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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 16 Dec 2008 07:21:32 -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/t1229437366oru8xsy5utjybyi.htm/, Retrieved Wed, 15 May 2024 23:27:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33959, Retrieved Wed, 15 May 2024 23:27:51 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

200

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

-     [Standard Deviation-Mean Plot] [Paper Hoofdstuk 4...] [2008-12-05 10:14:55] [6fea0e9a9b3b29a63badf2c274e82506]
- RM D  [Variance Reduction Matrix] [Paper, hoofdstuk ...] [2008-12-06 15:48:43] [79c17183721a40a589db5f9f561947d8]
- RMP     [(Partial) Autocorrelation Function] [Paper, hoofdstuk ...] [2008-12-06 16:56:09] [79c17183721a40a589db5f9f561947d8]
-   P       [(Partial) Autocorrelation Function] [Paper, hoofdstuk ...] [2008-12-06 17:05:19] [79c17183721a40a589db5f9f561947d8]
-   P           [(Partial) Autocorrelation Function] [Paper 4.3 (P)ACF ...] [2008-12-16 14:21:32] [3bb0537fcae9c337e49b9ce75ff3d4da] [Current]
-   P             [(Partial) Autocorrelation Function] [Paper 4.3 (P)ACF ...] [2008-12-16 14:24:05] [79c17183721a40a589db5f9f561947d8] 
-                 [(Partial) Autocorrelation Function] [Paper 4.3 (P)ACF ...] [2008-12-16 14:28:29] [79c17183721a40a589db5f9f561947d8] 

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Dataseries X:

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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=33959&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=33959&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33959&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	-0.594215	-4.0302	0.000104
2	0.154407	1.0472	0.150231
3	0.024087	0.1634	0.435474
4	-0.077122	-0.5231	0.301719
5	-0.060357	-0.4094	0.342089
6	0.198592	1.3469	0.092303
7	-0.224658	-1.5237	0.067214
8	0.050989	0.3458	0.365526
9	0.22209	1.5063	0.069415
10	-0.252237	-1.7108	0.046932
11	0.167072	1.1331	0.131515
12	-0.095326	-0.6465	0.260573
13	-0.006482	-0.044	0.482562
14	-0.109984	-0.7459	0.229748
15	0.275354	1.8675	0.034102
16	-0.258131	-1.7507	0.04333
17	0.121119	0.8215	0.207809
18	0.108293	0.7345	0.233192
19	-0.254055	-1.7231	0.045795
20	0.269558	1.8282	0.037002
21	-0.172729	-1.1715	0.123714
22	-0.024063	-0.1632	0.435536
23	0.023507	0.1594	0.437013
24	0.116516	0.7903	0.216718

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.594215 & -4.0302 & 0.000104 \tabularnewline
2 & 0.154407 & 1.0472 & 0.150231 \tabularnewline
3 & 0.024087 & 0.1634 & 0.435474 \tabularnewline
4 & -0.077122 & -0.5231 & 0.301719 \tabularnewline
5 & -0.060357 & -0.4094 & 0.342089 \tabularnewline
6 & 0.198592 & 1.3469 & 0.092303 \tabularnewline
7 & -0.224658 & -1.5237 & 0.067214 \tabularnewline
8 & 0.050989 & 0.3458 & 0.365526 \tabularnewline
9 & 0.22209 & 1.5063 & 0.069415 \tabularnewline
10 & -0.252237 & -1.7108 & 0.046932 \tabularnewline
11 & 0.167072 & 1.1331 & 0.131515 \tabularnewline
12 & -0.095326 & -0.6465 & 0.260573 \tabularnewline
13 & -0.006482 & -0.044 & 0.482562 \tabularnewline
14 & -0.109984 & -0.7459 & 0.229748 \tabularnewline
15 & 0.275354 & 1.8675 & 0.034102 \tabularnewline
16 & -0.258131 & -1.7507 & 0.04333 \tabularnewline
17 & 0.121119 & 0.8215 & 0.207809 \tabularnewline
18 & 0.108293 & 0.7345 & 0.233192 \tabularnewline
19 & -0.254055 & -1.7231 & 0.045795 \tabularnewline
20 & 0.269558 & 1.8282 & 0.037002 \tabularnewline
21 & -0.172729 & -1.1715 & 0.123714 \tabularnewline
22 & -0.024063 & -0.1632 & 0.435536 \tabularnewline
23 & 0.023507 & 0.1594 & 0.437013 \tabularnewline
24 & 0.116516 & 0.7903 & 0.216718 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33959&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]-0.594215[/C][C]-4.0302[/C][C]0.000104[/C][/ROW]
[ROW][C]2[/C][C]0.154407[/C][C]1.0472[/C][C]0.150231[/C][/ROW]
[ROW][C]3[/C][C]0.024087[/C][C]0.1634[/C][C]0.435474[/C][/ROW]
[ROW][C]4[/C][C]-0.077122[/C][C]-0.5231[/C][C]0.301719[/C][/ROW]
[ROW][C]5[/C][C]-0.060357[/C][C]-0.4094[/C][C]0.342089[/C][/ROW]
[ROW][C]6[/C][C]0.198592[/C][C]1.3469[/C][C]0.092303[/C][/ROW]
[ROW][C]7[/C][C]-0.224658[/C][C]-1.5237[/C][C]0.067214[/C][/ROW]
[ROW][C]8[/C][C]0.050989[/C][C]0.3458[/C][C]0.365526[/C][/ROW]
[ROW][C]9[/C][C]0.22209[/C][C]1.5063[/C][C]0.069415[/C][/ROW]
[ROW][C]10[/C][C]-0.252237[/C][C]-1.7108[/C][C]0.046932[/C][/ROW]
[ROW][C]11[/C][C]0.167072[/C][C]1.1331[/C][C]0.131515[/C][/ROW]
[ROW][C]12[/C][C]-0.095326[/C][C]-0.6465[/C][C]0.260573[/C][/ROW]
[ROW][C]13[/C][C]-0.006482[/C][C]-0.044[/C][C]0.482562[/C][/ROW]
[ROW][C]14[/C][C]-0.109984[/C][C]-0.7459[/C][C]0.229748[/C][/ROW]
[ROW][C]15[/C][C]0.275354[/C][C]1.8675[/C][C]0.034102[/C][/ROW]
[ROW][C]16[/C][C]-0.258131[/C][C]-1.7507[/C][C]0.04333[/C][/ROW]
[ROW][C]17[/C][C]0.121119[/C][C]0.8215[/C][C]0.207809[/C][/ROW]
[ROW][C]18[/C][C]0.108293[/C][C]0.7345[/C][C]0.233192[/C][/ROW]
[ROW][C]19[/C][C]-0.254055[/C][C]-1.7231[/C][C]0.045795[/C][/ROW]
[ROW][C]20[/C][C]0.269558[/C][C]1.8282[/C][C]0.037002[/C][/ROW]
[ROW][C]21[/C][C]-0.172729[/C][C]-1.1715[/C][C]0.123714[/C][/ROW]
[ROW][C]22[/C][C]-0.024063[/C][C]-0.1632[/C][C]0.435536[/C][/ROW]
[ROW][C]23[/C][C]0.023507[/C][C]0.1594[/C][C]0.437013[/C][/ROW]
[ROW][C]24[/C][C]0.116516[/C][C]0.7903[/C][C]0.216718[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33959&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33959&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	-0.594215	-4.0302	0.000104
2	0.154407	1.0472	0.150231
3	0.024087	0.1634	0.435474
4	-0.077122	-0.5231	0.301719
5	-0.060357	-0.4094	0.342089
6	0.198592	1.3469	0.092303
7	-0.224658	-1.5237	0.067214
8	0.050989	0.3458	0.365526
9	0.22209	1.5063	0.069415
10	-0.252237	-1.7108	0.046932
11	0.167072	1.1331	0.131515
12	-0.095326	-0.6465	0.260573
13	-0.006482	-0.044	0.482562
14	-0.109984	-0.7459	0.229748
15	0.275354	1.8675	0.034102
16	-0.258131	-1.7507	0.04333
17	0.121119	0.8215	0.207809
18	0.108293	0.7345	0.233192
19	-0.254055	-1.7231	0.045795
20	0.269558	1.8282	0.037002
21	-0.172729	-1.1715	0.123714
22	-0.024063	-0.1632	0.435536
23	0.023507	0.1594	0.437013
24	0.116516	0.7903	0.216718

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.594215	-4.0302	0.000104
2	-0.307131	-2.0831	0.021416
3	-0.065686	-0.4455	0.329022
4	-0.071412	-0.4843	0.315223
5	-0.235083	-1.5944	0.058847
6	0.041838	0.2838	0.388933
7	-0.077359	-0.5247	0.301164
8	-0.216188	-1.4663	0.074691
9	0.184936	1.2543	0.108035
10	0.083714	0.5678	0.286474
11	0.081477	0.5526	0.291604
12	-0.051733	-0.3509	0.363644
13	-0.014759	-0.1001	0.460351
14	-0.261727	-1.7751	0.041247
15	0.034776	0.2359	0.407292
16	0.074795	0.5073	0.307188
17	-0.079386	-0.5384	0.29644
18	0.137714	0.934	0.177584
19	-0.105295	-0.7141	0.239373
20	0.115574	0.7839	0.21857
21	-0.024492	-0.1661	0.434398
22	-0.041788	-0.2834	0.389063
23	-0.071585	-0.4855	0.314808
24	-0.025845	-0.1753	0.430811

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.594215 & -4.0302 & 0.000104 \tabularnewline
2 & -0.307131 & -2.0831 & 0.021416 \tabularnewline
3 & -0.065686 & -0.4455 & 0.329022 \tabularnewline
4 & -0.071412 & -0.4843 & 0.315223 \tabularnewline
5 & -0.235083 & -1.5944 & 0.058847 \tabularnewline
6 & 0.041838 & 0.2838 & 0.388933 \tabularnewline
7 & -0.077359 & -0.5247 & 0.301164 \tabularnewline
8 & -0.216188 & -1.4663 & 0.074691 \tabularnewline
9 & 0.184936 & 1.2543 & 0.108035 \tabularnewline
10 & 0.083714 & 0.5678 & 0.286474 \tabularnewline
11 & 0.081477 & 0.5526 & 0.291604 \tabularnewline
12 & -0.051733 & -0.3509 & 0.363644 \tabularnewline
13 & -0.014759 & -0.1001 & 0.460351 \tabularnewline
14 & -0.261727 & -1.7751 & 0.041247 \tabularnewline
15 & 0.034776 & 0.2359 & 0.407292 \tabularnewline
16 & 0.074795 & 0.5073 & 0.307188 \tabularnewline
17 & -0.079386 & -0.5384 & 0.29644 \tabularnewline
18 & 0.137714 & 0.934 & 0.177584 \tabularnewline
19 & -0.105295 & -0.7141 & 0.239373 \tabularnewline
20 & 0.115574 & 0.7839 & 0.21857 \tabularnewline
21 & -0.024492 & -0.1661 & 0.434398 \tabularnewline
22 & -0.041788 & -0.2834 & 0.389063 \tabularnewline
23 & -0.071585 & -0.4855 & 0.314808 \tabularnewline
24 & -0.025845 & -0.1753 & 0.430811 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33959&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]-0.594215[/C][C]-4.0302[/C][C]0.000104[/C][/ROW]
[ROW][C]2[/C][C]-0.307131[/C][C]-2.0831[/C][C]0.021416[/C][/ROW]
[ROW][C]3[/C][C]-0.065686[/C][C]-0.4455[/C][C]0.329022[/C][/ROW]
[ROW][C]4[/C][C]-0.071412[/C][C]-0.4843[/C][C]0.315223[/C][/ROW]
[ROW][C]5[/C][C]-0.235083[/C][C]-1.5944[/C][C]0.058847[/C][/ROW]
[ROW][C]6[/C][C]0.041838[/C][C]0.2838[/C][C]0.388933[/C][/ROW]
[ROW][C]7[/C][C]-0.077359[/C][C]-0.5247[/C][C]0.301164[/C][/ROW]
[ROW][C]8[/C][C]-0.216188[/C][C]-1.4663[/C][C]0.074691[/C][/ROW]
[ROW][C]9[/C][C]0.184936[/C][C]1.2543[/C][C]0.108035[/C][/ROW]
[ROW][C]10[/C][C]0.083714[/C][C]0.5678[/C][C]0.286474[/C][/ROW]
[ROW][C]11[/C][C]0.081477[/C][C]0.5526[/C][C]0.291604[/C][/ROW]
[ROW][C]12[/C][C]-0.051733[/C][C]-0.3509[/C][C]0.363644[/C][/ROW]
[ROW][C]13[/C][C]-0.014759[/C][C]-0.1001[/C][C]0.460351[/C][/ROW]
[ROW][C]14[/C][C]-0.261727[/C][C]-1.7751[/C][C]0.041247[/C][/ROW]
[ROW][C]15[/C][C]0.034776[/C][C]0.2359[/C][C]0.407292[/C][/ROW]
[ROW][C]16[/C][C]0.074795[/C][C]0.5073[/C][C]0.307188[/C][/ROW]
[ROW][C]17[/C][C]-0.079386[/C][C]-0.5384[/C][C]0.29644[/C][/ROW]
[ROW][C]18[/C][C]0.137714[/C][C]0.934[/C][C]0.177584[/C][/ROW]
[ROW][C]19[/C][C]-0.105295[/C][C]-0.7141[/C][C]0.239373[/C][/ROW]
[ROW][C]20[/C][C]0.115574[/C][C]0.7839[/C][C]0.21857[/C][/ROW]
[ROW][C]21[/C][C]-0.024492[/C][C]-0.1661[/C][C]0.434398[/C][/ROW]
[ROW][C]22[/C][C]-0.041788[/C][C]-0.2834[/C][C]0.389063[/C][/ROW]
[ROW][C]23[/C][C]-0.071585[/C][C]-0.4855[/C][C]0.314808[/C][/ROW]
[ROW][C]24[/C][C]-0.025845[/C][C]-0.1753[/C][C]0.430811[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33959&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33959&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	-0.594215	-4.0302	0.000104
2	-0.307131	-2.0831	0.021416
3	-0.065686	-0.4455	0.329022
4	-0.071412	-0.4843	0.315223
5	-0.235083	-1.5944	0.058847
6	0.041838	0.2838	0.388933
7	-0.077359	-0.5247	0.301164
8	-0.216188	-1.4663	0.074691
9	0.184936	1.2543	0.108035
10	0.083714	0.5678	0.286474
11	0.081477	0.5526	0.291604
12	-0.051733	-0.3509	0.363644
13	-0.014759	-0.1001	0.460351
14	-0.261727	-1.7751	0.041247
15	0.034776	0.2359	0.407292
16	0.074795	0.5073	0.307188
17	-0.079386	-0.5384	0.29644
18	0.137714	0.934	0.177584
19	-0.105295	-0.7141	0.239373
20	0.115574	0.7839	0.21857
21	-0.024492	-0.1661	0.434398
22	-0.041788	-0.2834	0.389063
23	-0.071585	-0.4855	0.314808
24	-0.025845	-0.1753	0.430811

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 2 ; 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