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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

Fri, 11 Dec 2009 03:27:22 -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/2009/Dec/11/t1260527315x13viov1sp9vdri.htm/, Retrieved Mon, 29 Apr 2024 04:02:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=65959, Retrieved Mon, 29 Apr 2024 04:02:36 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

161

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

-     [ARIMA Forecasting] [] [2009-12-06 10:44:58] [1e83ffa964db6f7ea6ccc4e7b5acbbff]
-   PD  [ARIMA Forecasting] [ws 10 deel 2 prblm] [2009-12-09 19:29:01] [134dc66689e3d457a82860db6471d419]
- RMP       [(Partial) Autocorrelation Function] [] [2009-12-11 10:27:22] [eba9f01697e64705b70041e6f338cb22] [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	'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=65959&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=65959&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65959&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	-0.367144	-3.9372	7.1e-05
2	-0.099582	-1.0679	0.143901
3	0.020181	0.2164	0.414524
4	-0.024963	-0.2677	0.394707
5	0.073374	0.7868	0.216494
6	-0.132224	-1.4179	0.079456
7	0.029069	0.3117	0.377905
8	-0.01053	-0.1129	0.455143
9	-0.125429	-1.3451	0.090623
10	0.112156	1.2027	0.115774
11	0.092778	0.9949	0.160929
12	0.019611	0.2103	0.416902
13	-0.133324	-1.4297	0.077752
14	-0.015067	-0.1616	0.43596
15	0.117811	1.2634	0.104503
16	-0.079129	-0.8486	0.198943
17	0.00583	0.0625	0.47513
18	0.020438	0.2192	0.413454
19	-0.006723	-0.0721	0.471326
20	0.021607	0.2317	0.408587

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.367144 & -3.9372 & 7.1e-05 \tabularnewline
2 & -0.099582 & -1.0679 & 0.143901 \tabularnewline
3 & 0.020181 & 0.2164 & 0.414524 \tabularnewline
4 & -0.024963 & -0.2677 & 0.394707 \tabularnewline
5 & 0.073374 & 0.7868 & 0.216494 \tabularnewline
6 & -0.132224 & -1.4179 & 0.079456 \tabularnewline
7 & 0.029069 & 0.3117 & 0.377905 \tabularnewline
8 & -0.01053 & -0.1129 & 0.455143 \tabularnewline
9 & -0.125429 & -1.3451 & 0.090623 \tabularnewline
10 & 0.112156 & 1.2027 & 0.115774 \tabularnewline
11 & 0.092778 & 0.9949 & 0.160929 \tabularnewline
12 & 0.019611 & 0.2103 & 0.416902 \tabularnewline
13 & -0.133324 & -1.4297 & 0.077752 \tabularnewline
14 & -0.015067 & -0.1616 & 0.43596 \tabularnewline
15 & 0.117811 & 1.2634 & 0.104503 \tabularnewline
16 & -0.079129 & -0.8486 & 0.198943 \tabularnewline
17 & 0.00583 & 0.0625 & 0.47513 \tabularnewline
18 & 0.020438 & 0.2192 & 0.413454 \tabularnewline
19 & -0.006723 & -0.0721 & 0.471326 \tabularnewline
20 & 0.021607 & 0.2317 & 0.408587 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65959&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]-0.367144[/C][C]-3.9372[/C][C]7.1e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.099582[/C][C]-1.0679[/C][C]0.143901[/C][/ROW]
[ROW][C]3[/C][C]0.020181[/C][C]0.2164[/C][C]0.414524[/C][/ROW]
[ROW][C]4[/C][C]-0.024963[/C][C]-0.2677[/C][C]0.394707[/C][/ROW]
[ROW][C]5[/C][C]0.073374[/C][C]0.7868[/C][C]0.216494[/C][/ROW]
[ROW][C]6[/C][C]-0.132224[/C][C]-1.4179[/C][C]0.079456[/C][/ROW]
[ROW][C]7[/C][C]0.029069[/C][C]0.3117[/C][C]0.377905[/C][/ROW]
[ROW][C]8[/C][C]-0.01053[/C][C]-0.1129[/C][C]0.455143[/C][/ROW]
[ROW][C]9[/C][C]-0.125429[/C][C]-1.3451[/C][C]0.090623[/C][/ROW]
[ROW][C]10[/C][C]0.112156[/C][C]1.2027[/C][C]0.115774[/C][/ROW]
[ROW][C]11[/C][C]0.092778[/C][C]0.9949[/C][C]0.160929[/C][/ROW]
[ROW][C]12[/C][C]0.019611[/C][C]0.2103[/C][C]0.416902[/C][/ROW]
[ROW][C]13[/C][C]-0.133324[/C][C]-1.4297[/C][C]0.077752[/C][/ROW]
[ROW][C]14[/C][C]-0.015067[/C][C]-0.1616[/C][C]0.43596[/C][/ROW]
[ROW][C]15[/C][C]0.117811[/C][C]1.2634[/C][C]0.104503[/C][/ROW]
[ROW][C]16[/C][C]-0.079129[/C][C]-0.8486[/C][C]0.198943[/C][/ROW]
[ROW][C]17[/C][C]0.00583[/C][C]0.0625[/C][C]0.47513[/C][/ROW]
[ROW][C]18[/C][C]0.020438[/C][C]0.2192[/C][C]0.413454[/C][/ROW]
[ROW][C]19[/C][C]-0.006723[/C][C]-0.0721[/C][C]0.471326[/C][/ROW]
[ROW][C]20[/C][C]0.021607[/C][C]0.2317[/C][C]0.408587[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65959&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65959&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	-0.367144	-3.9372	7.1e-05
2	-0.099582	-1.0679	0.143901
3	0.020181	0.2164	0.414524
4	-0.024963	-0.2677	0.394707
5	0.073374	0.7868	0.216494
6	-0.132224	-1.4179	0.079456
7	0.029069	0.3117	0.377905
8	-0.01053	-0.1129	0.455143
9	-0.125429	-1.3451	0.090623
10	0.112156	1.2027	0.115774
11	0.092778	0.9949	0.160929
12	0.019611	0.2103	0.416902
13	-0.133324	-1.4297	0.077752
14	-0.015067	-0.1616	0.43596
15	0.117811	1.2634	0.104503
16	-0.079129	-0.8486	0.198943
17	0.00583	0.0625	0.47513
18	0.020438	0.2192	0.413454
19	-0.006723	-0.0721	0.471326
20	0.021607	0.2317	0.408587

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.367144	-3.9372	7.1e-05
2	-0.270892	-2.905	0.002203
3	-0.15684	-1.6819	0.047649
4	-0.136236	-1.461	0.073376
5	-0.005891	-0.0632	0.47487
6	-0.149149	-1.5994	0.056232
7	-0.102324	-1.0973	0.137401
8	-0.121904	-1.3073	0.096864
9	-0.273111	-2.9288	0.002052
10	-0.161249	-1.7292	0.043228
11	-0.00311	-0.0333	0.486728
12	0.071509	0.7669	0.222371
13	-0.086229	-0.9247	0.178529
14	-0.142783	-1.5312	0.064236
15	-0.059631	-0.6395	0.261895
16	-0.130069	-1.3948	0.082877
17	-0.09689	-1.039	0.150485
18	-0.043882	-0.4706	0.319416
19	-0.024225	-0.2598	0.397746
20	0.010247	0.1099	0.456345

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.367144 & -3.9372 & 7.1e-05 \tabularnewline
2 & -0.270892 & -2.905 & 0.002203 \tabularnewline
3 & -0.15684 & -1.6819 & 0.047649 \tabularnewline
4 & -0.136236 & -1.461 & 0.073376 \tabularnewline
5 & -0.005891 & -0.0632 & 0.47487 \tabularnewline
6 & -0.149149 & -1.5994 & 0.056232 \tabularnewline
7 & -0.102324 & -1.0973 & 0.137401 \tabularnewline
8 & -0.121904 & -1.3073 & 0.096864 \tabularnewline
9 & -0.273111 & -2.9288 & 0.002052 \tabularnewline
10 & -0.161249 & -1.7292 & 0.043228 \tabularnewline
11 & -0.00311 & -0.0333 & 0.486728 \tabularnewline
12 & 0.071509 & 0.7669 & 0.222371 \tabularnewline
13 & -0.086229 & -0.9247 & 0.178529 \tabularnewline
14 & -0.142783 & -1.5312 & 0.064236 \tabularnewline
15 & -0.059631 & -0.6395 & 0.261895 \tabularnewline
16 & -0.130069 & -1.3948 & 0.082877 \tabularnewline
17 & -0.09689 & -1.039 & 0.150485 \tabularnewline
18 & -0.043882 & -0.4706 & 0.319416 \tabularnewline
19 & -0.024225 & -0.2598 & 0.397746 \tabularnewline
20 & 0.010247 & 0.1099 & 0.456345 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65959&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]-0.367144[/C][C]-3.9372[/C][C]7.1e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.270892[/C][C]-2.905[/C][C]0.002203[/C][/ROW]
[ROW][C]3[/C][C]-0.15684[/C][C]-1.6819[/C][C]0.047649[/C][/ROW]
[ROW][C]4[/C][C]-0.136236[/C][C]-1.461[/C][C]0.073376[/C][/ROW]
[ROW][C]5[/C][C]-0.005891[/C][C]-0.0632[/C][C]0.47487[/C][/ROW]
[ROW][C]6[/C][C]-0.149149[/C][C]-1.5994[/C][C]0.056232[/C][/ROW]
[ROW][C]7[/C][C]-0.102324[/C][C]-1.0973[/C][C]0.137401[/C][/ROW]
[ROW][C]8[/C][C]-0.121904[/C][C]-1.3073[/C][C]0.096864[/C][/ROW]
[ROW][C]9[/C][C]-0.273111[/C][C]-2.9288[/C][C]0.002052[/C][/ROW]
[ROW][C]10[/C][C]-0.161249[/C][C]-1.7292[/C][C]0.043228[/C][/ROW]
[ROW][C]11[/C][C]-0.00311[/C][C]-0.0333[/C][C]0.486728[/C][/ROW]
[ROW][C]12[/C][C]0.071509[/C][C]0.7669[/C][C]0.222371[/C][/ROW]
[ROW][C]13[/C][C]-0.086229[/C][C]-0.9247[/C][C]0.178529[/C][/ROW]
[ROW][C]14[/C][C]-0.142783[/C][C]-1.5312[/C][C]0.064236[/C][/ROW]
[ROW][C]15[/C][C]-0.059631[/C][C]-0.6395[/C][C]0.261895[/C][/ROW]
[ROW][C]16[/C][C]-0.130069[/C][C]-1.3948[/C][C]0.082877[/C][/ROW]
[ROW][C]17[/C][C]-0.09689[/C][C]-1.039[/C][C]0.150485[/C][/ROW]
[ROW][C]18[/C][C]-0.043882[/C][C]-0.4706[/C][C]0.319416[/C][/ROW]
[ROW][C]19[/C][C]-0.024225[/C][C]-0.2598[/C][C]0.397746[/C][/ROW]
[ROW][C]20[/C][C]0.010247[/C][C]0.1099[/C][C]0.456345[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65959&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65959&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	-0.367144	-3.9372	7.1e-05
2	-0.270892	-2.905	0.002203
3	-0.15684	-1.6819	0.047649
4	-0.136236	-1.461	0.073376
5	-0.005891	-0.0632	0.47487
6	-0.149149	-1.5994	0.056232
7	-0.102324	-1.0973	0.137401
8	-0.121904	-1.3073	0.096864
9	-0.273111	-2.9288	0.002052
10	-0.161249	-1.7292	0.043228
11	-0.00311	-0.0333	0.486728
12	0.071509	0.7669	0.222371
13	-0.086229	-0.9247	0.178529
14	-0.142783	-1.5312	0.064236
15	-0.059631	-0.6395	0.261895
16	-0.130069	-1.3948	0.082877
17	-0.09689	-1.039	0.150485
18	-0.043882	-0.4706	0.319416
19	-0.024225	-0.2598	0.397746
20	0.010247	0.1099	0.456345

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = -0.5 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = -0.5 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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