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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 14:03:21 -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/t1228770334udyn5d04z80jibt.htm/, Retrieved Thu, 16 May 2024 22:51:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31019, Retrieved Thu, 16 May 2024 22:51:41 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

172

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] [00a0a665d7a07edd2e460056b0c0c354] [Current]
F   P         [(Partial) Autocorrelation Function] [acf] [2008-12-08 21:58:33] [82d201ca7b4e7cd2c6f885d29b5b6937] 
- RMP         [ARIMA Backward Selection] [step 5] [2008-12-15 18:33:03] [38f43994ada0e6172896e12525dcc585] 
-   P         [(Partial) Autocorrelation Function] [ACF] [2008-12-15 22:14:24] [82d201ca7b4e7cd2c6f885d29b5b6937] 

Feedback Forum

2008-12-15 22:19:40 [Inge Meelberghs] [reply] 
lags = 60 
Λ = 1 
d = 0 
D = 1 
Seasonal period = 12 
 
Ook hier had ik dus beter de lags op 60 gezet. Zo zie je veel beter of er na de differentiatie van d = 0 en D =1 nog een seizonaliteitspatroon te bespeuren is of niet. 
 
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/15/t1229379310f807xf9s88zxp83.htm  
 
We kunnen dus stellen dat er nu geen sprake meer is van seizonaliteit. Ook de LT-trend is verdwenen door 1 keer seizonaal te differentiëren. 
2008-12-15 22:48:57 [Inge Meelberghs] [reply] 
opmerking over mijn vorige uitleg: 
 
er was in deze tijdreeks sowieso al geen LT-trend te bespeuren waardoor 'Ook de LT-trend is verdwenen door 1 keer seizonaal te differentiëren' wegvalt. Enkel de seizonaliteit is dus uit de reeks gehaald door 1 keer seizonaal te differentiëren.

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Dataseries X:

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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	3 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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31019&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]3 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=31019&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31019&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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.133181	-0.9323	0.177885
2	0.105118	0.7358	0.232672
3	0.425624	2.9794	0.002242
4	-0.064091	-0.4486	0.327834
5	0.011675	0.0817	0.467599
6	0.23651	1.6556	0.0521
7	-0.211688	-1.4818	0.072396
8	0.02162	0.1513	0.440165
9	0.172949	1.2106	0.11592
10	-0.106141	-0.743	0.230519
11	-0.097161	-0.6801	0.249812
12	0.072442	0.5071	0.307181
13	-0.114252	-0.7998	0.213854
14	-0.091584	-0.6411	0.262226
15	0.036712	0.257	0.399132
16	-0.220544	-1.5438	0.064535
17	-0.005512	-0.0386	0.48469

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.133181 & -0.9323 & 0.177885 \tabularnewline
2 & 0.105118 & 0.7358 & 0.232672 \tabularnewline
3 & 0.425624 & 2.9794 & 0.002242 \tabularnewline
4 & -0.064091 & -0.4486 & 0.327834 \tabularnewline
5 & 0.011675 & 0.0817 & 0.467599 \tabularnewline
6 & 0.23651 & 1.6556 & 0.0521 \tabularnewline
7 & -0.211688 & -1.4818 & 0.072396 \tabularnewline
8 & 0.02162 & 0.1513 & 0.440165 \tabularnewline
9 & 0.172949 & 1.2106 & 0.11592 \tabularnewline
10 & -0.106141 & -0.743 & 0.230519 \tabularnewline
11 & -0.097161 & -0.6801 & 0.249812 \tabularnewline
12 & 0.072442 & 0.5071 & 0.307181 \tabularnewline
13 & -0.114252 & -0.7998 & 0.213854 \tabularnewline
14 & -0.091584 & -0.6411 & 0.262226 \tabularnewline
15 & 0.036712 & 0.257 & 0.399132 \tabularnewline
16 & -0.220544 & -1.5438 & 0.064535 \tabularnewline
17 & -0.005512 & -0.0386 & 0.48469 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31019&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]-0.133181[/C][C]-0.9323[/C][C]0.177885[/C][/ROW]
[ROW][C]2[/C][C]0.105118[/C][C]0.7358[/C][C]0.232672[/C][/ROW]
[ROW][C]3[/C][C]0.425624[/C][C]2.9794[/C][C]0.002242[/C][/ROW]
[ROW][C]4[/C][C]-0.064091[/C][C]-0.4486[/C][C]0.327834[/C][/ROW]
[ROW][C]5[/C][C]0.011675[/C][C]0.0817[/C][C]0.467599[/C][/ROW]
[ROW][C]6[/C][C]0.23651[/C][C]1.6556[/C][C]0.0521[/C][/ROW]
[ROW][C]7[/C][C]-0.211688[/C][C]-1.4818[/C][C]0.072396[/C][/ROW]
[ROW][C]8[/C][C]0.02162[/C][C]0.1513[/C][C]0.440165[/C][/ROW]
[ROW][C]9[/C][C]0.172949[/C][C]1.2106[/C][C]0.11592[/C][/ROW]
[ROW][C]10[/C][C]-0.106141[/C][C]-0.743[/C][C]0.230519[/C][/ROW]
[ROW][C]11[/C][C]-0.097161[/C][C]-0.6801[/C][C]0.249812[/C][/ROW]
[ROW][C]12[/C][C]0.072442[/C][C]0.5071[/C][C]0.307181[/C][/ROW]
[ROW][C]13[/C][C]-0.114252[/C][C]-0.7998[/C][C]0.213854[/C][/ROW]
[ROW][C]14[/C][C]-0.091584[/C][C]-0.6411[/C][C]0.262226[/C][/ROW]
[ROW][C]15[/C][C]0.036712[/C][C]0.257[/C][C]0.399132[/C][/ROW]
[ROW][C]16[/C][C]-0.220544[/C][C]-1.5438[/C][C]0.064535[/C][/ROW]
[ROW][C]17[/C][C]-0.005512[/C][C]-0.0386[/C][C]0.48469[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31019&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31019&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	-0.133181	-0.9323	0.177885
2	0.105118	0.7358	0.232672
3	0.425624	2.9794	0.002242
4	-0.064091	-0.4486	0.327834
5	0.011675	0.0817	0.467599
6	0.23651	1.6556	0.0521
7	-0.211688	-1.4818	0.072396
8	0.02162	0.1513	0.440165
9	0.172949	1.2106	0.11592
10	-0.106141	-0.743	0.230519
11	-0.097161	-0.6801	0.249812
12	0.072442	0.5071	0.307181
13	-0.114252	-0.7998	0.213854
14	-0.091584	-0.6411	0.262226
15	0.036712	0.257	0.399132
16	-0.220544	-1.5438	0.064535
17	-0.005512	-0.0386	0.48469

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.133181	-0.9323	0.177885
2	0.088959	0.6227	0.268181
3	0.462012	3.2341	0.001094
4	0.066971	0.4688	0.320648
5	-0.129872	-0.9091	0.183873
6	0.02776	0.1943	0.423364
7	-0.185787	-1.3005	0.099755
8	-0.055987	-0.3919	0.348412
9	0.147234	1.0306	0.153885
10	0.143805	1.0066	0.159527
11	-0.157209	-1.1005	0.138253
12	-0.176291	-1.234	0.111537
13	-0.065328	-0.4573	0.324741
14	-0.027334	-0.1913	0.424526
15	0.060539	0.4238	0.336793
16	-0.099718	-0.698	0.24423
17	0.027953	0.1957	0.422839

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.133181 & -0.9323 & 0.177885 \tabularnewline
2 & 0.088959 & 0.6227 & 0.268181 \tabularnewline
3 & 0.462012 & 3.2341 & 0.001094 \tabularnewline
4 & 0.066971 & 0.4688 & 0.320648 \tabularnewline
5 & -0.129872 & -0.9091 & 0.183873 \tabularnewline
6 & 0.02776 & 0.1943 & 0.423364 \tabularnewline
7 & -0.185787 & -1.3005 & 0.099755 \tabularnewline
8 & -0.055987 & -0.3919 & 0.348412 \tabularnewline
9 & 0.147234 & 1.0306 & 0.153885 \tabularnewline
10 & 0.143805 & 1.0066 & 0.159527 \tabularnewline
11 & -0.157209 & -1.1005 & 0.138253 \tabularnewline
12 & -0.176291 & -1.234 & 0.111537 \tabularnewline
13 & -0.065328 & -0.4573 & 0.324741 \tabularnewline
14 & -0.027334 & -0.1913 & 0.424526 \tabularnewline
15 & 0.060539 & 0.4238 & 0.336793 \tabularnewline
16 & -0.099718 & -0.698 & 0.24423 \tabularnewline
17 & 0.027953 & 0.1957 & 0.422839 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31019&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]-0.133181[/C][C]-0.9323[/C][C]0.177885[/C][/ROW]
[ROW][C]2[/C][C]0.088959[/C][C]0.6227[/C][C]0.268181[/C][/ROW]
[ROW][C]3[/C][C]0.462012[/C][C]3.2341[/C][C]0.001094[/C][/ROW]
[ROW][C]4[/C][C]0.066971[/C][C]0.4688[/C][C]0.320648[/C][/ROW]
[ROW][C]5[/C][C]-0.129872[/C][C]-0.9091[/C][C]0.183873[/C][/ROW]
[ROW][C]6[/C][C]0.02776[/C][C]0.1943[/C][C]0.423364[/C][/ROW]
[ROW][C]7[/C][C]-0.185787[/C][C]-1.3005[/C][C]0.099755[/C][/ROW]
[ROW][C]8[/C][C]-0.055987[/C][C]-0.3919[/C][C]0.348412[/C][/ROW]
[ROW][C]9[/C][C]0.147234[/C][C]1.0306[/C][C]0.153885[/C][/ROW]
[ROW][C]10[/C][C]0.143805[/C][C]1.0066[/C][C]0.159527[/C][/ROW]
[ROW][C]11[/C][C]-0.157209[/C][C]-1.1005[/C][C]0.138253[/C][/ROW]
[ROW][C]12[/C][C]-0.176291[/C][C]-1.234[/C][C]0.111537[/C][/ROW]
[ROW][C]13[/C][C]-0.065328[/C][C]-0.4573[/C][C]0.324741[/C][/ROW]
[ROW][C]14[/C][C]-0.027334[/C][C]-0.1913[/C][C]0.424526[/C][/ROW]
[ROW][C]15[/C][C]0.060539[/C][C]0.4238[/C][C]0.336793[/C][/ROW]
[ROW][C]16[/C][C]-0.099718[/C][C]-0.698[/C][C]0.24423[/C][/ROW]
[ROW][C]17[/C][C]0.027953[/C][C]0.1957[/C][C]0.422839[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31019&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31019&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	-0.133181	-0.9323	0.177885
2	0.088959	0.6227	0.268181
3	0.462012	3.2341	0.001094
4	0.066971	0.4688	0.320648
5	-0.129872	-0.9091	0.183873
6	0.02776	0.1943	0.423364
7	-0.185787	-1.3005	0.099755
8	-0.055987	-0.3919	0.348412
9	0.147234	1.0306	0.153885
10	0.143805	1.0066	0.159527
11	-0.157209	-1.1005	0.138253
12	-0.176291	-1.234	0.111537
13	-0.065328	-0.4573	0.324741
14	-0.027334	-0.1913	0.424526
15	0.060539	0.4238	0.336793
16	-0.099718	-0.698	0.24423
17	0.027953	0.1957	0.422839

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 = 1 ; par5 = 12 ;

Parameters (R input):

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