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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, 16 Dec 2008 05:52:35 -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/16/t12294320403xhpfack6jzr9s8.htm/, Retrieved Tue, 14 May 2024 03:06:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33941, Retrieved Tue, 14 May 2024 03:06:54 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

184

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

-     [Variance Reduction Matrix] [vrm bel20] [2008-12-10 18:40:53] [74be16979710d4c4e7c6647856088456]
-    D  [Variance Reduction Matrix] [VRM paper dow jones] [2008-12-14 19:19:01] [629740e107727857ef4896c7a406110f]
-    D    [Variance Reduction Matrix] [] [2008-12-16 12:43:25] [74be16979710d4c4e7c6647856088456]
- RMPD        [(Partial) Autocorrelation Function] [] [2008-12-16 12:52:35] [d41d8cd98f00b204e9800998ecf8427e] [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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33941&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33941&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33941&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.962777	10.5906	0
2	0.915886	10.0747	0
3	0.876929	9.6462	0
4	0.836294	9.1992	0
5	0.793239	8.7256	0
6	0.751072	8.2618	0
7	0.710093	7.811	0
8	0.663704	7.3007	0
9	0.608401	6.6924	0
10	0.550981	6.0608	0
11	0.48978	5.3876	0
12	0.435145	4.7866	2e-06
13	0.382049	4.2025	2.5e-05
14	0.33572	3.6929	0.000167
15	0.280781	3.0886	0.001247
16	0.225082	2.4759	0.007337
17	0.174559	1.9201	0.028597
18	0.127281	1.4001	0.082023
19	0.080134	0.8815	0.189906
20	0.033655	0.3702	0.355938

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.962777 & 10.5906 & 0 \tabularnewline
2 & 0.915886 & 10.0747 & 0 \tabularnewline
3 & 0.876929 & 9.6462 & 0 \tabularnewline
4 & 0.836294 & 9.1992 & 0 \tabularnewline
5 & 0.793239 & 8.7256 & 0 \tabularnewline
6 & 0.751072 & 8.2618 & 0 \tabularnewline
7 & 0.710093 & 7.811 & 0 \tabularnewline
8 & 0.663704 & 7.3007 & 0 \tabularnewline
9 & 0.608401 & 6.6924 & 0 \tabularnewline
10 & 0.550981 & 6.0608 & 0 \tabularnewline
11 & 0.48978 & 5.3876 & 0 \tabularnewline
12 & 0.435145 & 4.7866 & 2e-06 \tabularnewline
13 & 0.382049 & 4.2025 & 2.5e-05 \tabularnewline
14 & 0.33572 & 3.6929 & 0.000167 \tabularnewline
15 & 0.280781 & 3.0886 & 0.001247 \tabularnewline
16 & 0.225082 & 2.4759 & 0.007337 \tabularnewline
17 & 0.174559 & 1.9201 & 0.028597 \tabularnewline
18 & 0.127281 & 1.4001 & 0.082023 \tabularnewline
19 & 0.080134 & 0.8815 & 0.189906 \tabularnewline
20 & 0.033655 & 0.3702 & 0.355938 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33941&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]0.962777[/C][C]10.5906[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.915886[/C][C]10.0747[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.876929[/C][C]9.6462[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.836294[/C][C]9.1992[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.793239[/C][C]8.7256[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.751072[/C][C]8.2618[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.710093[/C][C]7.811[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.663704[/C][C]7.3007[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.608401[/C][C]6.6924[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.550981[/C][C]6.0608[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.48978[/C][C]5.3876[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.435145[/C][C]4.7866[/C][C]2e-06[/C][/ROW]
[ROW][C]13[/C][C]0.382049[/C][C]4.2025[/C][C]2.5e-05[/C][/ROW]
[ROW][C]14[/C][C]0.33572[/C][C]3.6929[/C][C]0.000167[/C][/ROW]
[ROW][C]15[/C][C]0.280781[/C][C]3.0886[/C][C]0.001247[/C][/ROW]
[ROW][C]16[/C][C]0.225082[/C][C]2.4759[/C][C]0.007337[/C][/ROW]
[ROW][C]17[/C][C]0.174559[/C][C]1.9201[/C][C]0.028597[/C][/ROW]
[ROW][C]18[/C][C]0.127281[/C][C]1.4001[/C][C]0.082023[/C][/ROW]
[ROW][C]19[/C][C]0.080134[/C][C]0.8815[/C][C]0.189906[/C][/ROW]
[ROW][C]20[/C][C]0.033655[/C][C]0.3702[/C][C]0.355938[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33941&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33941&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	0.962777	10.5906	0
2	0.915886	10.0747	0
3	0.876929	9.6462	0
4	0.836294	9.1992	0
5	0.793239	8.7256	0
6	0.751072	8.2618	0
7	0.710093	7.811	0
8	0.663704	7.3007	0
9	0.608401	6.6924	0
10	0.550981	6.0608	0
11	0.48978	5.3876	0
12	0.435145	4.7866	2e-06
13	0.382049	4.2025	2.5e-05
14	0.33572	3.6929	0.000167
15	0.280781	3.0886	0.001247
16	0.225082	2.4759	0.007337
17	0.174559	1.9201	0.028597
18	0.127281	1.4001	0.082023
19	0.080134	0.8815	0.189906
20	0.033655	0.3702	0.355938

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.962777	10.5906	0
2	-0.151309	-1.6644	0.04931
3	0.103493	1.1384	0.128597
4	-0.077381	-0.8512	0.198172
5	-0.030845	-0.3393	0.367488
6	-0.014213	-0.1563	0.438014
7	-0.01455	-0.1601	0.436552
8	-0.100432	-1.1048	0.13573
9	-0.130754	-1.4383	0.076466
10	-0.052694	-0.5796	0.28162
11	-0.110746	-1.2182	0.112757
12	0.075657	0.8322	0.20346
13	-0.058937	-0.6483	0.259009
14	0.088869	0.9776	0.16512
15	-0.203259	-2.2359	0.013597
16	0.033827	0.3721	0.355238
17	-0.014987	-0.1649	0.434667
18	0.026651	0.2932	0.384952
19	-0.037838	-0.4162	0.338995
20	-0.045966	-0.5056	0.307019

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.962777 & 10.5906 & 0 \tabularnewline
2 & -0.151309 & -1.6644 & 0.04931 \tabularnewline
3 & 0.103493 & 1.1384 & 0.128597 \tabularnewline
4 & -0.077381 & -0.8512 & 0.198172 \tabularnewline
5 & -0.030845 & -0.3393 & 0.367488 \tabularnewline
6 & -0.014213 & -0.1563 & 0.438014 \tabularnewline
7 & -0.01455 & -0.1601 & 0.436552 \tabularnewline
8 & -0.100432 & -1.1048 & 0.13573 \tabularnewline
9 & -0.130754 & -1.4383 & 0.076466 \tabularnewline
10 & -0.052694 & -0.5796 & 0.28162 \tabularnewline
11 & -0.110746 & -1.2182 & 0.112757 \tabularnewline
12 & 0.075657 & 0.8322 & 0.20346 \tabularnewline
13 & -0.058937 & -0.6483 & 0.259009 \tabularnewline
14 & 0.088869 & 0.9776 & 0.16512 \tabularnewline
15 & -0.203259 & -2.2359 & 0.013597 \tabularnewline
16 & 0.033827 & 0.3721 & 0.355238 \tabularnewline
17 & -0.014987 & -0.1649 & 0.434667 \tabularnewline
18 & 0.026651 & 0.2932 & 0.384952 \tabularnewline
19 & -0.037838 & -0.4162 & 0.338995 \tabularnewline
20 & -0.045966 & -0.5056 & 0.307019 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33941&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]0.962777[/C][C]10.5906[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.151309[/C][C]-1.6644[/C][C]0.04931[/C][/ROW]
[ROW][C]3[/C][C]0.103493[/C][C]1.1384[/C][C]0.128597[/C][/ROW]
[ROW][C]4[/C][C]-0.077381[/C][C]-0.8512[/C][C]0.198172[/C][/ROW]
[ROW][C]5[/C][C]-0.030845[/C][C]-0.3393[/C][C]0.367488[/C][/ROW]
[ROW][C]6[/C][C]-0.014213[/C][C]-0.1563[/C][C]0.438014[/C][/ROW]
[ROW][C]7[/C][C]-0.01455[/C][C]-0.1601[/C][C]0.436552[/C][/ROW]
[ROW][C]8[/C][C]-0.100432[/C][C]-1.1048[/C][C]0.13573[/C][/ROW]
[ROW][C]9[/C][C]-0.130754[/C][C]-1.4383[/C][C]0.076466[/C][/ROW]
[ROW][C]10[/C][C]-0.052694[/C][C]-0.5796[/C][C]0.28162[/C][/ROW]
[ROW][C]11[/C][C]-0.110746[/C][C]-1.2182[/C][C]0.112757[/C][/ROW]
[ROW][C]12[/C][C]0.075657[/C][C]0.8322[/C][C]0.20346[/C][/ROW]
[ROW][C]13[/C][C]-0.058937[/C][C]-0.6483[/C][C]0.259009[/C][/ROW]
[ROW][C]14[/C][C]0.088869[/C][C]0.9776[/C][C]0.16512[/C][/ROW]
[ROW][C]15[/C][C]-0.203259[/C][C]-2.2359[/C][C]0.013597[/C][/ROW]
[ROW][C]16[/C][C]0.033827[/C][C]0.3721[/C][C]0.355238[/C][/ROW]
[ROW][C]17[/C][C]-0.014987[/C][C]-0.1649[/C][C]0.434667[/C][/ROW]
[ROW][C]18[/C][C]0.026651[/C][C]0.2932[/C][C]0.384952[/C][/ROW]
[ROW][C]19[/C][C]-0.037838[/C][C]-0.4162[/C][C]0.338995[/C][/ROW]
[ROW][C]20[/C][C]-0.045966[/C][C]-0.5056[/C][C]0.307019[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33941&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33941&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	0.962777	10.5906	0
2	-0.151309	-1.6644	0.04931
3	0.103493	1.1384	0.128597
4	-0.077381	-0.8512	0.198172
5	-0.030845	-0.3393	0.367488
6	-0.014213	-0.1563	0.438014
7	-0.01455	-0.1601	0.436552
8	-0.100432	-1.1048	0.13573
9	-0.130754	-1.4383	0.076466
10	-0.052694	-0.5796	0.28162
11	-0.110746	-1.2182	0.112757
12	0.075657	0.8322	0.20346
13	-0.058937	-0.6483	0.259009
14	0.088869	0.9776	0.16512
15	-0.203259	-2.2359	0.013597
16	0.033827	0.3721	0.355238
17	-0.014987	-0.1649	0.434667
18	0.026651	0.2932	0.384952
19	-0.037838	-0.4162	0.338995
20	-0.045966	-0.5056	0.307019

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 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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