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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, 09 Dec 2008 11:41:47 -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/09/t1228848134yjnn5jihzcol2pw.htm/, Retrieved Fri, 17 May 2024 03:03:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31682, Retrieved Fri, 17 May 2024 03:03:22 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

207

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

F     [(Partial) Autocorrelation Function] [step acf] [2008-12-09 15:39:34] [74be16979710d4c4e7c6647856088456]
-   P     [(Partial) Autocorrelation Function] [step 3 acf] [2008-12-09 18:41:47] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-   P       [(Partial) Autocorrelation Function] [step 2 met d=0] [2008-12-11 10:51:35] [74be16979710d4c4e7c6647856088456] 
- RMP       [Spectral Analysis] [step 2 met d=0 sp...] [2008-12-11 10:50:31] [74be16979710d4c4e7c6647856088456] 
-   P       [(Partial) Autocorrelation Function] [sdsdsd] [2008-12-11 11:20:34] [74be16979710d4c4e7c6647856088456] 

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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=31682&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=31682&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31682&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	-0.447318	-3.7956	0.000152
2	-0.17933	-1.5217	0.066236
3	0.321971	2.732	0.003956
4	-0.124937	-1.0601	0.146316
5	-0.126373	-1.0723	0.143582
6	0.184163	1.5627	0.061257
7	-0.158811	-1.3476	0.091013
8	0.172469	1.4634	0.073849
9	-0.132251	-1.1222	0.132755
10	-0.004065	-0.0345	0.486289
11	0.205332	1.7423	0.042863
12	-0.259038	-2.198	0.015582
13	0.064733	0.5493	0.292259
14	0.071033	0.6027	0.27429
15	-0.074573	-0.6328	0.264444
16	-0.023065	-0.1957	0.422691
17	0.148088	1.2566	0.106486
18	-0.234233	-1.9875	0.025334
19	0.106535	0.904	0.18451

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.447318 & -3.7956 & 0.000152 \tabularnewline
2 & -0.17933 & -1.5217 & 0.066236 \tabularnewline
3 & 0.321971 & 2.732 & 0.003956 \tabularnewline
4 & -0.124937 & -1.0601 & 0.146316 \tabularnewline
5 & -0.126373 & -1.0723 & 0.143582 \tabularnewline
6 & 0.184163 & 1.5627 & 0.061257 \tabularnewline
7 & -0.158811 & -1.3476 & 0.091013 \tabularnewline
8 & 0.172469 & 1.4634 & 0.073849 \tabularnewline
9 & -0.132251 & -1.1222 & 0.132755 \tabularnewline
10 & -0.004065 & -0.0345 & 0.486289 \tabularnewline
11 & 0.205332 & 1.7423 & 0.042863 \tabularnewline
12 & -0.259038 & -2.198 & 0.015582 \tabularnewline
13 & 0.064733 & 0.5493 & 0.292259 \tabularnewline
14 & 0.071033 & 0.6027 & 0.27429 \tabularnewline
15 & -0.074573 & -0.6328 & 0.264444 \tabularnewline
16 & -0.023065 & -0.1957 & 0.422691 \tabularnewline
17 & 0.148088 & 1.2566 & 0.106486 \tabularnewline
18 & -0.234233 & -1.9875 & 0.025334 \tabularnewline
19 & 0.106535 & 0.904 & 0.18451 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31682&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]-0.447318[/C][C]-3.7956[/C][C]0.000152[/C][/ROW]
[ROW][C]2[/C][C]-0.17933[/C][C]-1.5217[/C][C]0.066236[/C][/ROW]
[ROW][C]3[/C][C]0.321971[/C][C]2.732[/C][C]0.003956[/C][/ROW]
[ROW][C]4[/C][C]-0.124937[/C][C]-1.0601[/C][C]0.146316[/C][/ROW]
[ROW][C]5[/C][C]-0.126373[/C][C]-1.0723[/C][C]0.143582[/C][/ROW]
[ROW][C]6[/C][C]0.184163[/C][C]1.5627[/C][C]0.061257[/C][/ROW]
[ROW][C]7[/C][C]-0.158811[/C][C]-1.3476[/C][C]0.091013[/C][/ROW]
[ROW][C]8[/C][C]0.172469[/C][C]1.4634[/C][C]0.073849[/C][/ROW]
[ROW][C]9[/C][C]-0.132251[/C][C]-1.1222[/C][C]0.132755[/C][/ROW]
[ROW][C]10[/C][C]-0.004065[/C][C]-0.0345[/C][C]0.486289[/C][/ROW]
[ROW][C]11[/C][C]0.205332[/C][C]1.7423[/C][C]0.042863[/C][/ROW]
[ROW][C]12[/C][C]-0.259038[/C][C]-2.198[/C][C]0.015582[/C][/ROW]
[ROW][C]13[/C][C]0.064733[/C][C]0.5493[/C][C]0.292259[/C][/ROW]
[ROW][C]14[/C][C]0.071033[/C][C]0.6027[/C][C]0.27429[/C][/ROW]
[ROW][C]15[/C][C]-0.074573[/C][C]-0.6328[/C][C]0.264444[/C][/ROW]
[ROW][C]16[/C][C]-0.023065[/C][C]-0.1957[/C][C]0.422691[/C][/ROW]
[ROW][C]17[/C][C]0.148088[/C][C]1.2566[/C][C]0.106486[/C][/ROW]
[ROW][C]18[/C][C]-0.234233[/C][C]-1.9875[/C][C]0.025334[/C][/ROW]
[ROW][C]19[/C][C]0.106535[/C][C]0.904[/C][C]0.18451[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31682&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31682&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	-0.447318	-3.7956	0.000152
2	-0.17933	-1.5217	0.066236
3	0.321971	2.732	0.003956
4	-0.124937	-1.0601	0.146316
5	-0.126373	-1.0723	0.143582
6	0.184163	1.5627	0.061257
7	-0.158811	-1.3476	0.091013
8	0.172469	1.4634	0.073849
9	-0.132251	-1.1222	0.132755
10	-0.004065	-0.0345	0.486289
11	0.205332	1.7423	0.042863
12	-0.259038	-2.198	0.015582
13	0.064733	0.5493	0.292259
14	0.071033	0.6027	0.27429
15	-0.074573	-0.6328	0.264444
16	-0.023065	-0.1957	0.422691
17	0.148088	1.2566	0.106486
18	-0.234233	-1.9875	0.025334
19	0.106535	0.904	0.18451

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.447318	-3.7956	0.000152
2	-0.474334	-4.0249	7e-05
3	-0.01367	-0.116	0.45399
4	-0.005331	-0.0452	0.482021
5	-0.094556	-0.8023	0.2125
6	0.007825	0.0664	0.473622
7	-0.15845	-1.3445	0.091505
8	0.176907	1.5011	0.06885
9	-0.07507	-0.637	0.263075
10	-0.005548	-0.0471	0.481293
11	0.165321	1.4028	0.082487
12	-0.106113	-0.9004	0.185455
13	0.023459	0.1991	0.421391
14	-0.171604	-1.4561	0.074854
15	0.045909	0.3896	0.349009
16	-0.099898	-0.8477	0.199718
17	0.112282	0.9527	0.171954
18	-0.179572	-1.5237	0.065979
19	-0.143856	-1.2207	0.113099

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.447318 & -3.7956 & 0.000152 \tabularnewline
2 & -0.474334 & -4.0249 & 7e-05 \tabularnewline
3 & -0.01367 & -0.116 & 0.45399 \tabularnewline
4 & -0.005331 & -0.0452 & 0.482021 \tabularnewline
5 & -0.094556 & -0.8023 & 0.2125 \tabularnewline
6 & 0.007825 & 0.0664 & 0.473622 \tabularnewline
7 & -0.15845 & -1.3445 & 0.091505 \tabularnewline
8 & 0.176907 & 1.5011 & 0.06885 \tabularnewline
9 & -0.07507 & -0.637 & 0.263075 \tabularnewline
10 & -0.005548 & -0.0471 & 0.481293 \tabularnewline
11 & 0.165321 & 1.4028 & 0.082487 \tabularnewline
12 & -0.106113 & -0.9004 & 0.185455 \tabularnewline
13 & 0.023459 & 0.1991 & 0.421391 \tabularnewline
14 & -0.171604 & -1.4561 & 0.074854 \tabularnewline
15 & 0.045909 & 0.3896 & 0.349009 \tabularnewline
16 & -0.099898 & -0.8477 & 0.199718 \tabularnewline
17 & 0.112282 & 0.9527 & 0.171954 \tabularnewline
18 & -0.179572 & -1.5237 & 0.065979 \tabularnewline
19 & -0.143856 & -1.2207 & 0.113099 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31682&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]-0.447318[/C][C]-3.7956[/C][C]0.000152[/C][/ROW]
[ROW][C]2[/C][C]-0.474334[/C][C]-4.0249[/C][C]7e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.01367[/C][C]-0.116[/C][C]0.45399[/C][/ROW]
[ROW][C]4[/C][C]-0.005331[/C][C]-0.0452[/C][C]0.482021[/C][/ROW]
[ROW][C]5[/C][C]-0.094556[/C][C]-0.8023[/C][C]0.2125[/C][/ROW]
[ROW][C]6[/C][C]0.007825[/C][C]0.0664[/C][C]0.473622[/C][/ROW]
[ROW][C]7[/C][C]-0.15845[/C][C]-1.3445[/C][C]0.091505[/C][/ROW]
[ROW][C]8[/C][C]0.176907[/C][C]1.5011[/C][C]0.06885[/C][/ROW]
[ROW][C]9[/C][C]-0.07507[/C][C]-0.637[/C][C]0.263075[/C][/ROW]
[ROW][C]10[/C][C]-0.005548[/C][C]-0.0471[/C][C]0.481293[/C][/ROW]
[ROW][C]11[/C][C]0.165321[/C][C]1.4028[/C][C]0.082487[/C][/ROW]
[ROW][C]12[/C][C]-0.106113[/C][C]-0.9004[/C][C]0.185455[/C][/ROW]
[ROW][C]13[/C][C]0.023459[/C][C]0.1991[/C][C]0.421391[/C][/ROW]
[ROW][C]14[/C][C]-0.171604[/C][C]-1.4561[/C][C]0.074854[/C][/ROW]
[ROW][C]15[/C][C]0.045909[/C][C]0.3896[/C][C]0.349009[/C][/ROW]
[ROW][C]16[/C][C]-0.099898[/C][C]-0.8477[/C][C]0.199718[/C][/ROW]
[ROW][C]17[/C][C]0.112282[/C][C]0.9527[/C][C]0.171954[/C][/ROW]
[ROW][C]18[/C][C]-0.179572[/C][C]-1.5237[/C][C]0.065979[/C][/ROW]
[ROW][C]19[/C][C]-0.143856[/C][C]-1.2207[/C][C]0.113099[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31682&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31682&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	-0.447318	-3.7956	0.000152
2	-0.474334	-4.0249	7e-05
3	-0.01367	-0.116	0.45399
4	-0.005331	-0.0452	0.482021
5	-0.094556	-0.8023	0.2125
6	0.007825	0.0664	0.473622
7	-0.15845	-1.3445	0.091505
8	0.176907	1.5011	0.06885
9	-0.07507	-0.637	0.263075
10	-0.005548	-0.0471	0.481293
11	0.165321	1.4028	0.082487
12	-0.106113	-0.9004	0.185455
13	0.023459	0.1991	0.421391
14	-0.171604	-1.4561	0.074854
15	0.045909	0.3896	0.349009
16	-0.099898	-0.8477	0.199718
17	0.112282	0.9527	0.171954
18	-0.179572	-1.5237	0.065979
19	-0.143856	-1.2207	0.113099

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.0 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; 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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