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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 28 Nov 2007 11:58:24 -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/28/t1196275801fd8wemqql1ra340.htm/, Retrieved Thu, 02 May 2024 12:08:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7219, Retrieved Thu, 02 May 2024 12:08:12 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

171

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

-       [(Partial) Autocorrelation Function] [consumptiegoederen] [2007-11-28 18:58:24] [89d26cd0a44959d9c8b169f34617598a] [Current]

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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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7219&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7219&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7219&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.8102	0
1	0.90051	7.0332	0
2	0.801542	6.2602	0
3	0.707506	5.5258	0
4	0.614219	4.7972	5e-06
5	0.533509	4.1668	4.9e-05
6	0.452659	3.5354	0.000392
7	0.371006	2.8976	0.002608
8	0.288398	2.2525	0.013951
9	0.206845	1.6155	0.055681
10	0.129185	1.009	0.158487
11	0.056101	0.4382	0.331409
12	-0.010631	-0.083	0.532949
13	-0.061546	-0.4807	0.683773
14	-0.105919	-0.8273	0.794341
15	-0.148283	-1.1581	0.874336
16	-0.194107	-1.516	0.932661

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.8102 & 0 \tabularnewline
1 & 0.90051 & 7.0332 & 0 \tabularnewline
2 & 0.801542 & 6.2602 & 0 \tabularnewline
3 & 0.707506 & 5.5258 & 0 \tabularnewline
4 & 0.614219 & 4.7972 & 5e-06 \tabularnewline
5 & 0.533509 & 4.1668 & 4.9e-05 \tabularnewline
6 & 0.452659 & 3.5354 & 0.000392 \tabularnewline
7 & 0.371006 & 2.8976 & 0.002608 \tabularnewline
8 & 0.288398 & 2.2525 & 0.013951 \tabularnewline
9 & 0.206845 & 1.6155 & 0.055681 \tabularnewline
10 & 0.129185 & 1.009 & 0.158487 \tabularnewline
11 & 0.056101 & 0.4382 & 0.331409 \tabularnewline
12 & -0.010631 & -0.083 & 0.532949 \tabularnewline
13 & -0.061546 & -0.4807 & 0.683773 \tabularnewline
14 & -0.105919 & -0.8273 & 0.794341 \tabularnewline
15 & -0.148283 & -1.1581 & 0.874336 \tabularnewline
16 & -0.194107 & -1.516 & 0.932661 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7219&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]7.8102[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.90051[/C][C]7.0332[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.801542[/C][C]6.2602[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.707506[/C][C]5.5258[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.614219[/C][C]4.7972[/C][C]5e-06[/C][/ROW]
[ROW][C]5[/C][C]0.533509[/C][C]4.1668[/C][C]4.9e-05[/C][/ROW]
[ROW][C]6[/C][C]0.452659[/C][C]3.5354[/C][C]0.000392[/C][/ROW]
[ROW][C]7[/C][C]0.371006[/C][C]2.8976[/C][C]0.002608[/C][/ROW]
[ROW][C]8[/C][C]0.288398[/C][C]2.2525[/C][C]0.013951[/C][/ROW]
[ROW][C]9[/C][C]0.206845[/C][C]1.6155[/C][C]0.055681[/C][/ROW]
[ROW][C]10[/C][C]0.129185[/C][C]1.009[/C][C]0.158487[/C][/ROW]
[ROW][C]11[/C][C]0.056101[/C][C]0.4382[/C][C]0.331409[/C][/ROW]
[ROW][C]12[/C][C]-0.010631[/C][C]-0.083[/C][C]0.532949[/C][/ROW]
[ROW][C]13[/C][C]-0.061546[/C][C]-0.4807[/C][C]0.683773[/C][/ROW]
[ROW][C]14[/C][C]-0.105919[/C][C]-0.8273[/C][C]0.794341[/C][/ROW]
[ROW][C]15[/C][C]-0.148283[/C][C]-1.1581[/C][C]0.874336[/C][/ROW]
[ROW][C]16[/C][C]-0.194107[/C][C]-1.516[/C][C]0.932661[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7219&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7219&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	7.8102	0
1	0.90051	7.0332	0
2	0.801542	6.2602	0
3	0.707506	5.5258	0
4	0.614219	4.7972	5e-06
5	0.533509	4.1668	4.9e-05
6	0.452659	3.5354	0.000392
7	0.371006	2.8976	0.002608
8	0.288398	2.2525	0.013951
9	0.206845	1.6155	0.055681
10	0.129185	1.009	0.158487
11	0.056101	0.4382	0.331409
12	-0.010631	-0.083	0.532949
13	-0.061546	-0.4807	0.683773
14	-0.105919	-0.8273	0.794341
15	-0.148283	-1.1581	0.874336
16	-0.194107	-1.516	0.932661

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.90051	7.0332	0
1	-0.049591	-0.3873	0.650065
2	-0.028781	-0.2248	0.588551
3	-0.051045	-0.3987	0.654238
4	0.009677	0.0756	0.469999
5	-0.053834	-0.4205	0.662185
6	-0.057569	-0.4496	0.672714
7	-0.064877	-0.5067	0.692906
8	-0.054901	-0.4288	0.665207
9	-0.04714	-0.3682	0.642991
10	-0.044929	-0.3509	0.636567
11	-0.0363	-0.2835	0.611128
12	0.016845	0.1316	0.447882
13	-0.023415	-0.1829	0.572251
14	-0.043717	-0.3414	0.633027
15	-0.076292	-0.5959	0.723263
16	-0.067075	-0.5239	0.698867

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.90051 & 7.0332 & 0 \tabularnewline
1 & -0.049591 & -0.3873 & 0.650065 \tabularnewline
2 & -0.028781 & -0.2248 & 0.588551 \tabularnewline
3 & -0.051045 & -0.3987 & 0.654238 \tabularnewline
4 & 0.009677 & 0.0756 & 0.469999 \tabularnewline
5 & -0.053834 & -0.4205 & 0.662185 \tabularnewline
6 & -0.057569 & -0.4496 & 0.672714 \tabularnewline
7 & -0.064877 & -0.5067 & 0.692906 \tabularnewline
8 & -0.054901 & -0.4288 & 0.665207 \tabularnewline
9 & -0.04714 & -0.3682 & 0.642991 \tabularnewline
10 & -0.044929 & -0.3509 & 0.636567 \tabularnewline
11 & -0.0363 & -0.2835 & 0.611128 \tabularnewline
12 & 0.016845 & 0.1316 & 0.447882 \tabularnewline
13 & -0.023415 & -0.1829 & 0.572251 \tabularnewline
14 & -0.043717 & -0.3414 & 0.633027 \tabularnewline
15 & -0.076292 & -0.5959 & 0.723263 \tabularnewline
16 & -0.067075 & -0.5239 & 0.698867 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7219&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]0.90051[/C][C]7.0332[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.049591[/C][C]-0.3873[/C][C]0.650065[/C][/ROW]
[ROW][C]2[/C][C]-0.028781[/C][C]-0.2248[/C][C]0.588551[/C][/ROW]
[ROW][C]3[/C][C]-0.051045[/C][C]-0.3987[/C][C]0.654238[/C][/ROW]
[ROW][C]4[/C][C]0.009677[/C][C]0.0756[/C][C]0.469999[/C][/ROW]
[ROW][C]5[/C][C]-0.053834[/C][C]-0.4205[/C][C]0.662185[/C][/ROW]
[ROW][C]6[/C][C]-0.057569[/C][C]-0.4496[/C][C]0.672714[/C][/ROW]
[ROW][C]7[/C][C]-0.064877[/C][C]-0.5067[/C][C]0.692906[/C][/ROW]
[ROW][C]8[/C][C]-0.054901[/C][C]-0.4288[/C][C]0.665207[/C][/ROW]
[ROW][C]9[/C][C]-0.04714[/C][C]-0.3682[/C][C]0.642991[/C][/ROW]
[ROW][C]10[/C][C]-0.044929[/C][C]-0.3509[/C][C]0.636567[/C][/ROW]
[ROW][C]11[/C][C]-0.0363[/C][C]-0.2835[/C][C]0.611128[/C][/ROW]
[ROW][C]12[/C][C]0.016845[/C][C]0.1316[/C][C]0.447882[/C][/ROW]
[ROW][C]13[/C][C]-0.023415[/C][C]-0.1829[/C][C]0.572251[/C][/ROW]
[ROW][C]14[/C][C]-0.043717[/C][C]-0.3414[/C][C]0.633027[/C][/ROW]
[ROW][C]15[/C][C]-0.076292[/C][C]-0.5959[/C][C]0.723263[/C][/ROW]
[ROW][C]16[/C][C]-0.067075[/C][C]-0.5239[/C][C]0.698867[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7219&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7219&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	0.90051	7.0332	0
1	-0.049591	-0.3873	0.650065
2	-0.028781	-0.2248	0.588551
3	-0.051045	-0.3987	0.654238
4	0.009677	0.0756	0.469999
5	-0.053834	-0.4205	0.662185
6	-0.057569	-0.4496	0.672714
7	-0.064877	-0.5067	0.692906
8	-0.054901	-0.4288	0.665207
9	-0.04714	-0.3682	0.642991
10	-0.044929	-0.3509	0.636567
11	-0.0363	-0.2835	0.611128
12	0.016845	0.1316	0.447882
13	-0.023415	-0.1829	0.572251
14	-0.043717	-0.3414	0.633027
15	-0.076292	-0.5959	0.723263
16	-0.067075	-0.5239	0.698867

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 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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