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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 06:40:41 -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/t1228743669mkthydr0dct7wi4.htm/, Retrieved Thu, 16 May 2024 10:36:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30484, Retrieved Thu, 16 May 2024 10:36:13 +0000

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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 13:17:45] [3ffd109c9e040b1ae7e5dbe576d4698c]
- RM              [Spectral Analysis] [spectraal] [2008-12-08 13:23:27] [3ffd109c9e040b1ae7e5dbe576d4698c]
F RM                  [(Partial) Autocorrelation Function] [ACF] [2008-12-08 13:40:41] [962e6c9020896982bc8283b8971710a9] [Current]
- 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] 

Feedback Forum

2008-12-15 14:33:34 [Charis Berrevoets] [reply] 
Op het eerste zicht lijkt er inderdaad geen overeenkomst te zijn met de theoretische modellen en zijn er dus geen ARMA-processen aanwezig. Het enige wat je nog had kunnen doen is weer het aantal lags verhogen. Dan zie je een lichte aanwijzing voor een seizoenaal MA-proces in de PACF. In de ACF zien we dat het staafje op lag 12 significant is en dat er dus wel eens sprake zou kunnen zijn van een SMA(1)-proces. Aangezien je dit ook hebt gevonden bij stap 5 denk ik wel dat dit klopt. Maar ik moet toegeven dat het absoluut niet duidelijk is. 

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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=30484&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=30484&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30484&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	-0.176994	-1.2262	0.113044
2	-0.053656	-0.3717	0.355862
3	-0.04127	-0.2859	0.388081
4	0.076313	0.5287	0.299722
5	-0.12994	-0.9002	0.186241
6	0.164354	1.1387	0.130245
7	0.024424	0.1692	0.433171
8	-0.01957	-0.1356	0.446357
9	0.030189	0.2092	0.417607
10	-0.115006	-0.7968	0.214749
11	0.331391	2.2959	0.013044
12	-0.303442	-2.1023	0.020398
13	-0.098681	-0.6837	0.248731
14	0.057497	0.3983	0.346069
15	0.030985	0.2147	0.415466
16	-0.281325	-1.9491	0.028572
17	0.088131	0.6106	0.272176

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.176994 & -1.2262 & 0.113044 \tabularnewline
2 & -0.053656 & -0.3717 & 0.355862 \tabularnewline
3 & -0.04127 & -0.2859 & 0.388081 \tabularnewline
4 & 0.076313 & 0.5287 & 0.299722 \tabularnewline
5 & -0.12994 & -0.9002 & 0.186241 \tabularnewline
6 & 0.164354 & 1.1387 & 0.130245 \tabularnewline
7 & 0.024424 & 0.1692 & 0.433171 \tabularnewline
8 & -0.01957 & -0.1356 & 0.446357 \tabularnewline
9 & 0.030189 & 0.2092 & 0.417607 \tabularnewline
10 & -0.115006 & -0.7968 & 0.214749 \tabularnewline
11 & 0.331391 & 2.2959 & 0.013044 \tabularnewline
12 & -0.303442 & -2.1023 & 0.020398 \tabularnewline
13 & -0.098681 & -0.6837 & 0.248731 \tabularnewline
14 & 0.057497 & 0.3983 & 0.346069 \tabularnewline
15 & 0.030985 & 0.2147 & 0.415466 \tabularnewline
16 & -0.281325 & -1.9491 & 0.028572 \tabularnewline
17 & 0.088131 & 0.6106 & 0.272176 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30484&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]-0.176994[/C][C]-1.2262[/C][C]0.113044[/C][/ROW]
[ROW][C]2[/C][C]-0.053656[/C][C]-0.3717[/C][C]0.355862[/C][/ROW]
[ROW][C]3[/C][C]-0.04127[/C][C]-0.2859[/C][C]0.388081[/C][/ROW]
[ROW][C]4[/C][C]0.076313[/C][C]0.5287[/C][C]0.299722[/C][/ROW]
[ROW][C]5[/C][C]-0.12994[/C][C]-0.9002[/C][C]0.186241[/C][/ROW]
[ROW][C]6[/C][C]0.164354[/C][C]1.1387[/C][C]0.130245[/C][/ROW]
[ROW][C]7[/C][C]0.024424[/C][C]0.1692[/C][C]0.433171[/C][/ROW]
[ROW][C]8[/C][C]-0.01957[/C][C]-0.1356[/C][C]0.446357[/C][/ROW]
[ROW][C]9[/C][C]0.030189[/C][C]0.2092[/C][C]0.417607[/C][/ROW]
[ROW][C]10[/C][C]-0.115006[/C][C]-0.7968[/C][C]0.214749[/C][/ROW]
[ROW][C]11[/C][C]0.331391[/C][C]2.2959[/C][C]0.013044[/C][/ROW]
[ROW][C]12[/C][C]-0.303442[/C][C]-2.1023[/C][C]0.020398[/C][/ROW]
[ROW][C]13[/C][C]-0.098681[/C][C]-0.6837[/C][C]0.248731[/C][/ROW]
[ROW][C]14[/C][C]0.057497[/C][C]0.3983[/C][C]0.346069[/C][/ROW]
[ROW][C]15[/C][C]0.030985[/C][C]0.2147[/C][C]0.415466[/C][/ROW]
[ROW][C]16[/C][C]-0.281325[/C][C]-1.9491[/C][C]0.028572[/C][/ROW]
[ROW][C]17[/C][C]0.088131[/C][C]0.6106[/C][C]0.272176[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30484&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30484&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	-0.176994	-1.2262	0.113044
2	-0.053656	-0.3717	0.355862
3	-0.04127	-0.2859	0.388081
4	0.076313	0.5287	0.299722
5	-0.12994	-0.9002	0.186241
6	0.164354	1.1387	0.130245
7	0.024424	0.1692	0.433171
8	-0.01957	-0.1356	0.446357
9	0.030189	0.2092	0.417607
10	-0.115006	-0.7968	0.214749
11	0.331391	2.2959	0.013044
12	-0.303442	-2.1023	0.020398
13	-0.098681	-0.6837	0.248731
14	0.057497	0.3983	0.346069
15	0.030985	0.2147	0.415466
16	-0.281325	-1.9491	0.028572
17	0.088131	0.6106	0.272176

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.176994	-1.2262	0.113044
2	-0.087731	-0.6078	0.273087
3	-0.069837	-0.4838	0.315349
4	0.052612	0.3645	0.35854
5	-0.118349	-0.8199	0.20815
6	0.133328	0.9237	0.180125
7	0.069315	0.4802	0.316624
8	0.006439	0.0446	0.482302
9	0.0687	0.476	0.318129
10	-0.136709	-0.9471	0.174153
11	0.358316	2.4825	0.008298
12	-0.300118	-2.0793	0.021479
13	-0.155929	-1.0803	0.142701
14	0.060289	0.4177	0.339017
15	-0.152453	-1.0562	0.148077
16	-0.167456	-1.1602	0.125859
17	-0.186424	-1.2916	0.101344

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.176994 & -1.2262 & 0.113044 \tabularnewline
2 & -0.087731 & -0.6078 & 0.273087 \tabularnewline
3 & -0.069837 & -0.4838 & 0.315349 \tabularnewline
4 & 0.052612 & 0.3645 & 0.35854 \tabularnewline
5 & -0.118349 & -0.8199 & 0.20815 \tabularnewline
6 & 0.133328 & 0.9237 & 0.180125 \tabularnewline
7 & 0.069315 & 0.4802 & 0.316624 \tabularnewline
8 & 0.006439 & 0.0446 & 0.482302 \tabularnewline
9 & 0.0687 & 0.476 & 0.318129 \tabularnewline
10 & -0.136709 & -0.9471 & 0.174153 \tabularnewline
11 & 0.358316 & 2.4825 & 0.008298 \tabularnewline
12 & -0.300118 & -2.0793 & 0.021479 \tabularnewline
13 & -0.155929 & -1.0803 & 0.142701 \tabularnewline
14 & 0.060289 & 0.4177 & 0.339017 \tabularnewline
15 & -0.152453 & -1.0562 & 0.148077 \tabularnewline
16 & -0.167456 & -1.1602 & 0.125859 \tabularnewline
17 & -0.186424 & -1.2916 & 0.101344 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30484&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]-0.176994[/C][C]-1.2262[/C][C]0.113044[/C][/ROW]
[ROW][C]2[/C][C]-0.087731[/C][C]-0.6078[/C][C]0.273087[/C][/ROW]
[ROW][C]3[/C][C]-0.069837[/C][C]-0.4838[/C][C]0.315349[/C][/ROW]
[ROW][C]4[/C][C]0.052612[/C][C]0.3645[/C][C]0.35854[/C][/ROW]
[ROW][C]5[/C][C]-0.118349[/C][C]-0.8199[/C][C]0.20815[/C][/ROW]
[ROW][C]6[/C][C]0.133328[/C][C]0.9237[/C][C]0.180125[/C][/ROW]
[ROW][C]7[/C][C]0.069315[/C][C]0.4802[/C][C]0.316624[/C][/ROW]
[ROW][C]8[/C][C]0.006439[/C][C]0.0446[/C][C]0.482302[/C][/ROW]
[ROW][C]9[/C][C]0.0687[/C][C]0.476[/C][C]0.318129[/C][/ROW]
[ROW][C]10[/C][C]-0.136709[/C][C]-0.9471[/C][C]0.174153[/C][/ROW]
[ROW][C]11[/C][C]0.358316[/C][C]2.4825[/C][C]0.008298[/C][/ROW]
[ROW][C]12[/C][C]-0.300118[/C][C]-2.0793[/C][C]0.021479[/C][/ROW]
[ROW][C]13[/C][C]-0.155929[/C][C]-1.0803[/C][C]0.142701[/C][/ROW]
[ROW][C]14[/C][C]0.060289[/C][C]0.4177[/C][C]0.339017[/C][/ROW]
[ROW][C]15[/C][C]-0.152453[/C][C]-1.0562[/C][C]0.148077[/C][/ROW]
[ROW][C]16[/C][C]-0.167456[/C][C]-1.1602[/C][C]0.125859[/C][/ROW]
[ROW][C]17[/C][C]-0.186424[/C][C]-1.2916[/C][C]0.101344[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30484&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30484&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	-0.176994	-1.2262	0.113044
2	-0.087731	-0.6078	0.273087
3	-0.069837	-0.4838	0.315349
4	0.052612	0.3645	0.35854
5	-0.118349	-0.8199	0.20815
6	0.133328	0.9237	0.180125
7	0.069315	0.4802	0.316624
8	0.006439	0.0446	0.482302
9	0.0687	0.476	0.318129
10	-0.136709	-0.9471	0.174153
11	0.358316	2.4825	0.008298
12	-0.300118	-2.0793	0.021479
13	-0.155929	-1.0803	0.142701
14	0.060289	0.4177	0.339017
15	-0.152453	-1.0562	0.148077
16	-0.167456	-1.1602	0.125859
17	-0.186424	-1.2916	0.101344

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 = -0.1 ; 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')

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Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code