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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 06:17:45 -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/t1228742299o441zxi2p9wzgu2.htm/, Retrieved Thu, 16 May 2024 21:26:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30464, Retrieved Thu, 16 May 2024 21:26:47 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

ACF

Estimated Impact

221

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 13:17:45] [962e6c9020896982bc8283b8971710a9] [Current]
F RM                [Spectral Analysis] [spectraal] [2008-12-08 13:20:34] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- R P                 [Spectral Analysis] [Spectraal] [2008-12-18 16:27:12] [3ffd109c9e040b1ae7e5dbe576d4698c] 
-                       [Spectral Analysis] [spectraal analyse] [2008-12-24 12:59:19] [b28ef2aea2cd58ceb5ad90223572c703] 
- R P                 [Spectral Analysis] [spectraal] [2008-12-18 18:22:50] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- RM                [Spectral Analysis] [spectraal] [2008-12-08 13:22:13] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- R P                 [Spectral Analysis] [spectraal] [2008-12-18 18:23:46] [3ffd109c9e040b1ae7e5dbe576d4698c] 
-                       [Spectral Analysis] [spectraal analyse] [2008-12-24 13:02:50] [b28ef2aea2cd58ceb5ad90223572c703] 
-   P                   [Spectral Analysis] [spectraal] [2008-12-24 13:21:21] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- RM                [Spectral Analysis] [spectraal] [2008-12-08 13:23:27] [3ffd109c9e040b1ae7e5dbe576d4698c] 
F RM                  [(Partial) Autocorrelation Function] [ACF] [2008-12-08 13:40:41] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- R P                   [(Partial) Autocorrelation Function] [acf] [2008-12-18 18:26:49] [3ffd109c9e040b1ae7e5dbe576d4698c] 
-   P                   [(Partial) Autocorrelation Function] [autocorrelatie en...] [2008-12-19 10:44:18] [3f66c6f083b1153972739491b89fa2dd] 
-                     [Spectral Analysis] [spectraal] [2008-12-08 13:42:55] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- R P                   [Spectral Analysis] [spectraal] [2008-12-18 18:28:37] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- R P                 [Spectral Analysis] [spectraal] [2008-12-18 18:25:11] [3ffd109c9e040b1ae7e5dbe576d4698c] 
-   P                   [Spectral Analysis] [spectraal analyse] [2008-12-24 13:07:13] [b28ef2aea2cd58ceb5ad90223572c703] 
-   P               [(Partial) Autocorrelation Function] [ACF met meer lags] [2008-12-15 14:18:46] [f77c9ab3b413812d7baee6b7ec69a15d] 
- R P               [(Partial) Autocorrelation Function] [ACF] [2008-12-18 16:54:54] [3ffd109c9e040b1ae7e5dbe576d4698c] 
-   P                 [(Partial) Autocorrelation Function] [ACF] [2008-12-24 13:04:28] [b28ef2aea2cd58ceb5ad90223572c703] 

Feedback Forum

2008-12-15 14:21:30 [Charis Berrevoets] [reply] 
Ook hier had het beter geweest om meer lags te gebruiken. Op jouw grafiek kan je immers niet met zekerheid zeggen dat de seizoenaliteit uit de reeks verdwenen is daar je enkel lag 12 ziet en dat dit staafje nog significant is. Wanneer je het aantal lags verhoogt tot 48 zie je dat er geen patroon meer is om de 12 maanden en dat seizoenaliteit dus wel degelijk uit de reeks is:  
http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/15/t1229350768tkouyodyd6e25dm.htm

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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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30464&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30464&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30464&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.077212	-0.5349	0.297581
2	0.091825	0.6362	0.263839
3	-0.13891	-0.9624	0.170337
4	0.045002	0.3118	0.378278
5	-0.218826	-1.5161	0.06803
6	0.013414	0.0929	0.463171
7	0.062307	0.4317	0.333955
8	-0.036507	-0.2529	0.400702
9	0.100854	0.6987	0.244044
10	-0.035118	-0.2433	0.404403
11	0.303079	2.0998	0.020514
12	-0.272631	-1.8888	0.032482
13	-0.016473	-0.1141	0.454805
14	0.002061	0.0143	0.494333
15	-0.057194	-0.3963	0.346837
16	-0.269854	-1.8696	0.033823
17	0.015562	0.1078	0.457295

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.077212 & -0.5349 & 0.297581 \tabularnewline
2 & 0.091825 & 0.6362 & 0.263839 \tabularnewline
3 & -0.13891 & -0.9624 & 0.170337 \tabularnewline
4 & 0.045002 & 0.3118 & 0.378278 \tabularnewline
5 & -0.218826 & -1.5161 & 0.06803 \tabularnewline
6 & 0.013414 & 0.0929 & 0.463171 \tabularnewline
7 & 0.062307 & 0.4317 & 0.333955 \tabularnewline
8 & -0.036507 & -0.2529 & 0.400702 \tabularnewline
9 & 0.100854 & 0.6987 & 0.244044 \tabularnewline
10 & -0.035118 & -0.2433 & 0.404403 \tabularnewline
11 & 0.303079 & 2.0998 & 0.020514 \tabularnewline
12 & -0.272631 & -1.8888 & 0.032482 \tabularnewline
13 & -0.016473 & -0.1141 & 0.454805 \tabularnewline
14 & 0.002061 & 0.0143 & 0.494333 \tabularnewline
15 & -0.057194 & -0.3963 & 0.346837 \tabularnewline
16 & -0.269854 & -1.8696 & 0.033823 \tabularnewline
17 & 0.015562 & 0.1078 & 0.457295 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30464&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]-0.077212[/C][C]-0.5349[/C][C]0.297581[/C][/ROW]
[ROW][C]2[/C][C]0.091825[/C][C]0.6362[/C][C]0.263839[/C][/ROW]
[ROW][C]3[/C][C]-0.13891[/C][C]-0.9624[/C][C]0.170337[/C][/ROW]
[ROW][C]4[/C][C]0.045002[/C][C]0.3118[/C][C]0.378278[/C][/ROW]
[ROW][C]5[/C][C]-0.218826[/C][C]-1.5161[/C][C]0.06803[/C][/ROW]
[ROW][C]6[/C][C]0.013414[/C][C]0.0929[/C][C]0.463171[/C][/ROW]
[ROW][C]7[/C][C]0.062307[/C][C]0.4317[/C][C]0.333955[/C][/ROW]
[ROW][C]8[/C][C]-0.036507[/C][C]-0.2529[/C][C]0.400702[/C][/ROW]
[ROW][C]9[/C][C]0.100854[/C][C]0.6987[/C][C]0.244044[/C][/ROW]
[ROW][C]10[/C][C]-0.035118[/C][C]-0.2433[/C][C]0.404403[/C][/ROW]
[ROW][C]11[/C][C]0.303079[/C][C]2.0998[/C][C]0.020514[/C][/ROW]
[ROW][C]12[/C][C]-0.272631[/C][C]-1.8888[/C][C]0.032482[/C][/ROW]
[ROW][C]13[/C][C]-0.016473[/C][C]-0.1141[/C][C]0.454805[/C][/ROW]
[ROW][C]14[/C][C]0.002061[/C][C]0.0143[/C][C]0.494333[/C][/ROW]
[ROW][C]15[/C][C]-0.057194[/C][C]-0.3963[/C][C]0.346837[/C][/ROW]
[ROW][C]16[/C][C]-0.269854[/C][C]-1.8696[/C][C]0.033823[/C][/ROW]
[ROW][C]17[/C][C]0.015562[/C][C]0.1078[/C][C]0.457295[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30464&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30464&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	-0.077212	-0.5349	0.297581
2	0.091825	0.6362	0.263839
3	-0.13891	-0.9624	0.170337
4	0.045002	0.3118	0.378278
5	-0.218826	-1.5161	0.06803
6	0.013414	0.0929	0.463171
7	0.062307	0.4317	0.333955
8	-0.036507	-0.2529	0.400702
9	0.100854	0.6987	0.244044
10	-0.035118	-0.2433	0.404403
11	0.303079	2.0998	0.020514
12	-0.272631	-1.8888	0.032482
13	-0.016473	-0.1141	0.454805
14	0.002061	0.0143	0.494333
15	-0.057194	-0.3963	0.346837
16	-0.269854	-1.8696	0.033823
17	0.015562	0.1078	0.457295

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.077212	-0.5349	0.297581
2	0.086379	0.5984	0.276177
3	-0.127468	-0.8831	0.190785
4	0.020384	0.1412	0.444142
5	-0.198484	-1.3751	0.087737
6	-0.03439	-0.2383	0.406347
7	0.103882	0.7197	0.237594
8	-0.085107	-0.5896	0.279099
9	0.101691	0.7045	0.242252
10	-0.045102	-0.3125	0.378016
11	0.291381	2.0187	0.024559
12	-0.22474	-1.557	0.063015
13	-0.10839	-0.751	0.228174
14	0.172781	1.1971	0.11858
15	-0.192491	-1.3336	0.094312
16	-0.203059	-1.4068	0.082959
17	-0.066299	-0.4593	0.324033

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.077212 & -0.5349 & 0.297581 \tabularnewline
2 & 0.086379 & 0.5984 & 0.276177 \tabularnewline
3 & -0.127468 & -0.8831 & 0.190785 \tabularnewline
4 & 0.020384 & 0.1412 & 0.444142 \tabularnewline
5 & -0.198484 & -1.3751 & 0.087737 \tabularnewline
6 & -0.03439 & -0.2383 & 0.406347 \tabularnewline
7 & 0.103882 & 0.7197 & 0.237594 \tabularnewline
8 & -0.085107 & -0.5896 & 0.279099 \tabularnewline
9 & 0.101691 & 0.7045 & 0.242252 \tabularnewline
10 & -0.045102 & -0.3125 & 0.378016 \tabularnewline
11 & 0.291381 & 2.0187 & 0.024559 \tabularnewline
12 & -0.22474 & -1.557 & 0.063015 \tabularnewline
13 & -0.10839 & -0.751 & 0.228174 \tabularnewline
14 & 0.172781 & 1.1971 & 0.11858 \tabularnewline
15 & -0.192491 & -1.3336 & 0.094312 \tabularnewline
16 & -0.203059 & -1.4068 & 0.082959 \tabularnewline
17 & -0.066299 & -0.4593 & 0.324033 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30464&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]-0.077212[/C][C]-0.5349[/C][C]0.297581[/C][/ROW]
[ROW][C]2[/C][C]0.086379[/C][C]0.5984[/C][C]0.276177[/C][/ROW]
[ROW][C]3[/C][C]-0.127468[/C][C]-0.8831[/C][C]0.190785[/C][/ROW]
[ROW][C]4[/C][C]0.020384[/C][C]0.1412[/C][C]0.444142[/C][/ROW]
[ROW][C]5[/C][C]-0.198484[/C][C]-1.3751[/C][C]0.087737[/C][/ROW]
[ROW][C]6[/C][C]-0.03439[/C][C]-0.2383[/C][C]0.406347[/C][/ROW]
[ROW][C]7[/C][C]0.103882[/C][C]0.7197[/C][C]0.237594[/C][/ROW]
[ROW][C]8[/C][C]-0.085107[/C][C]-0.5896[/C][C]0.279099[/C][/ROW]
[ROW][C]9[/C][C]0.101691[/C][C]0.7045[/C][C]0.242252[/C][/ROW]
[ROW][C]10[/C][C]-0.045102[/C][C]-0.3125[/C][C]0.378016[/C][/ROW]
[ROW][C]11[/C][C]0.291381[/C][C]2.0187[/C][C]0.024559[/C][/ROW]
[ROW][C]12[/C][C]-0.22474[/C][C]-1.557[/C][C]0.063015[/C][/ROW]
[ROW][C]13[/C][C]-0.10839[/C][C]-0.751[/C][C]0.228174[/C][/ROW]
[ROW][C]14[/C][C]0.172781[/C][C]1.1971[/C][C]0.11858[/C][/ROW]
[ROW][C]15[/C][C]-0.192491[/C][C]-1.3336[/C][C]0.094312[/C][/ROW]
[ROW][C]16[/C][C]-0.203059[/C][C]-1.4068[/C][C]0.082959[/C][/ROW]
[ROW][C]17[/C][C]-0.066299[/C][C]-0.4593[/C][C]0.324033[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30464&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30464&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	-0.077212	-0.5349	0.297581
2	0.086379	0.5984	0.276177
3	-0.127468	-0.8831	0.190785
4	0.020384	0.1412	0.444142
5	-0.198484	-1.3751	0.087737
6	-0.03439	-0.2383	0.406347
7	0.103882	0.7197	0.237594
8	-0.085107	-0.5896	0.279099
9	0.101691	0.7045	0.242252
10	-0.045102	-0.3125	0.378016
11	0.291381	2.0187	0.024559
12	-0.22474	-1.557	0.063015
13	-0.10839	-0.751	0.228174
14	0.172781	1.1971	0.11858
15	-0.192491	-1.3336	0.094312
16	-0.203059	-1.4068	0.082959
17	-0.066299	-0.4593	0.324033

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 = 1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code