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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, 11 Aug 2012 10:08:21 -0400

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/2012/Aug/11/t1344694128g0wvt0gqgrj9xlz.htm/, Retrieved Mon, 06 May 2024 12:51:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169222, Retrieved Mon, 06 May 2024 12:51:49 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

177

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

-     [(Partial) Autocorrelation Function] [Workshop 6: ACF 2 ] [2010-12-14 13:53:45] [b9eaf9df71639055b3e2389f5099ca2c]
- R  D    [(Partial) Autocorrelation Function] [Berekening 11] [2012-08-11 14:08:21] [0b94335bf72158573fe52322b9537409] [Current]

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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' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169222&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169222&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169222&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' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.10774	-0.7844	0.218161
2	-0.007954	-0.0579	0.47702
3	0.146864	1.0692	0.144915
4	-0.115064	-0.8377	0.202987
5	0.173977	1.2666	0.105423
6	-0.111852	-0.8143	0.209561
7	0.055509	0.4041	0.343878
8	0.032399	0.2359	0.407223
9	-0.385702	-2.8079	0.003482
10	0.094835	0.6904	0.246474
11	0.022931	0.1669	0.434027
12	-0.10647	-0.7751	0.220858
13	0.055643	0.4051	0.343521
14	-0.007366	-0.0536	0.478717
15	0.087204	0.6349	0.264127
16	-0.229917	-1.6738	0.050029
17	-0.086425	-0.6292	0.265965

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.10774 & -0.7844 & 0.218161 \tabularnewline
2 & -0.007954 & -0.0579 & 0.47702 \tabularnewline
3 & 0.146864 & 1.0692 & 0.144915 \tabularnewline
4 & -0.115064 & -0.8377 & 0.202987 \tabularnewline
5 & 0.173977 & 1.2666 & 0.105423 \tabularnewline
6 & -0.111852 & -0.8143 & 0.209561 \tabularnewline
7 & 0.055509 & 0.4041 & 0.343878 \tabularnewline
8 & 0.032399 & 0.2359 & 0.407223 \tabularnewline
9 & -0.385702 & -2.8079 & 0.003482 \tabularnewline
10 & 0.094835 & 0.6904 & 0.246474 \tabularnewline
11 & 0.022931 & 0.1669 & 0.434027 \tabularnewline
12 & -0.10647 & -0.7751 & 0.220858 \tabularnewline
13 & 0.055643 & 0.4051 & 0.343521 \tabularnewline
14 & -0.007366 & -0.0536 & 0.478717 \tabularnewline
15 & 0.087204 & 0.6349 & 0.264127 \tabularnewline
16 & -0.229917 & -1.6738 & 0.050029 \tabularnewline
17 & -0.086425 & -0.6292 & 0.265965 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169222&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]-0.10774[/C][C]-0.7844[/C][C]0.218161[/C][/ROW]
[ROW][C]2[/C][C]-0.007954[/C][C]-0.0579[/C][C]0.47702[/C][/ROW]
[ROW][C]3[/C][C]0.146864[/C][C]1.0692[/C][C]0.144915[/C][/ROW]
[ROW][C]4[/C][C]-0.115064[/C][C]-0.8377[/C][C]0.202987[/C][/ROW]
[ROW][C]5[/C][C]0.173977[/C][C]1.2666[/C][C]0.105423[/C][/ROW]
[ROW][C]6[/C][C]-0.111852[/C][C]-0.8143[/C][C]0.209561[/C][/ROW]
[ROW][C]7[/C][C]0.055509[/C][C]0.4041[/C][C]0.343878[/C][/ROW]
[ROW][C]8[/C][C]0.032399[/C][C]0.2359[/C][C]0.407223[/C][/ROW]
[ROW][C]9[/C][C]-0.385702[/C][C]-2.8079[/C][C]0.003482[/C][/ROW]
[ROW][C]10[/C][C]0.094835[/C][C]0.6904[/C][C]0.246474[/C][/ROW]
[ROW][C]11[/C][C]0.022931[/C][C]0.1669[/C][C]0.434027[/C][/ROW]
[ROW][C]12[/C][C]-0.10647[/C][C]-0.7751[/C][C]0.220858[/C][/ROW]
[ROW][C]13[/C][C]0.055643[/C][C]0.4051[/C][C]0.343521[/C][/ROW]
[ROW][C]14[/C][C]-0.007366[/C][C]-0.0536[/C][C]0.478717[/C][/ROW]
[ROW][C]15[/C][C]0.087204[/C][C]0.6349[/C][C]0.264127[/C][/ROW]
[ROW][C]16[/C][C]-0.229917[/C][C]-1.6738[/C][C]0.050029[/C][/ROW]
[ROW][C]17[/C][C]-0.086425[/C][C]-0.6292[/C][C]0.265965[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169222&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169222&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	-0.10774	-0.7844	0.218161
2	-0.007954	-0.0579	0.47702
3	0.146864	1.0692	0.144915
4	-0.115064	-0.8377	0.202987
5	0.173977	1.2666	0.105423
6	-0.111852	-0.8143	0.209561
7	0.055509	0.4041	0.343878
8	0.032399	0.2359	0.407223
9	-0.385702	-2.8079	0.003482
10	0.094835	0.6904	0.246474
11	0.022931	0.1669	0.434027
12	-0.10647	-0.7751	0.220858
13	0.055643	0.4051	0.343521
14	-0.007366	-0.0536	0.478717
15	0.087204	0.6349	0.264127
16	-0.229917	-1.6738	0.050029
17	-0.086425	-0.6292	0.265965

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.10774	-0.7844	0.218161
2	-0.019792	-0.1441	0.442989
3	0.145604	1.06	0.146972
4	-0.086545	-0.6301	0.265683
5	0.161992	1.1793	0.121769
6	-0.111404	-0.811	0.210488
7	0.078122	0.5687	0.285968
8	-0.024509	-0.1784	0.429534
9	-0.344365	-2.507	0.007638
10	-0.016081	-0.1171	0.453623
11	0.062956	0.4583	0.324297
12	-0.034984	-0.2547	0.399974
13	-0.002642	-0.0192	0.492364
14	0.112679	0.8203	0.207855
15	0.057308	0.4172	0.339106
16	-0.250891	-1.8265	0.036703
17	-0.143163	-1.0422	0.151016

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.10774 & -0.7844 & 0.218161 \tabularnewline
2 & -0.019792 & -0.1441 & 0.442989 \tabularnewline
3 & 0.145604 & 1.06 & 0.146972 \tabularnewline
4 & -0.086545 & -0.6301 & 0.265683 \tabularnewline
5 & 0.161992 & 1.1793 & 0.121769 \tabularnewline
6 & -0.111404 & -0.811 & 0.210488 \tabularnewline
7 & 0.078122 & 0.5687 & 0.285968 \tabularnewline
8 & -0.024509 & -0.1784 & 0.429534 \tabularnewline
9 & -0.344365 & -2.507 & 0.007638 \tabularnewline
10 & -0.016081 & -0.1171 & 0.453623 \tabularnewline
11 & 0.062956 & 0.4583 & 0.324297 \tabularnewline
12 & -0.034984 & -0.2547 & 0.399974 \tabularnewline
13 & -0.002642 & -0.0192 & 0.492364 \tabularnewline
14 & 0.112679 & 0.8203 & 0.207855 \tabularnewline
15 & 0.057308 & 0.4172 & 0.339106 \tabularnewline
16 & -0.250891 & -1.8265 & 0.036703 \tabularnewline
17 & -0.143163 & -1.0422 & 0.151016 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169222&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]-0.10774[/C][C]-0.7844[/C][C]0.218161[/C][/ROW]
[ROW][C]2[/C][C]-0.019792[/C][C]-0.1441[/C][C]0.442989[/C][/ROW]
[ROW][C]3[/C][C]0.145604[/C][C]1.06[/C][C]0.146972[/C][/ROW]
[ROW][C]4[/C][C]-0.086545[/C][C]-0.6301[/C][C]0.265683[/C][/ROW]
[ROW][C]5[/C][C]0.161992[/C][C]1.1793[/C][C]0.121769[/C][/ROW]
[ROW][C]6[/C][C]-0.111404[/C][C]-0.811[/C][C]0.210488[/C][/ROW]
[ROW][C]7[/C][C]0.078122[/C][C]0.5687[/C][C]0.285968[/C][/ROW]
[ROW][C]8[/C][C]-0.024509[/C][C]-0.1784[/C][C]0.429534[/C][/ROW]
[ROW][C]9[/C][C]-0.344365[/C][C]-2.507[/C][C]0.007638[/C][/ROW]
[ROW][C]10[/C][C]-0.016081[/C][C]-0.1171[/C][C]0.453623[/C][/ROW]
[ROW][C]11[/C][C]0.062956[/C][C]0.4583[/C][C]0.324297[/C][/ROW]
[ROW][C]12[/C][C]-0.034984[/C][C]-0.2547[/C][C]0.399974[/C][/ROW]
[ROW][C]13[/C][C]-0.002642[/C][C]-0.0192[/C][C]0.492364[/C][/ROW]
[ROW][C]14[/C][C]0.112679[/C][C]0.8203[/C][C]0.207855[/C][/ROW]
[ROW][C]15[/C][C]0.057308[/C][C]0.4172[/C][C]0.339106[/C][/ROW]
[ROW][C]16[/C][C]-0.250891[/C][C]-1.8265[/C][C]0.036703[/C][/ROW]
[ROW][C]17[/C][C]-0.143163[/C][C]-1.0422[/C][C]0.151016[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169222&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169222&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	-0.10774	-0.7844	0.218161
2	-0.019792	-0.1441	0.442989
3	0.145604	1.06	0.146972
4	-0.086545	-0.6301	0.265683
5	0.161992	1.1793	0.121769
6	-0.111404	-0.811	0.210488
7	0.078122	0.5687	0.285968
8	-0.024509	-0.1784	0.429534
9	-0.344365	-2.507	0.007638
10	-0.016081	-0.1171	0.453623
11	0.062956	0.4583	0.324297
12	-0.034984	-0.2547	0.399974
13	-0.002642	-0.0192	0.492364
14	0.112679	0.8203	0.207855
15	0.057308	0.4172	0.339106
16	-0.250891	-1.8265	0.036703
17	-0.143163	-1.0422	0.151016

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 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code