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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 13:26:52 -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/t1228249730rbw01yowdfhdlwm.htm/, Retrieved Sun, 19 May 2024 10:05:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28379, Retrieved Sun, 19 May 2024 10:05:28 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Van Dooren Leen

Estimated Impact

142

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] [NST Q8] [2008-12-02 20:26:52] [006ad2c49b6a7c2ad6ab685cfc1dae56] [Current]

Feedback Forum

2008-12-06 19:40:43 [Stefan Temmerman] [reply] 
De student heeft de tijdreeks mooi stationair gemaakt, alle correlaties vallen binnen het betrouwbaarheidsinterval na de differentiatie. De eerste verticale lijn is voor ons irrelevant.
2008-12-07 11:24:45 [006ad2c49b6a7c2ad6ab685cfc1dae56] [reply] 
Goede differentiaties.
2008-12-07 11:58:49 [Lana Van Wesemael] [reply] 
Ook hier geeft de studente haar stappen logisch weer. De studente schrijft dat alle correlatiecoëfficiënten binnen het betrouwbaarheidsinterval vallen, behalve de eerste. Maar we moeten echter niet kijken naar het streepje op lag 0. De studente is vergeten om de juiste lambda waarde te zoeken. Deze kan men vinden met behulp van de standard deviation mean plot, er wordt dan 2 tabellen gegenereerd waar de lambda waarde in gegeven staat.
2008-12-08 19:46:08 [Birgit Van Dyck] [reply] 
De student is vergeten de lambda te berrekenen. Dit kan met behulp van de standard deviation-mean plot. De tabel geeft dan de optimale Lambda waarde weer om de tijdreeks stationair te maken.

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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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28379&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]2 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=28379&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28379&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.014143	-0.1068	0.457671
2	0.055819	0.4214	0.337516
3	0.154012	1.1628	0.124885
4	0.024564	0.1855	0.426766
5	0.001983	0.015	0.494055
6	0.046239	0.3491	0.364152
7	-0.010477	-0.0791	0.468615
8	0.128692	0.9716	0.167677
9	-0.060857	-0.4595	0.323826
10	-0.199637	-1.5072	0.068637
11	0.121422	0.9167	0.181576
12	-0.233167	-1.7604	0.041855
13	-0.161938	-1.2226	0.113256
14	0.092059	0.695	0.24493
15	0.035985	0.2717	0.393423
16	-0.06958	-0.5253	0.300699
17	-0.044058	-0.3326	0.370316
18	0.052503	0.3964	0.34665

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.014143 & -0.1068 & 0.457671 \tabularnewline
2 & 0.055819 & 0.4214 & 0.337516 \tabularnewline
3 & 0.154012 & 1.1628 & 0.124885 \tabularnewline
4 & 0.024564 & 0.1855 & 0.426766 \tabularnewline
5 & 0.001983 & 0.015 & 0.494055 \tabularnewline
6 & 0.046239 & 0.3491 & 0.364152 \tabularnewline
7 & -0.010477 & -0.0791 & 0.468615 \tabularnewline
8 & 0.128692 & 0.9716 & 0.167677 \tabularnewline
9 & -0.060857 & -0.4595 & 0.323826 \tabularnewline
10 & -0.199637 & -1.5072 & 0.068637 \tabularnewline
11 & 0.121422 & 0.9167 & 0.181576 \tabularnewline
12 & -0.233167 & -1.7604 & 0.041855 \tabularnewline
13 & -0.161938 & -1.2226 & 0.113256 \tabularnewline
14 & 0.092059 & 0.695 & 0.24493 \tabularnewline
15 & 0.035985 & 0.2717 & 0.393423 \tabularnewline
16 & -0.06958 & -0.5253 & 0.300699 \tabularnewline
17 & -0.044058 & -0.3326 & 0.370316 \tabularnewline
18 & 0.052503 & 0.3964 & 0.34665 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28379&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]-0.014143[/C][C]-0.1068[/C][C]0.457671[/C][/ROW]
[ROW][C]2[/C][C]0.055819[/C][C]0.4214[/C][C]0.337516[/C][/ROW]
[ROW][C]3[/C][C]0.154012[/C][C]1.1628[/C][C]0.124885[/C][/ROW]
[ROW][C]4[/C][C]0.024564[/C][C]0.1855[/C][C]0.426766[/C][/ROW]
[ROW][C]5[/C][C]0.001983[/C][C]0.015[/C][C]0.494055[/C][/ROW]
[ROW][C]6[/C][C]0.046239[/C][C]0.3491[/C][C]0.364152[/C][/ROW]
[ROW][C]7[/C][C]-0.010477[/C][C]-0.0791[/C][C]0.468615[/C][/ROW]
[ROW][C]8[/C][C]0.128692[/C][C]0.9716[/C][C]0.167677[/C][/ROW]
[ROW][C]9[/C][C]-0.060857[/C][C]-0.4595[/C][C]0.323826[/C][/ROW]
[ROW][C]10[/C][C]-0.199637[/C][C]-1.5072[/C][C]0.068637[/C][/ROW]
[ROW][C]11[/C][C]0.121422[/C][C]0.9167[/C][C]0.181576[/C][/ROW]
[ROW][C]12[/C][C]-0.233167[/C][C]-1.7604[/C][C]0.041855[/C][/ROW]
[ROW][C]13[/C][C]-0.161938[/C][C]-1.2226[/C][C]0.113256[/C][/ROW]
[ROW][C]14[/C][C]0.092059[/C][C]0.695[/C][C]0.24493[/C][/ROW]
[ROW][C]15[/C][C]0.035985[/C][C]0.2717[/C][C]0.393423[/C][/ROW]
[ROW][C]16[/C][C]-0.06958[/C][C]-0.5253[/C][C]0.300699[/C][/ROW]
[ROW][C]17[/C][C]-0.044058[/C][C]-0.3326[/C][C]0.370316[/C][/ROW]
[ROW][C]18[/C][C]0.052503[/C][C]0.3964[/C][C]0.34665[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28379&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28379&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	-0.014143	-0.1068	0.457671
2	0.055819	0.4214	0.337516
3	0.154012	1.1628	0.124885
4	0.024564	0.1855	0.426766
5	0.001983	0.015	0.494055
6	0.046239	0.3491	0.364152
7	-0.010477	-0.0791	0.468615
8	0.128692	0.9716	0.167677
9	-0.060857	-0.4595	0.323826
10	-0.199637	-1.5072	0.068637
11	0.121422	0.9167	0.181576
12	-0.233167	-1.7604	0.041855
13	-0.161938	-1.2226	0.113256
14	0.092059	0.695	0.24493
15	0.035985	0.2717	0.393423
16	-0.06958	-0.5253	0.300699
17	-0.044058	-0.3326	0.370316
18	0.052503	0.3964	0.34665

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.014143	-0.1068	0.457671
2	0.05563	0.42	0.338034
3	0.156058	1.1782	0.121803
4	0.027707	0.2092	0.417525
5	-0.014784	-0.1116	0.45576
6	0.019418	0.1466	0.44198
7	-0.01664	-0.1256	0.450233
8	0.129272	0.976	0.166599
9	-0.065962	-0.498	0.310199
10	-0.225121	-1.6996	0.047326
11	0.08993	0.679	0.249955
12	-0.210376	-1.5883	0.058875
13	-0.125885	-0.9504	0.172958
14	0.103518	0.7815	0.218857
15	0.121145	0.9146	0.182121
16	-0.031042	-0.2344	0.407773
17	-0.077892	-0.5881	0.279403
18	0.116363	0.8785	0.191674

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.014143 & -0.1068 & 0.457671 \tabularnewline
2 & 0.05563 & 0.42 & 0.338034 \tabularnewline
3 & 0.156058 & 1.1782 & 0.121803 \tabularnewline
4 & 0.027707 & 0.2092 & 0.417525 \tabularnewline
5 & -0.014784 & -0.1116 & 0.45576 \tabularnewline
6 & 0.019418 & 0.1466 & 0.44198 \tabularnewline
7 & -0.01664 & -0.1256 & 0.450233 \tabularnewline
8 & 0.129272 & 0.976 & 0.166599 \tabularnewline
9 & -0.065962 & -0.498 & 0.310199 \tabularnewline
10 & -0.225121 & -1.6996 & 0.047326 \tabularnewline
11 & 0.08993 & 0.679 & 0.249955 \tabularnewline
12 & -0.210376 & -1.5883 & 0.058875 \tabularnewline
13 & -0.125885 & -0.9504 & 0.172958 \tabularnewline
14 & 0.103518 & 0.7815 & 0.218857 \tabularnewline
15 & 0.121145 & 0.9146 & 0.182121 \tabularnewline
16 & -0.031042 & -0.2344 & 0.407773 \tabularnewline
17 & -0.077892 & -0.5881 & 0.279403 \tabularnewline
18 & 0.116363 & 0.8785 & 0.191674 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28379&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]-0.014143[/C][C]-0.1068[/C][C]0.457671[/C][/ROW]
[ROW][C]2[/C][C]0.05563[/C][C]0.42[/C][C]0.338034[/C][/ROW]
[ROW][C]3[/C][C]0.156058[/C][C]1.1782[/C][C]0.121803[/C][/ROW]
[ROW][C]4[/C][C]0.027707[/C][C]0.2092[/C][C]0.417525[/C][/ROW]
[ROW][C]5[/C][C]-0.014784[/C][C]-0.1116[/C][C]0.45576[/C][/ROW]
[ROW][C]6[/C][C]0.019418[/C][C]0.1466[/C][C]0.44198[/C][/ROW]
[ROW][C]7[/C][C]-0.01664[/C][C]-0.1256[/C][C]0.450233[/C][/ROW]
[ROW][C]8[/C][C]0.129272[/C][C]0.976[/C][C]0.166599[/C][/ROW]
[ROW][C]9[/C][C]-0.065962[/C][C]-0.498[/C][C]0.310199[/C][/ROW]
[ROW][C]10[/C][C]-0.225121[/C][C]-1.6996[/C][C]0.047326[/C][/ROW]
[ROW][C]11[/C][C]0.08993[/C][C]0.679[/C][C]0.249955[/C][/ROW]
[ROW][C]12[/C][C]-0.210376[/C][C]-1.5883[/C][C]0.058875[/C][/ROW]
[ROW][C]13[/C][C]-0.125885[/C][C]-0.9504[/C][C]0.172958[/C][/ROW]
[ROW][C]14[/C][C]0.103518[/C][C]0.7815[/C][C]0.218857[/C][/ROW]
[ROW][C]15[/C][C]0.121145[/C][C]0.9146[/C][C]0.182121[/C][/ROW]
[ROW][C]16[/C][C]-0.031042[/C][C]-0.2344[/C][C]0.407773[/C][/ROW]
[ROW][C]17[/C][C]-0.077892[/C][C]-0.5881[/C][C]0.279403[/C][/ROW]
[ROW][C]18[/C][C]0.116363[/C][C]0.8785[/C][C]0.191674[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28379&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28379&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	-0.014143	-0.1068	0.457671
2	0.05563	0.42	0.338034
3	0.156058	1.1782	0.121803
4	0.027707	0.2092	0.417525
5	-0.014784	-0.1116	0.45576
6	0.019418	0.1466	0.44198
7	-0.01664	-0.1256	0.450233
8	0.129272	0.976	0.166599
9	-0.065962	-0.498	0.310199
10	-0.225121	-1.6996	0.047326
11	0.08993	0.679	0.249955
12	-0.210376	-1.5883	0.058875
13	-0.125885	-0.9504	0.172958
14	0.103518	0.7815	0.218857
15	0.121145	0.9146	0.182121
16	-0.031042	-0.2344	0.407773
17	-0.077892	-0.5881	0.279403
18	0.116363	0.8785	0.191674

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code