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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, 02 Dec 2008 06:12:03 -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/02/t1228223686oirsoo0ft4zdbkt.htm/, Retrieved Sun, 19 May 2024 02:42:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27724, Retrieved Sun, 19 May 2024 02:42:14 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

181

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

F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
F RMPD    [(Partial) Autocorrelation Function] [q6] [2008-12-02 13:12:03] [d41d8cd98f00b204e9800998ecf8427e] [Current]

Feedback Forum

2008-12-07 20:51:01 [Jasmine Hendrikx] [reply] 
Evaluatie Q6: 
De student heeft de berekening goed uitgevoerd. Wel zou de number of time lags beter op 36 staan, aangezien we dan het langzaam dalende patroon beter kunnen zien. De student heeft dus eerst de ACF berekend zonder aanpassingen (D=0 en d=0). We zien dat we dus kunnen spreken van positieve autocorrelaties. Er is een langzaam dalend patroon. Er is dus een trendmatig verloop in onze tijdreeksen. We zien ook dat in de periode 12, 24, 36 er telkens een stijging is, dit wijst natuurlijk op seizoenaliteit. Er is sprake van een hangmatpatroon. Er is ook een langzaam dalend patroon in de seizoenale autocorrelatiecoëfficiënten aanwezig.  
In de grafiek zijn alle autocorrelatiecoëfficiënten significant verschillend zijn van 0, aangezien ze allemaal buiten het betrouwbaarheidsinterval vallen.  
De volgende berekening die de student heeft gemaakt is ineens deze van de VRM. Maar aangezien we uit de grafiek duidelijk van een lange termijn trend en seizoenaliteit kunnen spreken, moeten we de tijdreeks differentiëren. Dit heeft de student wel in Q5 gedaan, hoewel het dus bij deze vraag zou gedaan moeten worden. De bijkomende feedback zal ik dus hier bijschrijven.  
Doordat we uit de grafiek een lange termijn trend kunnen afleiden, moet we dus eerst d gelijkstellen aan 1. Zoals de student correct vermeldt (in Q5) zien we dat de langetermijntrend nu volledig verdwenen is. We zien dus dat differentiëren helpt om de trend weg te werken. Wel zien we dat er toch nog een langzaam dalend patroon is in de seizoenale autocorrelatiefunctie (op lag 12, 24, 36). Wanneer we 60 periodes teruggaan, kunnen we enkel deze langzame daling bevestigen. Zoals er dan ook correct vermeld wordt, moeten we D dus gelijkstellen aan 1, we gaan dus 1 keer seizoenaal differentiëren om de seizoenaliteit eruit te halen. We zien nu dat het er veel beter uitziet. Het langzaam dalend patroon is volledig verdwenen en er is geen seizoenaliteit meer. De reeks is stationair  wat betreft de trend. Ook vallen de meeste verticale lijntjes nu binnen het betrouwbaarheidsinterval.  
2008-12-08 19:45:12 [Koen Van Baelen] [reply] 
Bespreking ACF: er is niet enkel een dalende trend op te merken maar ook seizoenaliteit, dit kan je zien aan de 'hangmatvormen' met steeds pieken op maand 12,24,...  
De bespreking van de VRM en de spectraalanalyse zijn correct en volledig. Aan het resultaat moet men nog wel opmerken dat nog niet alle voorspelbaarheid is verdwenen, het ideale zou zijn dat de cumulatieve periodogram op een diagonaal komt te liggen

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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=27724&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=27724&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27724&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=27724&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=27724&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27724&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=27724&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=27724&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27724&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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code