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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 15:50:25 -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/t122877667805wty80gsuba3py.htm/, Retrieved Thu, 16 May 2024 18:54:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31107, Retrieved Thu, 16 May 2024 18:54:39 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

182

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
F RMPD    [(Partial) Autocorrelation Function] [ACF] [2008-12-08 22:50:25] [d6e9f26c3644bfc30f06303d9993b878] [Current]
-   P       [(Partial) Autocorrelation Function] [feedback op blog] [2008-12-12 19:40:05] [b635de6fc42b001d22cbe6e730fec936] 
-   P       [(Partial) Autocorrelation Function] [verbetering] [2008-12-15 22:13:02] [8d78428855b119373cac369316c08983] 
-   P       [(Partial) Autocorrelation Function] [verbetering] [2008-12-15 22:21:20] [8d78428855b119373cac369316c08983] 

Feedback Forum

2008-12-12 19:46:40 [Bas van Keken] [reply] 
U had hier de parameters als volgt moeten invullen: 
Number of time lags: 60 
Lambda: 1 
d: 0 
D: 1 
seizoenaliteit: 12 
De volgende link laat deze computatie zien 
http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/12/t1229110965d3tpg6eo9k0f83p.htm 
Met behulp van de grafieken kunt u de ar of ma processen identificeren. 
2008-12-13 13:47:09 [An De Koninck] [reply] 
De student heeft de parameters niet correct ingesteld. Hij had de waarden die hij uitkwam bij de VRM hier moeten invullen in de R-module. 
Deze waren dus d=0 en D=1.  
Deze berekening heeft Bas gedaan en zo zie je dat er geen lange termijntrend is. Ook is er geen sprake van seizonaliteit. Als je kijkt naar lag 12, 24, 36, 48 en 60 zie je immers geen significante verschillen.
2008-12-15 11:54:08 [Romina Machiels] [reply] 
De vraag werd niet correct berekend. De student heeft niet de juiste parameters ingevuld, hij had deze moeten invullen die hij bij de vrm gevonden had. 
Dan had je gezien dat er geen langetermijntrend was en ook geen seizonaliteit.
2008-12-15 22:24:31 [df2ed12c9b09685cd516719b004050c5] [reply] 
http://www.freestatistics.org/blog/date/2008/Dec/15/t1229379806spz8tww44sf5uh1.htm  
We zien hier een seizoenaliteit op de ACF (12, 24) 
http://www.freestatistics.org/blog/date/2008/Dec/15/t1229379320luz3jfpfofango3.htm 
Dit is de juiste berekening van de ACF wanneer we de tijdreeks stationair maken, volgens de gevonden waarden van de SMP en VRM. 
Number of time lags moest op 60 staan ipv default, lambda op 1 (omdat niet aan de 2 voorwaarden was voldaan), d=o en D=1 volgens VRM en seizoenaliteit 12.  
Op de acf zien we dat er nu geen seizoenaliteit meer is (lag 12, 24, 36), want er is 1x seizoenaal gedifferentieerd. 

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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	0 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31107&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31107&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31107&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	0 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

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=31107&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=31107&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31107&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=31107&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=31107&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31107&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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code