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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

Wed, 03 Dec 2008 02:16:10 -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/03/t1228296011duo5m9fub5446jh.htm/, Retrieved Fri, 17 May 2024 18:34:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28586, Retrieved Fri, 17 May 2024 18:34:35 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

279

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

F       [(Partial) Autocorrelation Function] [] [2008-12-03 09:16:10] [ed75e673b8609ce7f7795f94157397be] [Current]
-   P     [(Partial) Autocorrelation Function] [Q6 ACF d=1 D=0] [2008-12-07 18:59:29] [b1bd16d1f47bfe13feacf1c27a0abba5] 

Feedback Forum

2008-12-06 12:52:39 [Nicolaj Wuyts] [reply] 
De student voert de berekening correct uit. Hij is echter een ding vergeten en dat is van de lamba gelijk te stellen aan -0.312592539725757. Door deze bewerking wordt de spreiding doorheen de tijd terug gelijk, wat nu niet het geval is.
2008-12-07 19:02:29 [Jasmine Hendrikx] [reply] 
Evaluatie Q6: 
De berekening is goed gemaakt. Uit de grafiek van de autocorrelatie is er duidelijk sprake van een langzaam dalend patroon. We kunnen dus spreken van positieve autocorrelaties. Alle autocorrelatiecoëfficiënten zijn ook significant verschillend van 0, aangezien ze allemaal buiten het 95% betrouwbaarheidsinterval vallen.  
Er is dus een trendmatig verloop in onze tijdreeks. De student vermeldt ook dat er seizoenaliteit aanwezig door het hangmattenpatroon. Dit is inderdaad correct, maar dit hangmattenpatroon komt beter tot uiting wanneer men in de berekening number of time lags gelijkstelt aan 36 of 60.Dan kunnen we zien dat er in de periode 12,24,36 er telkens een stijging is, en dit wijst dan op seizoenaliteit. In de seizoenale coëfficiënten kunnen we ook een langzaam dalend patroon waarnemen. De student heeft in de volgende stap ineens D en d gelijkgestelt aan 1, maar eigenlijk zou het beter zijn, als je stapsgewijs werkt. Zo kun je de evolutie beter zien. Zo kun je beter eerst d gelijkstellen aan 1 en D nog 0 laten. Hieronder de URL: http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/07/t1228676414blachrnxmt1ri9d.htm 
We zien dan dat de grafiek er helemaal anders uitziet. De lange termijn trend is nu volledig verdwenen. We zien dus dat differentiëren helpt om de langetermijntrend weg te werken.  
Wel zien we dat er nog een langzaam dalend patroon is in de seizoenale autocorrelatiecoëfficiënten (op lag 12, 24, 36). Wanneer we 60 periodes teruggaan, kunnen we enkel deze langzame daling bevestigen. Vandaar dat we D nu moeten gelijkstellen aan 1. In het document is ook de grafiek van partiële autocorrelatie gekopieerd. Dit is echter niet nodig, aangezien we deze niet gebruiken.  
2008-12-08 19:30:20 [Erik Geysen] [reply] 
We zien een positive correlatie, de figuur gaat langzaam dalend met bulten. We kunnen dus besluiten dat in deze tijdreeks een lange termijn trend zit. We stellen ook seizoenaliteit vast. (hangmatpatroon)  
De trend wordt verwijderd door d gelijk te stellen aan 1.  
we stellen nog steeds seizoenaliteit vast.  
Deze wordt ook weg gewerkt door D gelijk te stellen aan 1.  

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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	'George Udny Yule' @ 72.249.76.132

\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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28586&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28586&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28586&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.948047	11.3766	0
2	0.875575	10.5069	0
3	0.806681	9.6802	0
4	0.752625	9.0315	0
5	0.71377	8.5652	0
6	0.681734	8.1808	0
7	0.662904	7.9549	0
8	0.65561	7.8673	0
9	0.670948	8.0514	0
10	0.70272	8.4326	0
11	0.74324	8.9189	0
12	0.760395	9.1247	0
13	0.712661	8.5519	0
14	0.646342	7.7561	0
15	0.585923	7.0311	0
16	0.537955	6.4555	0
17	0.499748	5.997	0
18	0.468734	5.6248	0
19	0.449871	5.3984	0
20	0.441629	5.2995	0
21	0.457224	5.4867	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.948047 & 11.3766 & 0 \tabularnewline
2 & 0.875575 & 10.5069 & 0 \tabularnewline
3 & 0.806681 & 9.6802 & 0 \tabularnewline
4 & 0.752625 & 9.0315 & 0 \tabularnewline
5 & 0.71377 & 8.5652 & 0 \tabularnewline
6 & 0.681734 & 8.1808 & 0 \tabularnewline
7 & 0.662904 & 7.9549 & 0 \tabularnewline
8 & 0.65561 & 7.8673 & 0 \tabularnewline
9 & 0.670948 & 8.0514 & 0 \tabularnewline
10 & 0.70272 & 8.4326 & 0 \tabularnewline
11 & 0.74324 & 8.9189 & 0 \tabularnewline
12 & 0.760395 & 9.1247 & 0 \tabularnewline
13 & 0.712661 & 8.5519 & 0 \tabularnewline
14 & 0.646342 & 7.7561 & 0 \tabularnewline
15 & 0.585923 & 7.0311 & 0 \tabularnewline
16 & 0.537955 & 6.4555 & 0 \tabularnewline
17 & 0.499748 & 5.997 & 0 \tabularnewline
18 & 0.468734 & 5.6248 & 0 \tabularnewline
19 & 0.449871 & 5.3984 & 0 \tabularnewline
20 & 0.441629 & 5.2995 & 0 \tabularnewline
21 & 0.457224 & 5.4867 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28586&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]0.948047[/C][C]11.3766[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.875575[/C][C]10.5069[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.806681[/C][C]9.6802[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.752625[/C][C]9.0315[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.71377[/C][C]8.5652[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.681734[/C][C]8.1808[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.662904[/C][C]7.9549[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.65561[/C][C]7.8673[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.670948[/C][C]8.0514[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.70272[/C][C]8.4326[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.74324[/C][C]8.9189[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.760395[/C][C]9.1247[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.712661[/C][C]8.5519[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.646342[/C][C]7.7561[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.585923[/C][C]7.0311[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.537955[/C][C]6.4555[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.499748[/C][C]5.997[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.468734[/C][C]5.6248[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.449871[/C][C]5.3984[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.441629[/C][C]5.2995[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.457224[/C][C]5.4867[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28586&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28586&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	0.948047	11.3766	0
2	0.875575	10.5069	0
3	0.806681	9.6802	0
4	0.752625	9.0315	0
5	0.71377	8.5652	0
6	0.681734	8.1808	0
7	0.662904	7.9549	0
8	0.65561	7.8673	0
9	0.670948	8.0514	0
10	0.70272	8.4326	0
11	0.74324	8.9189	0
12	0.760395	9.1247	0
13	0.712661	8.5519	0
14	0.646342	7.7561	0
15	0.585923	7.0311	0
16	0.537955	6.4555	0
17	0.499748	5.997	0
18	0.468734	5.6248	0
19	0.449871	5.3984	0
20	0.441629	5.2995	0
21	0.457224	5.4867	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.948047	11.3766	0
2	-0.229422	-2.7531	0.003332
3	0.038148	0.4578	0.323903
4	0.093785	1.1254	0.131141
5	0.073607	0.8833	0.189279
6	0.007728	0.0927	0.463123
7	0.125597	1.5072	0.066979
8	0.089951	1.0794	0.141103
9	0.232489	2.7899	0.002994
10	0.166051	1.9926	0.024097
11	0.171274	2.0553	0.020829
12	-0.135431	-1.6252	0.053156
13	-0.539691	-6.4763	0
14	-0.02661	-0.3193	0.374973
15	0.090765	1.0892	0.138947
16	0.024956	0.2995	0.382508
17	0.032516	0.3902	0.348487
18	0.073433	0.8812	0.189841
19	0.048442	0.5813	0.280972
20	-0.045542	-0.5465	0.292784
21	0.045753	0.549	0.291916

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.948047 & 11.3766 & 0 \tabularnewline
2 & -0.229422 & -2.7531 & 0.003332 \tabularnewline
3 & 0.038148 & 0.4578 & 0.323903 \tabularnewline
4 & 0.093785 & 1.1254 & 0.131141 \tabularnewline
5 & 0.073607 & 0.8833 & 0.189279 \tabularnewline
6 & 0.007728 & 0.0927 & 0.463123 \tabularnewline
7 & 0.125597 & 1.5072 & 0.066979 \tabularnewline
8 & 0.089951 & 1.0794 & 0.141103 \tabularnewline
9 & 0.232489 & 2.7899 & 0.002994 \tabularnewline
10 & 0.166051 & 1.9926 & 0.024097 \tabularnewline
11 & 0.171274 & 2.0553 & 0.020829 \tabularnewline
12 & -0.135431 & -1.6252 & 0.053156 \tabularnewline
13 & -0.539691 & -6.4763 & 0 \tabularnewline
14 & -0.02661 & -0.3193 & 0.374973 \tabularnewline
15 & 0.090765 & 1.0892 & 0.138947 \tabularnewline
16 & 0.024956 & 0.2995 & 0.382508 \tabularnewline
17 & 0.032516 & 0.3902 & 0.348487 \tabularnewline
18 & 0.073433 & 0.8812 & 0.189841 \tabularnewline
19 & 0.048442 & 0.5813 & 0.280972 \tabularnewline
20 & -0.045542 & -0.5465 & 0.292784 \tabularnewline
21 & 0.045753 & 0.549 & 0.291916 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28586&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]0.948047[/C][C]11.3766[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.229422[/C][C]-2.7531[/C][C]0.003332[/C][/ROW]
[ROW][C]3[/C][C]0.038148[/C][C]0.4578[/C][C]0.323903[/C][/ROW]
[ROW][C]4[/C][C]0.093785[/C][C]1.1254[/C][C]0.131141[/C][/ROW]
[ROW][C]5[/C][C]0.073607[/C][C]0.8833[/C][C]0.189279[/C][/ROW]
[ROW][C]6[/C][C]0.007728[/C][C]0.0927[/C][C]0.463123[/C][/ROW]
[ROW][C]7[/C][C]0.125597[/C][C]1.5072[/C][C]0.066979[/C][/ROW]
[ROW][C]8[/C][C]0.089951[/C][C]1.0794[/C][C]0.141103[/C][/ROW]
[ROW][C]9[/C][C]0.232489[/C][C]2.7899[/C][C]0.002994[/C][/ROW]
[ROW][C]10[/C][C]0.166051[/C][C]1.9926[/C][C]0.024097[/C][/ROW]
[ROW][C]11[/C][C]0.171274[/C][C]2.0553[/C][C]0.020829[/C][/ROW]
[ROW][C]12[/C][C]-0.135431[/C][C]-1.6252[/C][C]0.053156[/C][/ROW]
[ROW][C]13[/C][C]-0.539691[/C][C]-6.4763[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]-0.02661[/C][C]-0.3193[/C][C]0.374973[/C][/ROW]
[ROW][C]15[/C][C]0.090765[/C][C]1.0892[/C][C]0.138947[/C][/ROW]
[ROW][C]16[/C][C]0.024956[/C][C]0.2995[/C][C]0.382508[/C][/ROW]
[ROW][C]17[/C][C]0.032516[/C][C]0.3902[/C][C]0.348487[/C][/ROW]
[ROW][C]18[/C][C]0.073433[/C][C]0.8812[/C][C]0.189841[/C][/ROW]
[ROW][C]19[/C][C]0.048442[/C][C]0.5813[/C][C]0.280972[/C][/ROW]
[ROW][C]20[/C][C]-0.045542[/C][C]-0.5465[/C][C]0.292784[/C][/ROW]
[ROW][C]21[/C][C]0.045753[/C][C]0.549[/C][C]0.291916[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28586&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28586&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	0.948047	11.3766	0
2	-0.229422	-2.7531	0.003332
3	0.038148	0.4578	0.323903
4	0.093785	1.1254	0.131141
5	0.073607	0.8833	0.189279
6	0.007728	0.0927	0.463123
7	0.125597	1.5072	0.066979
8	0.089951	1.0794	0.141103
9	0.232489	2.7899	0.002994
10	0.166051	1.9926	0.024097
11	0.171274	2.0553	0.020829
12	-0.135431	-1.6252	0.053156
13	-0.539691	-6.4763	0
14	-0.02661	-0.3193	0.374973
15	0.090765	1.0892	0.138947
16	0.024956	0.2995	0.382508
17	0.032516	0.3902	0.348487
18	0.073433	0.8812	0.189841
19	0.048442	0.5813	0.280972
20	-0.045542	-0.5465	0.292784
21	0.045753	0.549	0.291916

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