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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 08 Dec 2008 06:16:18 -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/t1228742210y2wghaui08vy9ov.htm/, Retrieved Thu, 16 May 2024 13:34:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30462, Retrieved Thu, 16 May 2024 13:34:06 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

ACF

Estimated Impact

202

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 RMP   [Standard Deviation-Mean Plot] [q1] [2008-12-08 12:37:39] [3ffd109c9e040b1ae7e5dbe576d4698c]
F    D    [Standard Deviation-Mean Plot] [SMP] [2008-12-08 12:41:29] [3ffd109c9e040b1ae7e5dbe576d4698c]
- RM        [Variance Reduction Matrix] [VRM] [2008-12-08 13:10:17] [3ffd109c9e040b1ae7e5dbe576d4698c]
- RM          [(Partial) Autocorrelation Function] [ACF] [2008-12-08 13:14:12] [3ffd109c9e040b1ae7e5dbe576d4698c]
F                 [(Partial) Autocorrelation Function] [ACF] [2008-12-08 13:16:18] [962e6c9020896982bc8283b8971710a9] [Current]
-   P               [(Partial) Autocorrelation Function] [ACF met meer lags] [2008-12-15 14:07:02] [f77c9ab3b413812d7baee6b7ec69a15d] 
-   P               [(Partial) Autocorrelation Function] [ACF] [2008-12-16 11:53:49] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- R P               [(Partial) Autocorrelation Function] [ACF] [2008-12-18 16:25:12] [3ffd109c9e040b1ae7e5dbe576d4698c] 
-   P                 [(Partial) Autocorrelation Function] [ACF] [2008-12-24 12:57:31] [b28ef2aea2cd58ceb5ad90223572c703] 

Feedback Forum

2008-12-15 14:11:17 [Charis Berrevoets] [reply] 
Je had een duidelijker beeld kunnen krijgen door het aantal lags te verhogen:  
http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/15/t1229350082i2vivg7c1sz2qfl.htm 
Op deze grafiek van de ACF zie je duidelijk dat er een wisselend patroon aanwezig is. Dit duidt op een korte termijn trend. Dit duidt duidelijk op een korte termijn trend, zoals je zelf reeds aanhaalde.  
In deze grafiek is er ook een duidelijkere aanwijzing naar seizoenaliteit, zij het nog steeds niet erg overtuigend. 

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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=30462&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=30462&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30462&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	0.808854	6.3173	0
2	0.524315	4.095	6.3e-05
3	0.283463	2.2139	0.015292
4	0.148625	1.1608	0.125123
5	0.092699	0.724	0.235915
6	0.069836	0.5454	0.293721
7	0.060076	0.4692	0.320296
8	0.078487	0.613	0.271076
9	0.195107	1.5238	0.066359
10	0.358588	2.8007	0.003411
11	0.539892	4.2167	4.2e-05
12	0.618954	4.8342	5e-06
13	0.447253	3.4932	0.000447
14	0.209653	1.6374	0.053344
15	0.014877	0.1162	0.45394
16	-0.091082	-0.7114	0.239783
17	-0.140891	-1.1004	0.137742

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.808854 & 6.3173 & 0 \tabularnewline
2 & 0.524315 & 4.095 & 6.3e-05 \tabularnewline
3 & 0.283463 & 2.2139 & 0.015292 \tabularnewline
4 & 0.148625 & 1.1608 & 0.125123 \tabularnewline
5 & 0.092699 & 0.724 & 0.235915 \tabularnewline
6 & 0.069836 & 0.5454 & 0.293721 \tabularnewline
7 & 0.060076 & 0.4692 & 0.320296 \tabularnewline
8 & 0.078487 & 0.613 & 0.271076 \tabularnewline
9 & 0.195107 & 1.5238 & 0.066359 \tabularnewline
10 & 0.358588 & 2.8007 & 0.003411 \tabularnewline
11 & 0.539892 & 4.2167 & 4.2e-05 \tabularnewline
12 & 0.618954 & 4.8342 & 5e-06 \tabularnewline
13 & 0.447253 & 3.4932 & 0.000447 \tabularnewline
14 & 0.209653 & 1.6374 & 0.053344 \tabularnewline
15 & 0.014877 & 0.1162 & 0.45394 \tabularnewline
16 & -0.091082 & -0.7114 & 0.239783 \tabularnewline
17 & -0.140891 & -1.1004 & 0.137742 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30462&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]0.808854[/C][C]6.3173[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.524315[/C][C]4.095[/C][C]6.3e-05[/C][/ROW]
[ROW][C]3[/C][C]0.283463[/C][C]2.2139[/C][C]0.015292[/C][/ROW]
[ROW][C]4[/C][C]0.148625[/C][C]1.1608[/C][C]0.125123[/C][/ROW]
[ROW][C]5[/C][C]0.092699[/C][C]0.724[/C][C]0.235915[/C][/ROW]
[ROW][C]6[/C][C]0.069836[/C][C]0.5454[/C][C]0.293721[/C][/ROW]
[ROW][C]7[/C][C]0.060076[/C][C]0.4692[/C][C]0.320296[/C][/ROW]
[ROW][C]8[/C][C]0.078487[/C][C]0.613[/C][C]0.271076[/C][/ROW]
[ROW][C]9[/C][C]0.195107[/C][C]1.5238[/C][C]0.066359[/C][/ROW]
[ROW][C]10[/C][C]0.358588[/C][C]2.8007[/C][C]0.003411[/C][/ROW]
[ROW][C]11[/C][C]0.539892[/C][C]4.2167[/C][C]4.2e-05[/C][/ROW]
[ROW][C]12[/C][C]0.618954[/C][C]4.8342[/C][C]5e-06[/C][/ROW]
[ROW][C]13[/C][C]0.447253[/C][C]3.4932[/C][C]0.000447[/C][/ROW]
[ROW][C]14[/C][C]0.209653[/C][C]1.6374[/C][C]0.053344[/C][/ROW]
[ROW][C]15[/C][C]0.014877[/C][C]0.1162[/C][C]0.45394[/C][/ROW]
[ROW][C]16[/C][C]-0.091082[/C][C]-0.7114[/C][C]0.239783[/C][/ROW]
[ROW][C]17[/C][C]-0.140891[/C][C]-1.1004[/C][C]0.137742[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30462&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30462&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	0.808854	6.3173	0
2	0.524315	4.095	6.3e-05
3	0.283463	2.2139	0.015292
4	0.148625	1.1608	0.125123
5	0.092699	0.724	0.235915
6	0.069836	0.5454	0.293721
7	0.060076	0.4692	0.320296
8	0.078487	0.613	0.271076
9	0.195107	1.5238	0.066359
10	0.358588	2.8007	0.003411
11	0.539892	4.2167	4.2e-05
12	0.618954	4.8342	5e-06
13	0.447253	3.4932	0.000447
14	0.209653	1.6374	0.053344
15	0.014877	0.1162	0.45394
16	-0.091082	-0.7114	0.239783
17	-0.140891	-1.1004	0.137742

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.808854	6.3173	0
2	-0.375784	-2.935	0.002348
3	0.01332	0.104	0.458743
4	0.086883	0.6786	0.249986
5	0.005091	0.0398	0.484205
6	-0.014057	-0.1098	0.456469
7	0.021284	0.1662	0.434261
8	0.09199	0.7185	0.237607
9	0.317452	2.4794	0.00797
10	0.155105	1.2114	0.115206
11	0.29473	2.3019	0.012384
12	0.010887	0.085	0.466259
13	-0.518357	-4.0485	7.4e-05
14	0.087503	0.6834	0.248464
15	-0.072215	-0.564	0.287406
16	-0.121677	-0.9503	0.172849
17	0.008256	0.0645	0.4744

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.808854 & 6.3173 & 0 \tabularnewline
2 & -0.375784 & -2.935 & 0.002348 \tabularnewline
3 & 0.01332 & 0.104 & 0.458743 \tabularnewline
4 & 0.086883 & 0.6786 & 0.249986 \tabularnewline
5 & 0.005091 & 0.0398 & 0.484205 \tabularnewline
6 & -0.014057 & -0.1098 & 0.456469 \tabularnewline
7 & 0.021284 & 0.1662 & 0.434261 \tabularnewline
8 & 0.09199 & 0.7185 & 0.237607 \tabularnewline
9 & 0.317452 & 2.4794 & 0.00797 \tabularnewline
10 & 0.155105 & 1.2114 & 0.115206 \tabularnewline
11 & 0.29473 & 2.3019 & 0.012384 \tabularnewline
12 & 0.010887 & 0.085 & 0.466259 \tabularnewline
13 & -0.518357 & -4.0485 & 7.4e-05 \tabularnewline
14 & 0.087503 & 0.6834 & 0.248464 \tabularnewline
15 & -0.072215 & -0.564 & 0.287406 \tabularnewline
16 & -0.121677 & -0.9503 & 0.172849 \tabularnewline
17 & 0.008256 & 0.0645 & 0.4744 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30462&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]0.808854[/C][C]6.3173[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.375784[/C][C]-2.935[/C][C]0.002348[/C][/ROW]
[ROW][C]3[/C][C]0.01332[/C][C]0.104[/C][C]0.458743[/C][/ROW]
[ROW][C]4[/C][C]0.086883[/C][C]0.6786[/C][C]0.249986[/C][/ROW]
[ROW][C]5[/C][C]0.005091[/C][C]0.0398[/C][C]0.484205[/C][/ROW]
[ROW][C]6[/C][C]-0.014057[/C][C]-0.1098[/C][C]0.456469[/C][/ROW]
[ROW][C]7[/C][C]0.021284[/C][C]0.1662[/C][C]0.434261[/C][/ROW]
[ROW][C]8[/C][C]0.09199[/C][C]0.7185[/C][C]0.237607[/C][/ROW]
[ROW][C]9[/C][C]0.317452[/C][C]2.4794[/C][C]0.00797[/C][/ROW]
[ROW][C]10[/C][C]0.155105[/C][C]1.2114[/C][C]0.115206[/C][/ROW]
[ROW][C]11[/C][C]0.29473[/C][C]2.3019[/C][C]0.012384[/C][/ROW]
[ROW][C]12[/C][C]0.010887[/C][C]0.085[/C][C]0.466259[/C][/ROW]
[ROW][C]13[/C][C]-0.518357[/C][C]-4.0485[/C][C]7.4e-05[/C][/ROW]
[ROW][C]14[/C][C]0.087503[/C][C]0.6834[/C][C]0.248464[/C][/ROW]
[ROW][C]15[/C][C]-0.072215[/C][C]-0.564[/C][C]0.287406[/C][/ROW]
[ROW][C]16[/C][C]-0.121677[/C][C]-0.9503[/C][C]0.172849[/C][/ROW]
[ROW][C]17[/C][C]0.008256[/C][C]0.0645[/C][C]0.4744[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30462&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30462&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	0.808854	6.3173	0
2	-0.375784	-2.935	0.002348
3	0.01332	0.104	0.458743
4	0.086883	0.6786	0.249986
5	0.005091	0.0398	0.484205
6	-0.014057	-0.1098	0.456469
7	0.021284	0.1662	0.434261
8	0.09199	0.7185	0.237607
9	0.317452	2.4794	0.00797
10	0.155105	1.2114	0.115206
11	0.29473	2.3019	0.012384
12	0.010887	0.085	0.466259
13	-0.518357	-4.0485	7.4e-05
14	0.087503	0.6834	0.248464
15	-0.072215	-0.564	0.287406
16	-0.121677	-0.9503	0.172849
17	0.008256	0.0645	0.4744

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 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