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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 04:12:23 -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/t1228821213oa42g8airu411kf.htm/, Retrieved Sat, 25 May 2024 01:14:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31296, Retrieved Sat, 25 May 2024 01:14:38 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

157

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

F     [(Partial) Autocorrelation Function] [] [2008-12-04 19:54:00] [03c8f0b5f6fe0fafd3d60ad5379ae7bd]
-   PD    [(Partial) Autocorrelation Function] [] [2008-12-09 11:12:23] [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	2 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31296&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31296&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31296&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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.268061	4.8251	1e-06
2	0.24895	4.4811	5e-06
3	0.18537	3.3367	0.000473
4	0.099035	1.7826	0.037792
5	0.151378	2.7248	0.003392
6	0.144319	2.5977	0.004906
7	0.071539	1.2877	0.099383
8	0.142761	2.5697	0.005313
9	0.081402	1.4652	0.071914
10	-0.026116	-0.4701	0.319303
11	-0.068843	-1.2392	0.10809
12	-0.395053	-7.1109	0
13	-0.086827	-1.5629	0.059527
14	-0.019515	-0.3513	0.362809
15	0.08028	1.445	0.074707
16	0.003371	0.0607	0.475826
17	0.109603	1.9729	0.024681
18	0.024213	0.4358	0.331626
19	0.012158	0.2188	0.413454
20	0.043987	0.7918	0.214537
21	0.091268	1.6428	0.050695
22	0.113323	2.0398	0.02109
23	0.214121	3.8542	7e-05
24	0.203557	3.664	0.000145
25	0.180873	3.2557	0.000625

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.268061 & 4.8251 & 1e-06 \tabularnewline
2 & 0.24895 & 4.4811 & 5e-06 \tabularnewline
3 & 0.18537 & 3.3367 & 0.000473 \tabularnewline
4 & 0.099035 & 1.7826 & 0.037792 \tabularnewline
5 & 0.151378 & 2.7248 & 0.003392 \tabularnewline
6 & 0.144319 & 2.5977 & 0.004906 \tabularnewline
7 & 0.071539 & 1.2877 & 0.099383 \tabularnewline
8 & 0.142761 & 2.5697 & 0.005313 \tabularnewline
9 & 0.081402 & 1.4652 & 0.071914 \tabularnewline
10 & -0.026116 & -0.4701 & 0.319303 \tabularnewline
11 & -0.068843 & -1.2392 & 0.10809 \tabularnewline
12 & -0.395053 & -7.1109 & 0 \tabularnewline
13 & -0.086827 & -1.5629 & 0.059527 \tabularnewline
14 & -0.019515 & -0.3513 & 0.362809 \tabularnewline
15 & 0.08028 & 1.445 & 0.074707 \tabularnewline
16 & 0.003371 & 0.0607 & 0.475826 \tabularnewline
17 & 0.109603 & 1.9729 & 0.024681 \tabularnewline
18 & 0.024213 & 0.4358 & 0.331626 \tabularnewline
19 & 0.012158 & 0.2188 & 0.413454 \tabularnewline
20 & 0.043987 & 0.7918 & 0.214537 \tabularnewline
21 & 0.091268 & 1.6428 & 0.050695 \tabularnewline
22 & 0.113323 & 2.0398 & 0.02109 \tabularnewline
23 & 0.214121 & 3.8542 & 7e-05 \tabularnewline
24 & 0.203557 & 3.664 & 0.000145 \tabularnewline
25 & 0.180873 & 3.2557 & 0.000625 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31296&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]0.268061[/C][C]4.8251[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.24895[/C][C]4.4811[/C][C]5e-06[/C][/ROW]
[ROW][C]3[/C][C]0.18537[/C][C]3.3367[/C][C]0.000473[/C][/ROW]
[ROW][C]4[/C][C]0.099035[/C][C]1.7826[/C][C]0.037792[/C][/ROW]
[ROW][C]5[/C][C]0.151378[/C][C]2.7248[/C][C]0.003392[/C][/ROW]
[ROW][C]6[/C][C]0.144319[/C][C]2.5977[/C][C]0.004906[/C][/ROW]
[ROW][C]7[/C][C]0.071539[/C][C]1.2877[/C][C]0.099383[/C][/ROW]
[ROW][C]8[/C][C]0.142761[/C][C]2.5697[/C][C]0.005313[/C][/ROW]
[ROW][C]9[/C][C]0.081402[/C][C]1.4652[/C][C]0.071914[/C][/ROW]
[ROW][C]10[/C][C]-0.026116[/C][C]-0.4701[/C][C]0.319303[/C][/ROW]
[ROW][C]11[/C][C]-0.068843[/C][C]-1.2392[/C][C]0.10809[/C][/ROW]
[ROW][C]12[/C][C]-0.395053[/C][C]-7.1109[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.086827[/C][C]-1.5629[/C][C]0.059527[/C][/ROW]
[ROW][C]14[/C][C]-0.019515[/C][C]-0.3513[/C][C]0.362809[/C][/ROW]
[ROW][C]15[/C][C]0.08028[/C][C]1.445[/C][C]0.074707[/C][/ROW]
[ROW][C]16[/C][C]0.003371[/C][C]0.0607[/C][C]0.475826[/C][/ROW]
[ROW][C]17[/C][C]0.109603[/C][C]1.9729[/C][C]0.024681[/C][/ROW]
[ROW][C]18[/C][C]0.024213[/C][C]0.4358[/C][C]0.331626[/C][/ROW]
[ROW][C]19[/C][C]0.012158[/C][C]0.2188[/C][C]0.413454[/C][/ROW]
[ROW][C]20[/C][C]0.043987[/C][C]0.7918[/C][C]0.214537[/C][/ROW]
[ROW][C]21[/C][C]0.091268[/C][C]1.6428[/C][C]0.050695[/C][/ROW]
[ROW][C]22[/C][C]0.113323[/C][C]2.0398[/C][C]0.02109[/C][/ROW]
[ROW][C]23[/C][C]0.214121[/C][C]3.8542[/C][C]7e-05[/C][/ROW]
[ROW][C]24[/C][C]0.203557[/C][C]3.664[/C][C]0.000145[/C][/ROW]
[ROW][C]25[/C][C]0.180873[/C][C]3.2557[/C][C]0.000625[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31296&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31296&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	0.268061	4.8251	1e-06
2	0.24895	4.4811	5e-06
3	0.18537	3.3367	0.000473
4	0.099035	1.7826	0.037792
5	0.151378	2.7248	0.003392
6	0.144319	2.5977	0.004906
7	0.071539	1.2877	0.099383
8	0.142761	2.5697	0.005313
9	0.081402	1.4652	0.071914
10	-0.026116	-0.4701	0.319303
11	-0.068843	-1.2392	0.10809
12	-0.395053	-7.1109	0
13	-0.086827	-1.5629	0.059527
14	-0.019515	-0.3513	0.362809
15	0.08028	1.445	0.074707
16	0.003371	0.0607	0.475826
17	0.109603	1.9729	0.024681
18	0.024213	0.4358	0.331626
19	0.012158	0.2188	0.413454
20	0.043987	0.7918	0.214537
21	0.091268	1.6428	0.050695
22	0.113323	2.0398	0.02109
23	0.214121	3.8542	7e-05
24	0.203557	3.664	0.000145
25	0.180873	3.2557	0.000625

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.268061	4.8251	1e-06
2	0.190804	3.4345	0.000335
3	0.089698	1.6146	0.053689
4	-0.005302	-0.0954	0.462016
5	0.088419	1.5915	0.056231
6	0.074634	1.3434	0.090039
7	-0.023161	-0.4169	0.338514
8	0.079573	1.4323	0.076508
9	0.007191	0.1294	0.448548
10	-0.111038	-1.9987	0.023239
11	-0.113004	-2.0341	0.021379
12	-0.421418	-7.5855	0
13	0.091179	1.6412	0.050861
14	0.158253	2.8486	0.002336
15	0.2347	4.2246	1.6e-05
16	-0.020598	-0.3708	0.355529
17	0.186742	3.3614	0.000434
18	0.05157	0.9283	0.17698
19	-0.047287	-0.8512	0.197655
20	0.054846	0.9872	0.162135
21	0.113494	2.0429	0.020936
22	-0.017302	-0.3114	0.377837
23	0.019687	0.3544	0.361648
24	-0.165112	-2.972	0.00159
25	0.069283	1.2471	0.106633

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.268061 & 4.8251 & 1e-06 \tabularnewline
2 & 0.190804 & 3.4345 & 0.000335 \tabularnewline
3 & 0.089698 & 1.6146 & 0.053689 \tabularnewline
4 & -0.005302 & -0.0954 & 0.462016 \tabularnewline
5 & 0.088419 & 1.5915 & 0.056231 \tabularnewline
6 & 0.074634 & 1.3434 & 0.090039 \tabularnewline
7 & -0.023161 & -0.4169 & 0.338514 \tabularnewline
8 & 0.079573 & 1.4323 & 0.076508 \tabularnewline
9 & 0.007191 & 0.1294 & 0.448548 \tabularnewline
10 & -0.111038 & -1.9987 & 0.023239 \tabularnewline
11 & -0.113004 & -2.0341 & 0.021379 \tabularnewline
12 & -0.421418 & -7.5855 & 0 \tabularnewline
13 & 0.091179 & 1.6412 & 0.050861 \tabularnewline
14 & 0.158253 & 2.8486 & 0.002336 \tabularnewline
15 & 0.2347 & 4.2246 & 1.6e-05 \tabularnewline
16 & -0.020598 & -0.3708 & 0.355529 \tabularnewline
17 & 0.186742 & 3.3614 & 0.000434 \tabularnewline
18 & 0.05157 & 0.9283 & 0.17698 \tabularnewline
19 & -0.047287 & -0.8512 & 0.197655 \tabularnewline
20 & 0.054846 & 0.9872 & 0.162135 \tabularnewline
21 & 0.113494 & 2.0429 & 0.020936 \tabularnewline
22 & -0.017302 & -0.3114 & 0.377837 \tabularnewline
23 & 0.019687 & 0.3544 & 0.361648 \tabularnewline
24 & -0.165112 & -2.972 & 0.00159 \tabularnewline
25 & 0.069283 & 1.2471 & 0.106633 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31296&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]0.268061[/C][C]4.8251[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.190804[/C][C]3.4345[/C][C]0.000335[/C][/ROW]
[ROW][C]3[/C][C]0.089698[/C][C]1.6146[/C][C]0.053689[/C][/ROW]
[ROW][C]4[/C][C]-0.005302[/C][C]-0.0954[/C][C]0.462016[/C][/ROW]
[ROW][C]5[/C][C]0.088419[/C][C]1.5915[/C][C]0.056231[/C][/ROW]
[ROW][C]6[/C][C]0.074634[/C][C]1.3434[/C][C]0.090039[/C][/ROW]
[ROW][C]7[/C][C]-0.023161[/C][C]-0.4169[/C][C]0.338514[/C][/ROW]
[ROW][C]8[/C][C]0.079573[/C][C]1.4323[/C][C]0.076508[/C][/ROW]
[ROW][C]9[/C][C]0.007191[/C][C]0.1294[/C][C]0.448548[/C][/ROW]
[ROW][C]10[/C][C]-0.111038[/C][C]-1.9987[/C][C]0.023239[/C][/ROW]
[ROW][C]11[/C][C]-0.113004[/C][C]-2.0341[/C][C]0.021379[/C][/ROW]
[ROW][C]12[/C][C]-0.421418[/C][C]-7.5855[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.091179[/C][C]1.6412[/C][C]0.050861[/C][/ROW]
[ROW][C]14[/C][C]0.158253[/C][C]2.8486[/C][C]0.002336[/C][/ROW]
[ROW][C]15[/C][C]0.2347[/C][C]4.2246[/C][C]1.6e-05[/C][/ROW]
[ROW][C]16[/C][C]-0.020598[/C][C]-0.3708[/C][C]0.355529[/C][/ROW]
[ROW][C]17[/C][C]0.186742[/C][C]3.3614[/C][C]0.000434[/C][/ROW]
[ROW][C]18[/C][C]0.05157[/C][C]0.9283[/C][C]0.17698[/C][/ROW]
[ROW][C]19[/C][C]-0.047287[/C][C]-0.8512[/C][C]0.197655[/C][/ROW]
[ROW][C]20[/C][C]0.054846[/C][C]0.9872[/C][C]0.162135[/C][/ROW]
[ROW][C]21[/C][C]0.113494[/C][C]2.0429[/C][C]0.020936[/C][/ROW]
[ROW][C]22[/C][C]-0.017302[/C][C]-0.3114[/C][C]0.377837[/C][/ROW]
[ROW][C]23[/C][C]0.019687[/C][C]0.3544[/C][C]0.361648[/C][/ROW]
[ROW][C]24[/C][C]-0.165112[/C][C]-2.972[/C][C]0.00159[/C][/ROW]
[ROW][C]25[/C][C]0.069283[/C][C]1.2471[/C][C]0.106633[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31296&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31296&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	0.268061	4.8251	1e-06
2	0.190804	3.4345	0.000335
3	0.089698	1.6146	0.053689
4	-0.005302	-0.0954	0.462016
5	0.088419	1.5915	0.056231
6	0.074634	1.3434	0.090039
7	-0.023161	-0.4169	0.338514
8	0.079573	1.4323	0.076508
9	0.007191	0.1294	0.448548
10	-0.111038	-1.9987	0.023239
11	-0.113004	-2.0341	0.021379
12	-0.421418	-7.5855	0
13	0.091179	1.6412	0.050861
14	0.158253	2.8486	0.002336
15	0.2347	4.2246	1.6e-05
16	-0.020598	-0.3708	0.355529
17	0.186742	3.3614	0.000434
18	0.05157	0.9283	0.17698
19	-0.047287	-0.8512	0.197655
20	0.054846	0.9872	0.162135
21	0.113494	2.0429	0.020936
22	-0.017302	-0.3114	0.377837
23	0.019687	0.3544	0.361648
24	-0.165112	-2.972	0.00159
25	0.069283	1.2471	0.106633

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.0 ; par3 = 0 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; par3 = 0 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code