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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

Thu, 25 Nov 2010 09:37:04 +0000

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/2010/Nov/25/t1290677719g85wbkieb17wq1j.htm/, Retrieved Fri, 26 Apr 2024 22:07:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=100668, Retrieved Fri, 26 Apr 2024 22:07:22 +0000

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User-defined keywords

Estimated Impact

125

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

-     [(Partial) Autocorrelation Function] [] [2010-11-24 15:46:23] [43e84bd88d5f94b739fa54f225367516]
-         [(Partial) Autocorrelation Function] [Forecasting] [2010-11-25 09:37:04] [19046f4a6967f3fb6f5f17d42e7d38f2] [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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=100668&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=100668&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=100668&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.951667	12.6968	0
2	0.873265	11.6508	0
3	0.792247	10.5699	0
4	0.729426	9.7318	0
5	0.686154	9.1544	0
6	0.656718	8.7617	0
7	0.632084	8.433	0
8	0.596058	7.9524	0
9	0.563864	7.5229	0
10	0.524319	6.9953	0
11	0.486873	6.4957	0
12	0.448097	5.9784	0
13	0.409918	5.469	0
14	0.37756	5.0373	1e-06
15	0.35124	4.6861	3e-06
16	0.333449	4.4488	8e-06
17	0.314723	4.1989	2.1e-05
18	0.299874	4.0008	4.6e-05
19	0.277407	3.7011	0.000143
20	0.253266	3.379	0.000447
21	0.23737	3.1669	0.000907
22	0.231712	3.0914	0.001156

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.951667 & 12.6968 & 0 \tabularnewline
2 & 0.873265 & 11.6508 & 0 \tabularnewline
3 & 0.792247 & 10.5699 & 0 \tabularnewline
4 & 0.729426 & 9.7318 & 0 \tabularnewline
5 & 0.686154 & 9.1544 & 0 \tabularnewline
6 & 0.656718 & 8.7617 & 0 \tabularnewline
7 & 0.632084 & 8.433 & 0 \tabularnewline
8 & 0.596058 & 7.9524 & 0 \tabularnewline
9 & 0.563864 & 7.5229 & 0 \tabularnewline
10 & 0.524319 & 6.9953 & 0 \tabularnewline
11 & 0.486873 & 6.4957 & 0 \tabularnewline
12 & 0.448097 & 5.9784 & 0 \tabularnewline
13 & 0.409918 & 5.469 & 0 \tabularnewline
14 & 0.37756 & 5.0373 & 1e-06 \tabularnewline
15 & 0.35124 & 4.6861 & 3e-06 \tabularnewline
16 & 0.333449 & 4.4488 & 8e-06 \tabularnewline
17 & 0.314723 & 4.1989 & 2.1e-05 \tabularnewline
18 & 0.299874 & 4.0008 & 4.6e-05 \tabularnewline
19 & 0.277407 & 3.7011 & 0.000143 \tabularnewline
20 & 0.253266 & 3.379 & 0.000447 \tabularnewline
21 & 0.23737 & 3.1669 & 0.000907 \tabularnewline
22 & 0.231712 & 3.0914 & 0.001156 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=100668&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]0.951667[/C][C]12.6968[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.873265[/C][C]11.6508[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.792247[/C][C]10.5699[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.729426[/C][C]9.7318[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.686154[/C][C]9.1544[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.656718[/C][C]8.7617[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.632084[/C][C]8.433[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.596058[/C][C]7.9524[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.563864[/C][C]7.5229[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.524319[/C][C]6.9953[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.486873[/C][C]6.4957[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.448097[/C][C]5.9784[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.409918[/C][C]5.469[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.37756[/C][C]5.0373[/C][C]1e-06[/C][/ROW]
[ROW][C]15[/C][C]0.35124[/C][C]4.6861[/C][C]3e-06[/C][/ROW]
[ROW][C]16[/C][C]0.333449[/C][C]4.4488[/C][C]8e-06[/C][/ROW]
[ROW][C]17[/C][C]0.314723[/C][C]4.1989[/C][C]2.1e-05[/C][/ROW]
[ROW][C]18[/C][C]0.299874[/C][C]4.0008[/C][C]4.6e-05[/C][/ROW]
[ROW][C]19[/C][C]0.277407[/C][C]3.7011[/C][C]0.000143[/C][/ROW]
[ROW][C]20[/C][C]0.253266[/C][C]3.379[/C][C]0.000447[/C][/ROW]
[ROW][C]21[/C][C]0.23737[/C][C]3.1669[/C][C]0.000907[/C][/ROW]
[ROW][C]22[/C][C]0.231712[/C][C]3.0914[/C][C]0.001156[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=100668&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=100668&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	0.951667	12.6968	0
2	0.873265	11.6508	0
3	0.792247	10.5699	0
4	0.729426	9.7318	0
5	0.686154	9.1544	0
6	0.656718	8.7617	0
7	0.632084	8.433	0
8	0.596058	7.9524	0
9	0.563864	7.5229	0
10	0.524319	6.9953	0
11	0.486873	6.4957	0
12	0.448097	5.9784	0
13	0.409918	5.469	0
14	0.37756	5.0373	1e-06
15	0.35124	4.6861	3e-06
16	0.333449	4.4488	8e-06
17	0.314723	4.1989	2.1e-05
18	0.299874	4.0008	4.6e-05
19	0.277407	3.7011	0.000143
20	0.253266	3.379	0.000447
21	0.23737	3.1669	0.000907
22	0.231712	3.0914	0.001156

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.951667	12.6968	0
2	-0.343538	-4.5834	4e-06
3	0.031519	0.4205	0.337309
4	0.157343	2.0992	0.018604
5	0.066408	0.886	0.188408
6	0.034757	0.4637	0.321708
7	0.002842	0.0379	0.484896
8	-0.130956	-1.7472	0.041166
9	0.15487	2.0662	0.020128
10	-0.143475	-1.9142	0.028599
11	0.039494	0.5269	0.299456
12	-0.054205	-0.7232	0.23526
13	-0.027783	-0.3707	0.35566
14	0.05252	0.7007	0.242201
15	0.019512	0.2603	0.397456
16	0.002861	0.0382	0.4848
17	-0.00857	-0.1143	0.454551
18	0.026406	0.3523	0.362515
19	-0.074696	-0.9966	0.160164
20	0.027703	0.3696	0.35606
21	0.097064	1.295	0.0985
22	0.033957	0.453	0.325535

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.951667 & 12.6968 & 0 \tabularnewline
2 & -0.343538 & -4.5834 & 4e-06 \tabularnewline
3 & 0.031519 & 0.4205 & 0.337309 \tabularnewline
4 & 0.157343 & 2.0992 & 0.018604 \tabularnewline
5 & 0.066408 & 0.886 & 0.188408 \tabularnewline
6 & 0.034757 & 0.4637 & 0.321708 \tabularnewline
7 & 0.002842 & 0.0379 & 0.484896 \tabularnewline
8 & -0.130956 & -1.7472 & 0.041166 \tabularnewline
9 & 0.15487 & 2.0662 & 0.020128 \tabularnewline
10 & -0.143475 & -1.9142 & 0.028599 \tabularnewline
11 & 0.039494 & 0.5269 & 0.299456 \tabularnewline
12 & -0.054205 & -0.7232 & 0.23526 \tabularnewline
13 & -0.027783 & -0.3707 & 0.35566 \tabularnewline
14 & 0.05252 & 0.7007 & 0.242201 \tabularnewline
15 & 0.019512 & 0.2603 & 0.397456 \tabularnewline
16 & 0.002861 & 0.0382 & 0.4848 \tabularnewline
17 & -0.00857 & -0.1143 & 0.454551 \tabularnewline
18 & 0.026406 & 0.3523 & 0.362515 \tabularnewline
19 & -0.074696 & -0.9966 & 0.160164 \tabularnewline
20 & 0.027703 & 0.3696 & 0.35606 \tabularnewline
21 & 0.097064 & 1.295 & 0.0985 \tabularnewline
22 & 0.033957 & 0.453 & 0.325535 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=100668&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]0.951667[/C][C]12.6968[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.343538[/C][C]-4.5834[/C][C]4e-06[/C][/ROW]
[ROW][C]3[/C][C]0.031519[/C][C]0.4205[/C][C]0.337309[/C][/ROW]
[ROW][C]4[/C][C]0.157343[/C][C]2.0992[/C][C]0.018604[/C][/ROW]
[ROW][C]5[/C][C]0.066408[/C][C]0.886[/C][C]0.188408[/C][/ROW]
[ROW][C]6[/C][C]0.034757[/C][C]0.4637[/C][C]0.321708[/C][/ROW]
[ROW][C]7[/C][C]0.002842[/C][C]0.0379[/C][C]0.484896[/C][/ROW]
[ROW][C]8[/C][C]-0.130956[/C][C]-1.7472[/C][C]0.041166[/C][/ROW]
[ROW][C]9[/C][C]0.15487[/C][C]2.0662[/C][C]0.020128[/C][/ROW]
[ROW][C]10[/C][C]-0.143475[/C][C]-1.9142[/C][C]0.028599[/C][/ROW]
[ROW][C]11[/C][C]0.039494[/C][C]0.5269[/C][C]0.299456[/C][/ROW]
[ROW][C]12[/C][C]-0.054205[/C][C]-0.7232[/C][C]0.23526[/C][/ROW]
[ROW][C]13[/C][C]-0.027783[/C][C]-0.3707[/C][C]0.35566[/C][/ROW]
[ROW][C]14[/C][C]0.05252[/C][C]0.7007[/C][C]0.242201[/C][/ROW]
[ROW][C]15[/C][C]0.019512[/C][C]0.2603[/C][C]0.397456[/C][/ROW]
[ROW][C]16[/C][C]0.002861[/C][C]0.0382[/C][C]0.4848[/C][/ROW]
[ROW][C]17[/C][C]-0.00857[/C][C]-0.1143[/C][C]0.454551[/C][/ROW]
[ROW][C]18[/C][C]0.026406[/C][C]0.3523[/C][C]0.362515[/C][/ROW]
[ROW][C]19[/C][C]-0.074696[/C][C]-0.9966[/C][C]0.160164[/C][/ROW]
[ROW][C]20[/C][C]0.027703[/C][C]0.3696[/C][C]0.35606[/C][/ROW]
[ROW][C]21[/C][C]0.097064[/C][C]1.295[/C][C]0.0985[/C][/ROW]
[ROW][C]22[/C][C]0.033957[/C][C]0.453[/C][C]0.325535[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=100668&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=100668&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	0.951667	12.6968	0
2	-0.343538	-4.5834	4e-06
3	0.031519	0.4205	0.337309
4	0.157343	2.0992	0.018604
5	0.066408	0.886	0.188408
6	0.034757	0.4637	0.321708
7	0.002842	0.0379	0.484896
8	-0.130956	-1.7472	0.041166
9	0.15487	2.0662	0.020128
10	-0.143475	-1.9142	0.028599
11	0.039494	0.5269	0.299456
12	-0.054205	-0.7232	0.23526
13	-0.027783	-0.3707	0.35566
14	0.05252	0.7007	0.242201
15	0.019512	0.2603	0.397456
16	0.002861	0.0382	0.4848
17	-0.00857	-0.1143	0.454551
18	0.026406	0.3523	0.362515
19	-0.074696	-0.9966	0.160164
20	0.027703	0.3696	0.35606
21	0.097064	1.295	0.0985
22	0.033957	0.453	0.325535

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

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