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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, 01 Dec 2009 10:18:57 -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/01/t12596879919lrmzk0qm2jnuu2.htm/, Retrieved Sat, 20 Apr 2024 01:19:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62132, Retrieved Sat, 20 Apr 2024 01:19:22 +0000

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Original text written by user:

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User-defined keywords

Estimated Impact

190

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [] [2009-11-27 14:47:30] [b98453cac15ba1066b407e146608df68]
- R PD      [(Partial) Autocorrelation Function] [] [2009-12-01 17:18:57] [791a4a78a0a7ca497fb8791b982a539e] [Current]
-   PD        [(Partial) Autocorrelation Function] [] [2009-12-04 16:50:35] [78d53abea600e0825abda35dbfc51d4c] 
-   P           [(Partial) Autocorrelation Function] [] [2009-12-17 16:04:13] [78d53abea600e0825abda35dbfc51d4c] 
- RMPD        [ARIMA Backward Selection] [] [2009-12-04 16:57:04] [eba9b8a72d680086d9ebbb043233c887] 
- RMPD        [ARIMA Backward Selection] [] [2009-12-04 16:57:04] [eba9b8a72d680086d9ebbb043233c887] 
- RMPD        [ARIMA Backward Selection] [] [2009-12-04 16:57:04] [eba9b8a72d680086d9ebbb043233c887] 
- R PD        [(Partial) Autocorrelation Function] [] [2009-12-04 17:01:33] [eba9b8a72d680086d9ebbb043233c887] 
-   PD          [(Partial) Autocorrelation Function] [ARMA model] [2009-12-19 14:21:19] [eba9b8a72d680086d9ebbb043233c887] 
- RMPD        [ARIMA Backward Selection] [] [2009-12-04 17:24:02] [78d53abea600e0825abda35dbfc51d4c] 
-   P           [ARIMA Backward Selection] [] [2009-12-17 16:11:30] [78d53abea600e0825abda35dbfc51d4c] 
- RMPD        [Percentiles] [] [2009-12-04 18:04:34] [78d53abea600e0825abda35dbfc51d4c] 

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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=62132&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=62132&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62132&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	0.324571	2.5141	0.007317
2	0.13958	1.0812	0.141972
3	0.233297	1.8071	0.037879
4	0.248655	1.9261	0.029419
5	0.238771	1.8495	0.034655
6	-0.020655	-0.16	0.436711
7	-0.011905	-0.0922	0.463416
8	0.158733	1.2295	0.111835
9	0.037902	0.2936	0.385043
10	-0.150881	-1.1687	0.12357
11	0.096274	0.7457	0.229369
12	0.014168	0.1097	0.456488
13	0.00444	0.0344	0.48634
14	0.055541	0.4302	0.334289
15	-0.01043	-0.0808	0.467938
16	0.057927	0.4487	0.327631
17	-0.122494	-0.9488	0.173256

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.324571 & 2.5141 & 0.007317 \tabularnewline
2 & 0.13958 & 1.0812 & 0.141972 \tabularnewline
3 & 0.233297 & 1.8071 & 0.037879 \tabularnewline
4 & 0.248655 & 1.9261 & 0.029419 \tabularnewline
5 & 0.238771 & 1.8495 & 0.034655 \tabularnewline
6 & -0.020655 & -0.16 & 0.436711 \tabularnewline
7 & -0.011905 & -0.0922 & 0.463416 \tabularnewline
8 & 0.158733 & 1.2295 & 0.111835 \tabularnewline
9 & 0.037902 & 0.2936 & 0.385043 \tabularnewline
10 & -0.150881 & -1.1687 & 0.12357 \tabularnewline
11 & 0.096274 & 0.7457 & 0.229369 \tabularnewline
12 & 0.014168 & 0.1097 & 0.456488 \tabularnewline
13 & 0.00444 & 0.0344 & 0.48634 \tabularnewline
14 & 0.055541 & 0.4302 & 0.334289 \tabularnewline
15 & -0.01043 & -0.0808 & 0.467938 \tabularnewline
16 & 0.057927 & 0.4487 & 0.327631 \tabularnewline
17 & -0.122494 & -0.9488 & 0.173256 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62132&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]0.324571[/C][C]2.5141[/C][C]0.007317[/C][/ROW]
[ROW][C]2[/C][C]0.13958[/C][C]1.0812[/C][C]0.141972[/C][/ROW]
[ROW][C]3[/C][C]0.233297[/C][C]1.8071[/C][C]0.037879[/C][/ROW]
[ROW][C]4[/C][C]0.248655[/C][C]1.9261[/C][C]0.029419[/C][/ROW]
[ROW][C]5[/C][C]0.238771[/C][C]1.8495[/C][C]0.034655[/C][/ROW]
[ROW][C]6[/C][C]-0.020655[/C][C]-0.16[/C][C]0.436711[/C][/ROW]
[ROW][C]7[/C][C]-0.011905[/C][C]-0.0922[/C][C]0.463416[/C][/ROW]
[ROW][C]8[/C][C]0.158733[/C][C]1.2295[/C][C]0.111835[/C][/ROW]
[ROW][C]9[/C][C]0.037902[/C][C]0.2936[/C][C]0.385043[/C][/ROW]
[ROW][C]10[/C][C]-0.150881[/C][C]-1.1687[/C][C]0.12357[/C][/ROW]
[ROW][C]11[/C][C]0.096274[/C][C]0.7457[/C][C]0.229369[/C][/ROW]
[ROW][C]12[/C][C]0.014168[/C][C]0.1097[/C][C]0.456488[/C][/ROW]
[ROW][C]13[/C][C]0.00444[/C][C]0.0344[/C][C]0.48634[/C][/ROW]
[ROW][C]14[/C][C]0.055541[/C][C]0.4302[/C][C]0.334289[/C][/ROW]
[ROW][C]15[/C][C]-0.01043[/C][C]-0.0808[/C][C]0.467938[/C][/ROW]
[ROW][C]16[/C][C]0.057927[/C][C]0.4487[/C][C]0.327631[/C][/ROW]
[ROW][C]17[/C][C]-0.122494[/C][C]-0.9488[/C][C]0.173256[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62132&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62132&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	0.324571	2.5141	0.007317
2	0.13958	1.0812	0.141972
3	0.233297	1.8071	0.037879
4	0.248655	1.9261	0.029419
5	0.238771	1.8495	0.034655
6	-0.020655	-0.16	0.436711
7	-0.011905	-0.0922	0.463416
8	0.158733	1.2295	0.111835
9	0.037902	0.2936	0.385043
10	-0.150881	-1.1687	0.12357
11	0.096274	0.7457	0.229369
12	0.014168	0.1097	0.456488
13	0.00444	0.0344	0.48634
14	0.055541	0.4302	0.334289
15	-0.01043	-0.0808	0.467938
16	0.057927	0.4487	0.327631
17	-0.122494	-0.9488	0.173256

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.324571	2.5141	0.007317
2	0.038264	0.2964	0.383977
3	0.198477	1.5374	0.064727
4	0.135744	1.0515	0.14863
5	0.128839	0.998	0.161148
6	-0.200019	-1.5493	0.063279
7	-0.038324	-0.2969	0.3838
8	0.109938	0.8516	0.198918
9	-0.058704	-0.4547	0.325475
10	-0.17395	-1.3474	0.091457
11	0.256068	1.9835	0.025947
12	-0.119781	-0.9278	0.17861
13	0.008496	0.0658	0.473874
14	0.132179	1.0239	0.155008
15	-0.018036	-0.1397	0.444681
16	-0.096472	-0.7473	0.22891
17	-0.13957	-1.0811	0.141989

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.324571 & 2.5141 & 0.007317 \tabularnewline
2 & 0.038264 & 0.2964 & 0.383977 \tabularnewline
3 & 0.198477 & 1.5374 & 0.064727 \tabularnewline
4 & 0.135744 & 1.0515 & 0.14863 \tabularnewline
5 & 0.128839 & 0.998 & 0.161148 \tabularnewline
6 & -0.200019 & -1.5493 & 0.063279 \tabularnewline
7 & -0.038324 & -0.2969 & 0.3838 \tabularnewline
8 & 0.109938 & 0.8516 & 0.198918 \tabularnewline
9 & -0.058704 & -0.4547 & 0.325475 \tabularnewline
10 & -0.17395 & -1.3474 & 0.091457 \tabularnewline
11 & 0.256068 & 1.9835 & 0.025947 \tabularnewline
12 & -0.119781 & -0.9278 & 0.17861 \tabularnewline
13 & 0.008496 & 0.0658 & 0.473874 \tabularnewline
14 & 0.132179 & 1.0239 & 0.155008 \tabularnewline
15 & -0.018036 & -0.1397 & 0.444681 \tabularnewline
16 & -0.096472 & -0.7473 & 0.22891 \tabularnewline
17 & -0.13957 & -1.0811 & 0.141989 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62132&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]0.324571[/C][C]2.5141[/C][C]0.007317[/C][/ROW]
[ROW][C]2[/C][C]0.038264[/C][C]0.2964[/C][C]0.383977[/C][/ROW]
[ROW][C]3[/C][C]0.198477[/C][C]1.5374[/C][C]0.064727[/C][/ROW]
[ROW][C]4[/C][C]0.135744[/C][C]1.0515[/C][C]0.14863[/C][/ROW]
[ROW][C]5[/C][C]0.128839[/C][C]0.998[/C][C]0.161148[/C][/ROW]
[ROW][C]6[/C][C]-0.200019[/C][C]-1.5493[/C][C]0.063279[/C][/ROW]
[ROW][C]7[/C][C]-0.038324[/C][C]-0.2969[/C][C]0.3838[/C][/ROW]
[ROW][C]8[/C][C]0.109938[/C][C]0.8516[/C][C]0.198918[/C][/ROW]
[ROW][C]9[/C][C]-0.058704[/C][C]-0.4547[/C][C]0.325475[/C][/ROW]
[ROW][C]10[/C][C]-0.17395[/C][C]-1.3474[/C][C]0.091457[/C][/ROW]
[ROW][C]11[/C][C]0.256068[/C][C]1.9835[/C][C]0.025947[/C][/ROW]
[ROW][C]12[/C][C]-0.119781[/C][C]-0.9278[/C][C]0.17861[/C][/ROW]
[ROW][C]13[/C][C]0.008496[/C][C]0.0658[/C][C]0.473874[/C][/ROW]
[ROW][C]14[/C][C]0.132179[/C][C]1.0239[/C][C]0.155008[/C][/ROW]
[ROW][C]15[/C][C]-0.018036[/C][C]-0.1397[/C][C]0.444681[/C][/ROW]
[ROW][C]16[/C][C]-0.096472[/C][C]-0.7473[/C][C]0.22891[/C][/ROW]
[ROW][C]17[/C][C]-0.13957[/C][C]-1.0811[/C][C]0.141989[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62132&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62132&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	0.324571	2.5141	0.007317
2	0.038264	0.2964	0.383977
3	0.198477	1.5374	0.064727
4	0.135744	1.0515	0.14863
5	0.128839	0.998	0.161148
6	-0.200019	-1.5493	0.063279
7	-0.038324	-0.2969	0.3838
8	0.109938	0.8516	0.198918
9	-0.058704	-0.4547	0.325475
10	-0.17395	-1.3474	0.091457
11	0.256068	1.9835	0.025947
12	-0.119781	-0.9278	0.17861
13	0.008496	0.0658	0.473874
14	0.132179	1.0239	0.155008
15	-0.018036	-0.1397	0.444681
16	-0.096472	-0.7473	0.22891
17	-0.13957	-1.0811	0.141989

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 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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