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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 04 Dec 2008 09:19:01 -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/04/t1228407730ks137p1aw0o23h9.htm/, Retrieved Sun, 19 May 2024 08:01:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28954, Retrieved Sun, 19 May 2024 08:01:32 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

197

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

-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2008-12-04 16:19:01] [72e979bcc364082694890d2eccc1a66f] [Current]
-   P     [(Partial) Autocorrelation Function] [Autocorrelation F...] [2008-12-07 08:58:58] [3b5d63cebdc58ed6c519cdb5b6a36d46] 
- RMP       [Spectral Analysis] [Spectral Analysis] [2008-12-07 09:36:04] [c94d7012e41b73cfa20d93e879679ede] 

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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=28954&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=28954&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28954&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	0.091121	0.6999	0.243367
2	0.393208	3.0203	0.001864
3	0.056835	0.4366	0.332013
4	0.063637	0.4888	0.313396
5	0.025465	0.1956	0.422798
6	-0.057457	-0.4413	0.33029
7	-0.012314	-0.0946	0.462483
8	-0.130063	-0.999	0.160929
9	-0.054156	-0.416	0.339467
10	-0.123325	-0.9473	0.173682
11	-0.276203	-2.1216	0.019043
12	-0.119414	-0.9172	0.181376
13	-0.220796	-1.696	0.047582
14	0.004454	0.0342	0.486412
15	0.063559	0.4882	0.313607
16	-0.065402	-0.5024	0.308642
17	0.113007	0.868	0.194448

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.091121 & 0.6999 & 0.243367 \tabularnewline
2 & 0.393208 & 3.0203 & 0.001864 \tabularnewline
3 & 0.056835 & 0.4366 & 0.332013 \tabularnewline
4 & 0.063637 & 0.4888 & 0.313396 \tabularnewline
5 & 0.025465 & 0.1956 & 0.422798 \tabularnewline
6 & -0.057457 & -0.4413 & 0.33029 \tabularnewline
7 & -0.012314 & -0.0946 & 0.462483 \tabularnewline
8 & -0.130063 & -0.999 & 0.160929 \tabularnewline
9 & -0.054156 & -0.416 & 0.339467 \tabularnewline
10 & -0.123325 & -0.9473 & 0.173682 \tabularnewline
11 & -0.276203 & -2.1216 & 0.019043 \tabularnewline
12 & -0.119414 & -0.9172 & 0.181376 \tabularnewline
13 & -0.220796 & -1.696 & 0.047582 \tabularnewline
14 & 0.004454 & 0.0342 & 0.486412 \tabularnewline
15 & 0.063559 & 0.4882 & 0.313607 \tabularnewline
16 & -0.065402 & -0.5024 & 0.308642 \tabularnewline
17 & 0.113007 & 0.868 & 0.194448 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28954&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]0.091121[/C][C]0.6999[/C][C]0.243367[/C][/ROW]
[ROW][C]2[/C][C]0.393208[/C][C]3.0203[/C][C]0.001864[/C][/ROW]
[ROW][C]3[/C][C]0.056835[/C][C]0.4366[/C][C]0.332013[/C][/ROW]
[ROW][C]4[/C][C]0.063637[/C][C]0.4888[/C][C]0.313396[/C][/ROW]
[ROW][C]5[/C][C]0.025465[/C][C]0.1956[/C][C]0.422798[/C][/ROW]
[ROW][C]6[/C][C]-0.057457[/C][C]-0.4413[/C][C]0.33029[/C][/ROW]
[ROW][C]7[/C][C]-0.012314[/C][C]-0.0946[/C][C]0.462483[/C][/ROW]
[ROW][C]8[/C][C]-0.130063[/C][C]-0.999[/C][C]0.160929[/C][/ROW]
[ROW][C]9[/C][C]-0.054156[/C][C]-0.416[/C][C]0.339467[/C][/ROW]
[ROW][C]10[/C][C]-0.123325[/C][C]-0.9473[/C][C]0.173682[/C][/ROW]
[ROW][C]11[/C][C]-0.276203[/C][C]-2.1216[/C][C]0.019043[/C][/ROW]
[ROW][C]12[/C][C]-0.119414[/C][C]-0.9172[/C][C]0.181376[/C][/ROW]
[ROW][C]13[/C][C]-0.220796[/C][C]-1.696[/C][C]0.047582[/C][/ROW]
[ROW][C]14[/C][C]0.004454[/C][C]0.0342[/C][C]0.486412[/C][/ROW]
[ROW][C]15[/C][C]0.063559[/C][C]0.4882[/C][C]0.313607[/C][/ROW]
[ROW][C]16[/C][C]-0.065402[/C][C]-0.5024[/C][C]0.308642[/C][/ROW]
[ROW][C]17[/C][C]0.113007[/C][C]0.868[/C][C]0.194448[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28954&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28954&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	0.091121	0.6999	0.243367
2	0.393208	3.0203	0.001864
3	0.056835	0.4366	0.332013
4	0.063637	0.4888	0.313396
5	0.025465	0.1956	0.422798
6	-0.057457	-0.4413	0.33029
7	-0.012314	-0.0946	0.462483
8	-0.130063	-0.999	0.160929
9	-0.054156	-0.416	0.339467
10	-0.123325	-0.9473	0.173682
11	-0.276203	-2.1216	0.019043
12	-0.119414	-0.9172	0.181376
13	-0.220796	-1.696	0.047582
14	0.004454	0.0342	0.486412
15	0.063559	0.4882	0.313607
16	-0.065402	-0.5024	0.308642
17	0.113007	0.868	0.194448

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.091121	0.6999	0.243367
2	0.388127	2.9813	0.002083
3	-0.00054	-0.0041	0.498353
4	-0.109368	-0.8401	0.20213
5	0.006254	0.048	0.480924
6	-0.052741	-0.4051	0.343429
7	-0.016792	-0.129	0.448904
8	-0.09462	-0.7268	0.235113
9	-0.032294	-0.2481	0.402478
10	-0.038516	-0.2958	0.384194
11	-0.277329	-2.1302	0.018667
12	-0.048202	-0.3702	0.356261
13	-0.004249	-0.0326	0.487037
14	0.092114	0.7075	0.241007
15	0.194211	1.4918	0.070544
16	-0.157432	-1.2093	0.115693
17	-0.008297	-0.0637	0.474699

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.091121 & 0.6999 & 0.243367 \tabularnewline
2 & 0.388127 & 2.9813 & 0.002083 \tabularnewline
3 & -0.00054 & -0.0041 & 0.498353 \tabularnewline
4 & -0.109368 & -0.8401 & 0.20213 \tabularnewline
5 & 0.006254 & 0.048 & 0.480924 \tabularnewline
6 & -0.052741 & -0.4051 & 0.343429 \tabularnewline
7 & -0.016792 & -0.129 & 0.448904 \tabularnewline
8 & -0.09462 & -0.7268 & 0.235113 \tabularnewline
9 & -0.032294 & -0.2481 & 0.402478 \tabularnewline
10 & -0.038516 & -0.2958 & 0.384194 \tabularnewline
11 & -0.277329 & -2.1302 & 0.018667 \tabularnewline
12 & -0.048202 & -0.3702 & 0.356261 \tabularnewline
13 & -0.004249 & -0.0326 & 0.487037 \tabularnewline
14 & 0.092114 & 0.7075 & 0.241007 \tabularnewline
15 & 0.194211 & 1.4918 & 0.070544 \tabularnewline
16 & -0.157432 & -1.2093 & 0.115693 \tabularnewline
17 & -0.008297 & -0.0637 & 0.474699 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28954&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]0.091121[/C][C]0.6999[/C][C]0.243367[/C][/ROW]
[ROW][C]2[/C][C]0.388127[/C][C]2.9813[/C][C]0.002083[/C][/ROW]
[ROW][C]3[/C][C]-0.00054[/C][C]-0.0041[/C][C]0.498353[/C][/ROW]
[ROW][C]4[/C][C]-0.109368[/C][C]-0.8401[/C][C]0.20213[/C][/ROW]
[ROW][C]5[/C][C]0.006254[/C][C]0.048[/C][C]0.480924[/C][/ROW]
[ROW][C]6[/C][C]-0.052741[/C][C]-0.4051[/C][C]0.343429[/C][/ROW]
[ROW][C]7[/C][C]-0.016792[/C][C]-0.129[/C][C]0.448904[/C][/ROW]
[ROW][C]8[/C][C]-0.09462[/C][C]-0.7268[/C][C]0.235113[/C][/ROW]
[ROW][C]9[/C][C]-0.032294[/C][C]-0.2481[/C][C]0.402478[/C][/ROW]
[ROW][C]10[/C][C]-0.038516[/C][C]-0.2958[/C][C]0.384194[/C][/ROW]
[ROW][C]11[/C][C]-0.277329[/C][C]-2.1302[/C][C]0.018667[/C][/ROW]
[ROW][C]12[/C][C]-0.048202[/C][C]-0.3702[/C][C]0.356261[/C][/ROW]
[ROW][C]13[/C][C]-0.004249[/C][C]-0.0326[/C][C]0.487037[/C][/ROW]
[ROW][C]14[/C][C]0.092114[/C][C]0.7075[/C][C]0.241007[/C][/ROW]
[ROW][C]15[/C][C]0.194211[/C][C]1.4918[/C][C]0.070544[/C][/ROW]
[ROW][C]16[/C][C]-0.157432[/C][C]-1.2093[/C][C]0.115693[/C][/ROW]
[ROW][C]17[/C][C]-0.008297[/C][C]-0.0637[/C][C]0.474699[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28954&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28954&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	0.091121	0.6999	0.243367
2	0.388127	2.9813	0.002083
3	-0.00054	-0.0041	0.498353
4	-0.109368	-0.8401	0.20213
5	0.006254	0.048	0.480924
6	-0.052741	-0.4051	0.343429
7	-0.016792	-0.129	0.448904
8	-0.09462	-0.7268	0.235113
9	-0.032294	-0.2481	0.402478
10	-0.038516	-0.2958	0.384194
11	-0.277329	-2.1302	0.018667
12	-0.048202	-0.3702	0.356261
13	-0.004249	-0.0326	0.487037
14	0.092114	0.7075	0.241007
15	0.194211	1.4918	0.070544
16	-0.157432	-1.2093	0.115693
17	-0.008297	-0.0637	0.474699

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 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code