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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 24 Nov 2007 11:03:18 -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/2007/Nov/24/t1195926900cpla5vg3fm4p66s.htm/, Retrieved Fri, 03 May 2024 04:24:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6352, Retrieved Fri, 03 May 2024 04:24:48 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

235

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [WS10Q2FINSIT] [2007-11-24 18:03:18] [e0964b90cb3acfe235da067e79729c23] [Current]
-   PD    [(Partial) Autocorrelation Function] [WS10Q2FINSIT] [2007-11-25 01:00:49] [74be16979710d4c4e7c6647856088456] 
- RMPD    [Spectral Analysis] [WS10Q2FINSIT] [2007-11-25 01:25:07] [74be16979710d4c4e7c6647856088456] 
- RMPD    [Variance Reduction Matrix] [WS10Q2WERKL] [2007-11-25 01:43:46] [6b20c0ed55154a4fb9df5a5e4fa0b426] 
-   PD    [(Partial) Autocorrelation Function] [WS10Q2WERKL] [2007-11-25 01:47:19] [6b20c0ed55154a4fb9df5a5e4fa0b426] 
-   PD    [(Partial) Autocorrelation Function] [WS10Q2WERKL NA DI...] [2007-11-25 01:53:58] [6b20c0ed55154a4fb9df5a5e4fa0b426] 
- RMPD    [Spectral Analysis] [WS10Q2WERKL] [2007-11-25 02:03:21] [6b20c0ed55154a4fb9df5a5e4fa0b426] 
- RMPD    [Spectral Analysis] [WS10Q2WERKL NA DI...] [2007-11-25 02:06:22] [6b20c0ed55154a4fb9df5a5e4fa0b426] 
- RMPD    [Cross Correlation Function] [WS10Q5] [2007-11-25 02:29:25] [6b20c0ed55154a4fb9df5a5e4fa0b426] 
- RMPD    [Cross Correlation Function] [WS10Q5ZONDER DIFF] [2007-11-25 02:38:22] [6b20c0ed55154a4fb9df5a5e4fa0b426] 

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Summary of compuational 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 compuational 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=6352&T=0

[TABLE]
[ROW][C]Summary of compuational 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=6352&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6352&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 compuational 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
0	1	7.746	0
1	0.608163	4.7108	8e-06
2	0.475745	3.6851	0.000247
3	0.350323	2.7136	0.004338
4	0.337657	2.6155	0.005627
5	0.236186	1.8295	0.036148
6	0.212217	1.6438	0.052721
7	0.08841	0.6848	0.248046
8	0.03188	0.2469	0.402898
9	0.043972	0.3406	0.367295
10	0.100197	0.7761	0.220362
11	0.132741	1.0282	0.153989
12	0.103929	0.805	0.21199
13	0.030983	0.24	0.405576
14	-0.062146	-0.4814	0.684001
15	-0.103606	-0.8025	0.787293
16	-0.100664	-0.7797	0.780695

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.608163 & 4.7108 & 8e-06 \tabularnewline
2 & 0.475745 & 3.6851 & 0.000247 \tabularnewline
3 & 0.350323 & 2.7136 & 0.004338 \tabularnewline
4 & 0.337657 & 2.6155 & 0.005627 \tabularnewline
5 & 0.236186 & 1.8295 & 0.036148 \tabularnewline
6 & 0.212217 & 1.6438 & 0.052721 \tabularnewline
7 & 0.08841 & 0.6848 & 0.248046 \tabularnewline
8 & 0.03188 & 0.2469 & 0.402898 \tabularnewline
9 & 0.043972 & 0.3406 & 0.367295 \tabularnewline
10 & 0.100197 & 0.7761 & 0.220362 \tabularnewline
11 & 0.132741 & 1.0282 & 0.153989 \tabularnewline
12 & 0.103929 & 0.805 & 0.21199 \tabularnewline
13 & 0.030983 & 0.24 & 0.405576 \tabularnewline
14 & -0.062146 & -0.4814 & 0.684001 \tabularnewline
15 & -0.103606 & -0.8025 & 0.787293 \tabularnewline
16 & -0.100664 & -0.7797 & 0.780695 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6352&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]0[/C][C]1[/C][C]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.608163[/C][C]4.7108[/C][C]8e-06[/C][/ROW]
[ROW][C]2[/C][C]0.475745[/C][C]3.6851[/C][C]0.000247[/C][/ROW]
[ROW][C]3[/C][C]0.350323[/C][C]2.7136[/C][C]0.004338[/C][/ROW]
[ROW][C]4[/C][C]0.337657[/C][C]2.6155[/C][C]0.005627[/C][/ROW]
[ROW][C]5[/C][C]0.236186[/C][C]1.8295[/C][C]0.036148[/C][/ROW]
[ROW][C]6[/C][C]0.212217[/C][C]1.6438[/C][C]0.052721[/C][/ROW]
[ROW][C]7[/C][C]0.08841[/C][C]0.6848[/C][C]0.248046[/C][/ROW]
[ROW][C]8[/C][C]0.03188[/C][C]0.2469[/C][C]0.402898[/C][/ROW]
[ROW][C]9[/C][C]0.043972[/C][C]0.3406[/C][C]0.367295[/C][/ROW]
[ROW][C]10[/C][C]0.100197[/C][C]0.7761[/C][C]0.220362[/C][/ROW]
[ROW][C]11[/C][C]0.132741[/C][C]1.0282[/C][C]0.153989[/C][/ROW]
[ROW][C]12[/C][C]0.103929[/C][C]0.805[/C][C]0.21199[/C][/ROW]
[ROW][C]13[/C][C]0.030983[/C][C]0.24[/C][C]0.405576[/C][/ROW]
[ROW][C]14[/C][C]-0.062146[/C][C]-0.4814[/C][C]0.684001[/C][/ROW]
[ROW][C]15[/C][C]-0.103606[/C][C]-0.8025[/C][C]0.787293[/C][/ROW]
[ROW][C]16[/C][C]-0.100664[/C][C]-0.7797[/C][C]0.780695[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6352&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6352&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
0	1	7.746	0
1	0.608163	4.7108	8e-06
2	0.475745	3.6851	0.000247
3	0.350323	2.7136	0.004338
4	0.337657	2.6155	0.005627
5	0.236186	1.8295	0.036148
6	0.212217	1.6438	0.052721
7	0.08841	0.6848	0.248046
8	0.03188	0.2469	0.402898
9	0.043972	0.3406	0.367295
10	0.100197	0.7761	0.220362
11	0.132741	1.0282	0.153989
12	0.103929	0.805	0.21199
13	0.030983	0.24	0.405576
14	-0.062146	-0.4814	0.684001
15	-0.103606	-0.8025	0.787293
16	-0.100664	-0.7797	0.780695

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.608163	4.7108	8e-06
1	0.168031	1.3016	0.099021
2	0.012116	0.0938	0.462771
3	0.125315	0.9707	0.167802
4	-0.05808	-0.4499	0.672793
5	0.03636	0.2816	0.389594
6	-0.126233	-0.9778	0.83395
7	-0.05706	-0.442	0.669956
8	0.083824	0.6493	0.259311
9	0.098036	0.7594	0.225298
10	0.094142	0.7292	0.234352
11	-0.031964	-0.2476	0.597354
12	-0.10549	-0.8171	0.791455
13	-0.158017	-1.224	0.88713
14	-0.100452	-0.7781	0.780215
15	0.002713	0.021	0.491652
16	0.00592	0.0459	0.481788

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.608163 & 4.7108 & 8e-06 \tabularnewline
1 & 0.168031 & 1.3016 & 0.099021 \tabularnewline
2 & 0.012116 & 0.0938 & 0.462771 \tabularnewline
3 & 0.125315 & 0.9707 & 0.167802 \tabularnewline
4 & -0.05808 & -0.4499 & 0.672793 \tabularnewline
5 & 0.03636 & 0.2816 & 0.389594 \tabularnewline
6 & -0.126233 & -0.9778 & 0.83395 \tabularnewline
7 & -0.05706 & -0.442 & 0.669956 \tabularnewline
8 & 0.083824 & 0.6493 & 0.259311 \tabularnewline
9 & 0.098036 & 0.7594 & 0.225298 \tabularnewline
10 & 0.094142 & 0.7292 & 0.234352 \tabularnewline
11 & -0.031964 & -0.2476 & 0.597354 \tabularnewline
12 & -0.10549 & -0.8171 & 0.791455 \tabularnewline
13 & -0.158017 & -1.224 & 0.88713 \tabularnewline
14 & -0.100452 & -0.7781 & 0.780215 \tabularnewline
15 & 0.002713 & 0.021 & 0.491652 \tabularnewline
16 & 0.00592 & 0.0459 & 0.481788 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6352&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]0[/C][C]0.608163[/C][C]4.7108[/C][C]8e-06[/C][/ROW]
[ROW][C]1[/C][C]0.168031[/C][C]1.3016[/C][C]0.099021[/C][/ROW]
[ROW][C]2[/C][C]0.012116[/C][C]0.0938[/C][C]0.462771[/C][/ROW]
[ROW][C]3[/C][C]0.125315[/C][C]0.9707[/C][C]0.167802[/C][/ROW]
[ROW][C]4[/C][C]-0.05808[/C][C]-0.4499[/C][C]0.672793[/C][/ROW]
[ROW][C]5[/C][C]0.03636[/C][C]0.2816[/C][C]0.389594[/C][/ROW]
[ROW][C]6[/C][C]-0.126233[/C][C]-0.9778[/C][C]0.83395[/C][/ROW]
[ROW][C]7[/C][C]-0.05706[/C][C]-0.442[/C][C]0.669956[/C][/ROW]
[ROW][C]8[/C][C]0.083824[/C][C]0.6493[/C][C]0.259311[/C][/ROW]
[ROW][C]9[/C][C]0.098036[/C][C]0.7594[/C][C]0.225298[/C][/ROW]
[ROW][C]10[/C][C]0.094142[/C][C]0.7292[/C][C]0.234352[/C][/ROW]
[ROW][C]11[/C][C]-0.031964[/C][C]-0.2476[/C][C]0.597354[/C][/ROW]
[ROW][C]12[/C][C]-0.10549[/C][C]-0.8171[/C][C]0.791455[/C][/ROW]
[ROW][C]13[/C][C]-0.158017[/C][C]-1.224[/C][C]0.88713[/C][/ROW]
[ROW][C]14[/C][C]-0.100452[/C][C]-0.7781[/C][C]0.780215[/C][/ROW]
[ROW][C]15[/C][C]0.002713[/C][C]0.021[/C][C]0.491652[/C][/ROW]
[ROW][C]16[/C][C]0.00592[/C][C]0.0459[/C][C]0.481788[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6352&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6352&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
0	0.608163	4.7108	8e-06
1	0.168031	1.3016	0.099021
2	0.012116	0.0938	0.462771
3	0.125315	0.9707	0.167802
4	-0.05808	-0.4499	0.672793
5	0.03636	0.2816	0.389594
6	-0.126233	-0.9778	0.83395
7	-0.05706	-0.442	0.669956
8	0.083824	0.6493	0.259311
9	0.098036	0.7594	0.225298
10	0.094142	0.7292	0.234352
11	-0.031964	-0.2476	0.597354
12	-0.10549	-0.8171	0.791455
13	-0.158017	-1.224	0.88713
14	-0.100452	-0.7781	0.780215
15	0.002713	0.021	0.491652
16	0.00592	0.0459	0.481788

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 = 0 ; par5 = 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 1:par1) {
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(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-1,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(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