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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

Sat, 28 Nov 2009 07:13:10 -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/2009/Nov/28/t1259417633efa262ma2qwlmag.htm/, Retrieved Fri, 03 May 2024 14:09:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61471, Retrieved Fri, 03 May 2024 14:09:11 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

WS8 ACF reeks met d=1 seas = 12

Estimated Impact

128

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

-     [Univariate Data Series] [Populatieaangroei...] [2009-10-19 21:35:49] [9319fa3e1cb204243a6af248e59767c6]
- RMPD    [(Partial) Autocorrelation Function] [WS8 ACF reeks met...] [2009-11-28 14:13:10] [85defb7a20869746625978e6577e6e44] [Current]
- RMP       [ARIMA Backward Selection] [ARIMA backward se...] [2009-12-11 14:15:55] [9319fa3e1cb204243a6af248e59767c6] 

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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=61471&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=61471&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61471&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	-0.19479	-1.6528	0.051358
2	0.022942	0.1947	0.423099
3	0.142538	1.2095	0.115219
4	0.057944	0.4917	0.312225
5	0.001271	0.0108	0.495714
6	0.044215	0.3752	0.354315
7	-0.001971	-0.0167	0.493352
8	-0.04103	-0.3482	0.364371
9	0.036263	0.3077	0.379599
10	0.060119	0.5101	0.305761
11	-0.002106	-0.0179	0.492897
12	-0.072288	-0.6134	0.270777
13	0.014972	0.127	0.449632
14	0.170136	1.4437	0.076587
15	0.011434	0.097	0.461489
16	0.004081	0.0346	0.486235
17	0.038943	0.3304	0.371012
18	-0.013796	-0.1171	0.453569
19	0.022374	0.1899	0.424979

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.19479 & -1.6528 & 0.051358 \tabularnewline
2 & 0.022942 & 0.1947 & 0.423099 \tabularnewline
3 & 0.142538 & 1.2095 & 0.115219 \tabularnewline
4 & 0.057944 & 0.4917 & 0.312225 \tabularnewline
5 & 0.001271 & 0.0108 & 0.495714 \tabularnewline
6 & 0.044215 & 0.3752 & 0.354315 \tabularnewline
7 & -0.001971 & -0.0167 & 0.493352 \tabularnewline
8 & -0.04103 & -0.3482 & 0.364371 \tabularnewline
9 & 0.036263 & 0.3077 & 0.379599 \tabularnewline
10 & 0.060119 & 0.5101 & 0.305761 \tabularnewline
11 & -0.002106 & -0.0179 & 0.492897 \tabularnewline
12 & -0.072288 & -0.6134 & 0.270777 \tabularnewline
13 & 0.014972 & 0.127 & 0.449632 \tabularnewline
14 & 0.170136 & 1.4437 & 0.076587 \tabularnewline
15 & 0.011434 & 0.097 & 0.461489 \tabularnewline
16 & 0.004081 & 0.0346 & 0.486235 \tabularnewline
17 & 0.038943 & 0.3304 & 0.371012 \tabularnewline
18 & -0.013796 & -0.1171 & 0.453569 \tabularnewline
19 & 0.022374 & 0.1899 & 0.424979 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61471&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]-0.19479[/C][C]-1.6528[/C][C]0.051358[/C][/ROW]
[ROW][C]2[/C][C]0.022942[/C][C]0.1947[/C][C]0.423099[/C][/ROW]
[ROW][C]3[/C][C]0.142538[/C][C]1.2095[/C][C]0.115219[/C][/ROW]
[ROW][C]4[/C][C]0.057944[/C][C]0.4917[/C][C]0.312225[/C][/ROW]
[ROW][C]5[/C][C]0.001271[/C][C]0.0108[/C][C]0.495714[/C][/ROW]
[ROW][C]6[/C][C]0.044215[/C][C]0.3752[/C][C]0.354315[/C][/ROW]
[ROW][C]7[/C][C]-0.001971[/C][C]-0.0167[/C][C]0.493352[/C][/ROW]
[ROW][C]8[/C][C]-0.04103[/C][C]-0.3482[/C][C]0.364371[/C][/ROW]
[ROW][C]9[/C][C]0.036263[/C][C]0.3077[/C][C]0.379599[/C][/ROW]
[ROW][C]10[/C][C]0.060119[/C][C]0.5101[/C][C]0.305761[/C][/ROW]
[ROW][C]11[/C][C]-0.002106[/C][C]-0.0179[/C][C]0.492897[/C][/ROW]
[ROW][C]12[/C][C]-0.072288[/C][C]-0.6134[/C][C]0.270777[/C][/ROW]
[ROW][C]13[/C][C]0.014972[/C][C]0.127[/C][C]0.449632[/C][/ROW]
[ROW][C]14[/C][C]0.170136[/C][C]1.4437[/C][C]0.076587[/C][/ROW]
[ROW][C]15[/C][C]0.011434[/C][C]0.097[/C][C]0.461489[/C][/ROW]
[ROW][C]16[/C][C]0.004081[/C][C]0.0346[/C][C]0.486235[/C][/ROW]
[ROW][C]17[/C][C]0.038943[/C][C]0.3304[/C][C]0.371012[/C][/ROW]
[ROW][C]18[/C][C]-0.013796[/C][C]-0.1171[/C][C]0.453569[/C][/ROW]
[ROW][C]19[/C][C]0.022374[/C][C]0.1899[/C][C]0.424979[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61471&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61471&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	-0.19479	-1.6528	0.051358
2	0.022942	0.1947	0.423099
3	0.142538	1.2095	0.115219
4	0.057944	0.4917	0.312225
5	0.001271	0.0108	0.495714
6	0.044215	0.3752	0.354315
7	-0.001971	-0.0167	0.493352
8	-0.04103	-0.3482	0.364371
9	0.036263	0.3077	0.379599
10	0.060119	0.5101	0.305761
11	-0.002106	-0.0179	0.492897
12	-0.072288	-0.6134	0.270777
13	0.014972	0.127	0.449632
14	0.170136	1.4437	0.076587
15	0.011434	0.097	0.461489
16	0.004081	0.0346	0.486235
17	0.038943	0.3304	0.371012
18	-0.013796	-0.1171	0.453569
19	0.022374	0.1899	0.424979

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.19479	-1.6528	0.051358
2	-0.015592	-0.1323	0.447556
3	0.149756	1.2707	0.103959
4	0.121943	1.0347	0.15213
5	0.034191	0.2901	0.386278
6	0.025004	0.2122	0.41629
7	-0.017872	-0.1516	0.439945
8	-0.063969	-0.5428	0.294475
9	0.00185	0.0157	0.493759
10	0.073325	0.6222	0.267894
11	0.045563	0.3866	0.350092
12	-0.071789	-0.6091	0.272172
13	-0.045178	-0.3834	0.351294
14	0.167106	1.4179	0.08026
15	0.113194	0.9605	0.170014
16	0.032252	0.2737	0.392561
17	-0.010306	-0.0875	0.465277
18	-0.056504	-0.4795	0.316535
19	-0.020971	-0.1779	0.429632

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.19479 & -1.6528 & 0.051358 \tabularnewline
2 & -0.015592 & -0.1323 & 0.447556 \tabularnewline
3 & 0.149756 & 1.2707 & 0.103959 \tabularnewline
4 & 0.121943 & 1.0347 & 0.15213 \tabularnewline
5 & 0.034191 & 0.2901 & 0.386278 \tabularnewline
6 & 0.025004 & 0.2122 & 0.41629 \tabularnewline
7 & -0.017872 & -0.1516 & 0.439945 \tabularnewline
8 & -0.063969 & -0.5428 & 0.294475 \tabularnewline
9 & 0.00185 & 0.0157 & 0.493759 \tabularnewline
10 & 0.073325 & 0.6222 & 0.267894 \tabularnewline
11 & 0.045563 & 0.3866 & 0.350092 \tabularnewline
12 & -0.071789 & -0.6091 & 0.272172 \tabularnewline
13 & -0.045178 & -0.3834 & 0.351294 \tabularnewline
14 & 0.167106 & 1.4179 & 0.08026 \tabularnewline
15 & 0.113194 & 0.9605 & 0.170014 \tabularnewline
16 & 0.032252 & 0.2737 & 0.392561 \tabularnewline
17 & -0.010306 & -0.0875 & 0.465277 \tabularnewline
18 & -0.056504 & -0.4795 & 0.316535 \tabularnewline
19 & -0.020971 & -0.1779 & 0.429632 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61471&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]-0.19479[/C][C]-1.6528[/C][C]0.051358[/C][/ROW]
[ROW][C]2[/C][C]-0.015592[/C][C]-0.1323[/C][C]0.447556[/C][/ROW]
[ROW][C]3[/C][C]0.149756[/C][C]1.2707[/C][C]0.103959[/C][/ROW]
[ROW][C]4[/C][C]0.121943[/C][C]1.0347[/C][C]0.15213[/C][/ROW]
[ROW][C]5[/C][C]0.034191[/C][C]0.2901[/C][C]0.386278[/C][/ROW]
[ROW][C]6[/C][C]0.025004[/C][C]0.2122[/C][C]0.41629[/C][/ROW]
[ROW][C]7[/C][C]-0.017872[/C][C]-0.1516[/C][C]0.439945[/C][/ROW]
[ROW][C]8[/C][C]-0.063969[/C][C]-0.5428[/C][C]0.294475[/C][/ROW]
[ROW][C]9[/C][C]0.00185[/C][C]0.0157[/C][C]0.493759[/C][/ROW]
[ROW][C]10[/C][C]0.073325[/C][C]0.6222[/C][C]0.267894[/C][/ROW]
[ROW][C]11[/C][C]0.045563[/C][C]0.3866[/C][C]0.350092[/C][/ROW]
[ROW][C]12[/C][C]-0.071789[/C][C]-0.6091[/C][C]0.272172[/C][/ROW]
[ROW][C]13[/C][C]-0.045178[/C][C]-0.3834[/C][C]0.351294[/C][/ROW]
[ROW][C]14[/C][C]0.167106[/C][C]1.4179[/C][C]0.08026[/C][/ROW]
[ROW][C]15[/C][C]0.113194[/C][C]0.9605[/C][C]0.170014[/C][/ROW]
[ROW][C]16[/C][C]0.032252[/C][C]0.2737[/C][C]0.392561[/C][/ROW]
[ROW][C]17[/C][C]-0.010306[/C][C]-0.0875[/C][C]0.465277[/C][/ROW]
[ROW][C]18[/C][C]-0.056504[/C][C]-0.4795[/C][C]0.316535[/C][/ROW]
[ROW][C]19[/C][C]-0.020971[/C][C]-0.1779[/C][C]0.429632[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61471&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61471&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	-0.19479	-1.6528	0.051358
2	-0.015592	-0.1323	0.447556
3	0.149756	1.2707	0.103959
4	0.121943	1.0347	0.15213
5	0.034191	0.2901	0.386278
6	0.025004	0.2122	0.41629
7	-0.017872	-0.1516	0.439945
8	-0.063969	-0.5428	0.294475
9	0.00185	0.0157	0.493759
10	0.073325	0.6222	0.267894
11	0.045563	0.3866	0.350092
12	-0.071789	-0.6091	0.272172
13	-0.045178	-0.3834	0.351294
14	0.167106	1.4179	0.08026
15	0.113194	0.9605	0.170014
16	0.032252	0.2737	0.392561
17	-0.010306	-0.0875	0.465277
18	-0.056504	-0.4795	0.316535
19	-0.020971	-0.1779	0.429632

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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