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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

Tue, 15 Dec 2009 01:35:16 -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/15/t1260866173z7pyyg34egrkgs8.htm/, Retrieved Wed, 08 May 2024 14:21:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67764, Retrieved Wed, 08 May 2024 14:21:25 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

138

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

-       [(Partial) Autocorrelation Function] [Autocorrelation (...] [2009-12-15 08:35:16] [91da2e1ebdd83187f2515f461585cbee] [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	4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67764&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]4 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=67764&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67764&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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.522744	-5.7025	0
2	-0.051663	-0.5636	0.287052
3	0.357436	3.8992	8e-05
4	-0.29186	-3.1838	0.000928
5	0.064772	0.7066	0.240605
6	0.188147	2.0524	0.02116
7	-0.336994	-3.6762	0.000178
8	0.208195	2.2711	0.012468
9	0.04054	0.4422	0.32956
10	-0.175236	-1.9116	0.029166
11	0.074808	0.8161	0.20805
12	0.032146	0.3507	0.363229
13	-0.138201	-1.5076	0.067154
14	0.112534	1.2276	0.111011
15	0.056693	0.6184	0.268731
16	-0.235803	-2.5723	0.005666
17	0.195941	2.1375	0.017303
18	0.001942	0.0212	0.491568
19	-0.188648	-2.0579	0.020892
20	0.207003	2.2581	0.01288
21	-0.031531	-0.344	0.365739

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.522744 & -5.7025 & 0 \tabularnewline
2 & -0.051663 & -0.5636 & 0.287052 \tabularnewline
3 & 0.357436 & 3.8992 & 8e-05 \tabularnewline
4 & -0.29186 & -3.1838 & 0.000928 \tabularnewline
5 & 0.064772 & 0.7066 & 0.240605 \tabularnewline
6 & 0.188147 & 2.0524 & 0.02116 \tabularnewline
7 & -0.336994 & -3.6762 & 0.000178 \tabularnewline
8 & 0.208195 & 2.2711 & 0.012468 \tabularnewline
9 & 0.04054 & 0.4422 & 0.32956 \tabularnewline
10 & -0.175236 & -1.9116 & 0.029166 \tabularnewline
11 & 0.074808 & 0.8161 & 0.20805 \tabularnewline
12 & 0.032146 & 0.3507 & 0.363229 \tabularnewline
13 & -0.138201 & -1.5076 & 0.067154 \tabularnewline
14 & 0.112534 & 1.2276 & 0.111011 \tabularnewline
15 & 0.056693 & 0.6184 & 0.268731 \tabularnewline
16 & -0.235803 & -2.5723 & 0.005666 \tabularnewline
17 & 0.195941 & 2.1375 & 0.017303 \tabularnewline
18 & 0.001942 & 0.0212 & 0.491568 \tabularnewline
19 & -0.188648 & -2.0579 & 0.020892 \tabularnewline
20 & 0.207003 & 2.2581 & 0.01288 \tabularnewline
21 & -0.031531 & -0.344 & 0.365739 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67764&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]-0.522744[/C][C]-5.7025[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.051663[/C][C]-0.5636[/C][C]0.287052[/C][/ROW]
[ROW][C]3[/C][C]0.357436[/C][C]3.8992[/C][C]8e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.29186[/C][C]-3.1838[/C][C]0.000928[/C][/ROW]
[ROW][C]5[/C][C]0.064772[/C][C]0.7066[/C][C]0.240605[/C][/ROW]
[ROW][C]6[/C][C]0.188147[/C][C]2.0524[/C][C]0.02116[/C][/ROW]
[ROW][C]7[/C][C]-0.336994[/C][C]-3.6762[/C][C]0.000178[/C][/ROW]
[ROW][C]8[/C][C]0.208195[/C][C]2.2711[/C][C]0.012468[/C][/ROW]
[ROW][C]9[/C][C]0.04054[/C][C]0.4422[/C][C]0.32956[/C][/ROW]
[ROW][C]10[/C][C]-0.175236[/C][C]-1.9116[/C][C]0.029166[/C][/ROW]
[ROW][C]11[/C][C]0.074808[/C][C]0.8161[/C][C]0.20805[/C][/ROW]
[ROW][C]12[/C][C]0.032146[/C][C]0.3507[/C][C]0.363229[/C][/ROW]
[ROW][C]13[/C][C]-0.138201[/C][C]-1.5076[/C][C]0.067154[/C][/ROW]
[ROW][C]14[/C][C]0.112534[/C][C]1.2276[/C][C]0.111011[/C][/ROW]
[ROW][C]15[/C][C]0.056693[/C][C]0.6184[/C][C]0.268731[/C][/ROW]
[ROW][C]16[/C][C]-0.235803[/C][C]-2.5723[/C][C]0.005666[/C][/ROW]
[ROW][C]17[/C][C]0.195941[/C][C]2.1375[/C][C]0.017303[/C][/ROW]
[ROW][C]18[/C][C]0.001942[/C][C]0.0212[/C][C]0.491568[/C][/ROW]
[ROW][C]19[/C][C]-0.188648[/C][C]-2.0579[/C][C]0.020892[/C][/ROW]
[ROW][C]20[/C][C]0.207003[/C][C]2.2581[/C][C]0.01288[/C][/ROW]
[ROW][C]21[/C][C]-0.031531[/C][C]-0.344[/C][C]0.365739[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67764&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67764&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	-0.522744	-5.7025	0
2	-0.051663	-0.5636	0.287052
3	0.357436	3.8992	8e-05
4	-0.29186	-3.1838	0.000928
5	0.064772	0.7066	0.240605
6	0.188147	2.0524	0.02116
7	-0.336994	-3.6762	0.000178
8	0.208195	2.2711	0.012468
9	0.04054	0.4422	0.32956
10	-0.175236	-1.9116	0.029166
11	0.074808	0.8161	0.20805
12	0.032146	0.3507	0.363229
13	-0.138201	-1.5076	0.067154
14	0.112534	1.2276	0.111011
15	0.056693	0.6184	0.268731
16	-0.235803	-2.5723	0.005666
17	0.195941	2.1375	0.017303
18	0.001942	0.0212	0.491568
19	-0.188648	-2.0579	0.020892
20	0.207003	2.2581	0.01288
21	-0.031531	-0.344	0.365739

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.522744	-5.7025	0
2	-0.447098	-4.8773	2e-06
3	0.145559	1.5879	0.057485
4	0.024502	0.2673	0.394857
5	0.001139	0.0124	0.495055
6	0.14214	1.5506	0.061831
7	-0.161804	-1.7651	0.040058
8	-0.074638	-0.8142	0.208578
9	0.011191	0.1221	0.45152
10	0.046371	0.5059	0.306949
11	-0.11243	-1.2265	0.111222
12	-0.067098	-0.7319	0.232819
13	-0.103145	-1.1252	0.131389
14	-0.071298	-0.7778	0.219126
15	0.152849	1.6674	0.049034
16	-0.093878	-1.0241	0.153935
17	-0.056399	-0.6152	0.269785
18	-0.011675	-0.1274	0.449436
19	-0.071717	-0.7823	0.217784
20	-0.004148	-0.0452	0.481993
21	0.102776	1.1211	0.132241

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.522744 & -5.7025 & 0 \tabularnewline
2 & -0.447098 & -4.8773 & 2e-06 \tabularnewline
3 & 0.145559 & 1.5879 & 0.057485 \tabularnewline
4 & 0.024502 & 0.2673 & 0.394857 \tabularnewline
5 & 0.001139 & 0.0124 & 0.495055 \tabularnewline
6 & 0.14214 & 1.5506 & 0.061831 \tabularnewline
7 & -0.161804 & -1.7651 & 0.040058 \tabularnewline
8 & -0.074638 & -0.8142 & 0.208578 \tabularnewline
9 & 0.011191 & 0.1221 & 0.45152 \tabularnewline
10 & 0.046371 & 0.5059 & 0.306949 \tabularnewline
11 & -0.11243 & -1.2265 & 0.111222 \tabularnewline
12 & -0.067098 & -0.7319 & 0.232819 \tabularnewline
13 & -0.103145 & -1.1252 & 0.131389 \tabularnewline
14 & -0.071298 & -0.7778 & 0.219126 \tabularnewline
15 & 0.152849 & 1.6674 & 0.049034 \tabularnewline
16 & -0.093878 & -1.0241 & 0.153935 \tabularnewline
17 & -0.056399 & -0.6152 & 0.269785 \tabularnewline
18 & -0.011675 & -0.1274 & 0.449436 \tabularnewline
19 & -0.071717 & -0.7823 & 0.217784 \tabularnewline
20 & -0.004148 & -0.0452 & 0.481993 \tabularnewline
21 & 0.102776 & 1.1211 & 0.132241 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67764&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]-0.522744[/C][C]-5.7025[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.447098[/C][C]-4.8773[/C][C]2e-06[/C][/ROW]
[ROW][C]3[/C][C]0.145559[/C][C]1.5879[/C][C]0.057485[/C][/ROW]
[ROW][C]4[/C][C]0.024502[/C][C]0.2673[/C][C]0.394857[/C][/ROW]
[ROW][C]5[/C][C]0.001139[/C][C]0.0124[/C][C]0.495055[/C][/ROW]
[ROW][C]6[/C][C]0.14214[/C][C]1.5506[/C][C]0.061831[/C][/ROW]
[ROW][C]7[/C][C]-0.161804[/C][C]-1.7651[/C][C]0.040058[/C][/ROW]
[ROW][C]8[/C][C]-0.074638[/C][C]-0.8142[/C][C]0.208578[/C][/ROW]
[ROW][C]9[/C][C]0.011191[/C][C]0.1221[/C][C]0.45152[/C][/ROW]
[ROW][C]10[/C][C]0.046371[/C][C]0.5059[/C][C]0.306949[/C][/ROW]
[ROW][C]11[/C][C]-0.11243[/C][C]-1.2265[/C][C]0.111222[/C][/ROW]
[ROW][C]12[/C][C]-0.067098[/C][C]-0.7319[/C][C]0.232819[/C][/ROW]
[ROW][C]13[/C][C]-0.103145[/C][C]-1.1252[/C][C]0.131389[/C][/ROW]
[ROW][C]14[/C][C]-0.071298[/C][C]-0.7778[/C][C]0.219126[/C][/ROW]
[ROW][C]15[/C][C]0.152849[/C][C]1.6674[/C][C]0.049034[/C][/ROW]
[ROW][C]16[/C][C]-0.093878[/C][C]-1.0241[/C][C]0.153935[/C][/ROW]
[ROW][C]17[/C][C]-0.056399[/C][C]-0.6152[/C][C]0.269785[/C][/ROW]
[ROW][C]18[/C][C]-0.011675[/C][C]-0.1274[/C][C]0.449436[/C][/ROW]
[ROW][C]19[/C][C]-0.071717[/C][C]-0.7823[/C][C]0.217784[/C][/ROW]
[ROW][C]20[/C][C]-0.004148[/C][C]-0.0452[/C][C]0.481993[/C][/ROW]
[ROW][C]21[/C][C]0.102776[/C][C]1.1211[/C][C]0.132241[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67764&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67764&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	-0.522744	-5.7025	0
2	-0.447098	-4.8773	2e-06
3	0.145559	1.5879	0.057485
4	0.024502	0.2673	0.394857
5	0.001139	0.0124	0.495055
6	0.14214	1.5506	0.061831
7	-0.161804	-1.7651	0.040058
8	-0.074638	-0.8142	0.208578
9	0.011191	0.1221	0.45152
10	0.046371	0.5059	0.306949
11	-0.11243	-1.2265	0.111222
12	-0.067098	-0.7319	0.232819
13	-0.103145	-1.1252	0.131389
14	-0.071298	-0.7778	0.219126
15	0.152849	1.6674	0.049034
16	-0.093878	-1.0241	0.153935
17	-0.056399	-0.6152	0.269785
18	-0.011675	-0.1274	0.449436
19	-0.071717	-0.7823	0.217784
20	-0.004148	-0.0452	0.481993
21	0.102776	1.1211	0.132241

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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