]0.348443[/C][C]2.7214[/C][C]0.00423[/C][/ROW]
[ROW][C]4[/C][C]0.130198[/C][C]1.0169[/C][C]0.156614[/C][/ROW]
[ROW][C]5[/C][C]0.044282[/C][C]0.3459[/C][C]0.365321[/C][/ROW]
[ROW][C]6[/C][C]0.107264[/C][C]0.8378[/C][C]0.202719[/C][/ROW]
[ROW][C]7[/C][C]-0.217128[/C][C]-1.6958[/C][C]0.047509[/C][/ROW]
[ROW][C]8[/C][C]0.199537[/C][C]1.5584[/C][C]0.062152[/C][/ROW]
[ROW][C]9[/C][C]-0.149358[/C][C]-1.1665[/C][C]0.123972[/C][/ROW]
[ROW][C]10[/C][C]-0.128289[/C][C]-1.002[/C][C]0.160158[/C][/ROW]
[ROW][C]11[/C][C]0.128295[/C][C]1.002[/C][C]0.160147[/C][/ROW]
[ROW][C]12[/C][C]0.350836[/C][C]2.7401[/C][C]0.004022[/C][/ROW]
[ROW][C]13[/C][C]-0.220308[/C][C]-1.7207[/C][C]0.045191[/C][/ROW]
[ROW][C]14[/C][C]-0.185603[/C][C]-1.4496[/C][C]0.076145[/C][/ROW]
[ROW][C]15[/C][C]-0.081376[/C][C]-0.6356[/C][C]0.263719[/C][/ROW]
[ROW][C]16[/C][C]0.072958[/C][C]0.5698[/C][C]0.285447[/C][/ROW]
[ROW][C]17[/C][C]-0.058324[/C][C]-0.4555[/C][C]0.325176[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31093&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31093&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	0.576789	4.5049	1.5e-05
2	0.180181	1.4073	0.082213
3	0.348443	2.7214	0.00423
4	0.130198	1.0169	0.156614
5	0.044282	0.3459	0.365321
6	0.107264	0.8378	0.202719
7	-0.217128	-1.6958	0.047509
8	0.199537	1.5584	0.062152
9	-0.149358	-1.1665	0.123972
10	-0.128289	-1.002	0.160158
11	0.128295	1.002	0.160147
12	0.350836	2.7401	0.004022
13	-0.220308	-1.7207	0.045191
14	-0.185603	-1.4496	0.076145
15	-0.081376	-0.6356	0.263719
16	0.072958	0.5698	0.285447
17	-0.058324	-0.4555	0.325176

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x,par1,main='Autocorrelation',xlab='lags',ylab='ACF')
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code