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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

Wed, 08 Dec 2010 10:48:57 +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/Dec/08/t12918055377zvyisx8dck5cao.htm/, Retrieved Fri, 03 May 2024 06:02:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106844, Retrieved Fri, 03 May 2024 06:02:37 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

167

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [(Partial) Autocorrelation Function] [Births] [2010-11-29 09:36:27] [b98453cac15ba1066b407e146608df68]
-   PD            [(Partial) Autocorrelation Function] [ WS 9 : ACF - d=0...] [2010-12-08 10:48:57] [fea2623c21d84eea50328c29ea7301e7] [Current]
-   P               [(Partial) Autocorrelation Function] [ws 9 : ACF d=0 D=1 ] [2010-12-08 11:00:09] [2c786c21adba4dd4c8af44dce5258f06] 
-   P                 [(Partial) Autocorrelation Function] [Ws 9 : ACF d=1 D=1 ] [2010-12-08 11:07:30] [2c786c21adba4dd4c8af44dce5258f06] 
-   P                   [(Partial) Autocorrelation Function] [Ws 9 : ACF d=1 D=...] [2010-12-08 14:58:09] [2c786c21adba4dd4c8af44dce5258f06] 
-   P                 [(Partial) Autocorrelation Function] [ws 9 : ACF d=0 D=...] [2010-12-08 14:54:21] [2c786c21adba4dd4c8af44dce5258f06] 
- R PD                  [(Partial) Autocorrelation Function] [] [2011-12-23 14:14:36] [53298c36f9bda1a036c4d70d0e7a311d] 
-   P               [(Partial) Autocorrelation Function] [ws 9 : ACF d=0  D...] [2010-12-08 14:42:29] [2c786c21adba4dd4c8af44dce5258f06] 
- R PD                [(Partial) Autocorrelation Function] [] [2011-12-23 14:11:55] [53298c36f9bda1a036c4d70d0e7a311d] 

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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	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106844&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106844&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106844&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	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.140289	1.1904	0.118902
2	-0.272958	-2.3161	0.011701
3	0.172633	1.4648	0.073658
4	0.001615	0.0137	0.494553
5	-0.034428	-0.2921	0.385514
6	0.197239	1.6736	0.049272
7	-0.006224	-0.0528	0.479013
8	0.086649	0.7352	0.232289
9	0.155618	1.3205	0.095431
10	-0.274311	-2.3276	0.011374
11	0.076792	0.6516	0.258367
12	0.66264	5.6227	0
13	0.027428	0.2327	0.408315
14	-0.284418	-2.4134	0.009176
15	0.044232	0.3753	0.354264
16	-0.0405	-0.3437	0.366055
17	-0.052849	-0.4484	0.327593
18	0.045076	0.3825	0.351616

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.140289 & 1.1904 & 0.118902 \tabularnewline
2 & -0.272958 & -2.3161 & 0.011701 \tabularnewline
3 & 0.172633 & 1.4648 & 0.073658 \tabularnewline
4 & 0.001615 & 0.0137 & 0.494553 \tabularnewline
5 & -0.034428 & -0.2921 & 0.385514 \tabularnewline
6 & 0.197239 & 1.6736 & 0.049272 \tabularnewline
7 & -0.006224 & -0.0528 & 0.479013 \tabularnewline
8 & 0.086649 & 0.7352 & 0.232289 \tabularnewline
9 & 0.155618 & 1.3205 & 0.095431 \tabularnewline
10 & -0.274311 & -2.3276 & 0.011374 \tabularnewline
11 & 0.076792 & 0.6516 & 0.258367 \tabularnewline
12 & 0.66264 & 5.6227 & 0 \tabularnewline
13 & 0.027428 & 0.2327 & 0.408315 \tabularnewline
14 & -0.284418 & -2.4134 & 0.009176 \tabularnewline
15 & 0.044232 & 0.3753 & 0.354264 \tabularnewline
16 & -0.0405 & -0.3437 & 0.366055 \tabularnewline
17 & -0.052849 & -0.4484 & 0.327593 \tabularnewline
18 & 0.045076 & 0.3825 & 0.351616 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106844&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]0.140289[/C][C]1.1904[/C][C]0.118902[/C][/ROW]
[ROW][C]2[/C][C]-0.272958[/C][C]-2.3161[/C][C]0.011701[/C][/ROW]
[ROW][C]3[/C][C]0.172633[/C][C]1.4648[/C][C]0.073658[/C][/ROW]
[ROW][C]4[/C][C]0.001615[/C][C]0.0137[/C][C]0.494553[/C][/ROW]
[ROW][C]5[/C][C]-0.034428[/C][C]-0.2921[/C][C]0.385514[/C][/ROW]
[ROW][C]6[/C][C]0.197239[/C][C]1.6736[/C][C]0.049272[/C][/ROW]
[ROW][C]7[/C][C]-0.006224[/C][C]-0.0528[/C][C]0.479013[/C][/ROW]
[ROW][C]8[/C][C]0.086649[/C][C]0.7352[/C][C]0.232289[/C][/ROW]
[ROW][C]9[/C][C]0.155618[/C][C]1.3205[/C][C]0.095431[/C][/ROW]
[ROW][C]10[/C][C]-0.274311[/C][C]-2.3276[/C][C]0.011374[/C][/ROW]
[ROW][C]11[/C][C]0.076792[/C][C]0.6516[/C][C]0.258367[/C][/ROW]
[ROW][C]12[/C][C]0.66264[/C][C]5.6227[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.027428[/C][C]0.2327[/C][C]0.408315[/C][/ROW]
[ROW][C]14[/C][C]-0.284418[/C][C]-2.4134[/C][C]0.009176[/C][/ROW]
[ROW][C]15[/C][C]0.044232[/C][C]0.3753[/C][C]0.354264[/C][/ROW]
[ROW][C]16[/C][C]-0.0405[/C][C]-0.3437[/C][C]0.366055[/C][/ROW]
[ROW][C]17[/C][C]-0.052849[/C][C]-0.4484[/C][C]0.327593[/C][/ROW]
[ROW][C]18[/C][C]0.045076[/C][C]0.3825[/C][C]0.351616[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106844&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106844&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	0.140289	1.1904	0.118902
2	-0.272958	-2.3161	0.011701
3	0.172633	1.4648	0.073658
4	0.001615	0.0137	0.494553
5	-0.034428	-0.2921	0.385514
6	0.197239	1.6736	0.049272
7	-0.006224	-0.0528	0.479013
8	0.086649	0.7352	0.232289
9	0.155618	1.3205	0.095431
10	-0.274311	-2.3276	0.011374
11	0.076792	0.6516	0.258367
12	0.66264	5.6227	0
13	0.027428	0.2327	0.408315
14	-0.284418	-2.4134	0.009176
15	0.044232	0.3753	0.354264
16	-0.0405	-0.3437	0.366055
17	-0.052849	-0.4484	0.327593
18	0.045076	0.3825	0.351616

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.140289	1.1904	0.118902
2	-0.298514	-2.533	0.006745
3	0.295909	2.5109	0.007145
4	-0.224346	-1.9036	0.030477
5	0.217541	1.8459	0.034509
6	0.029594	0.2511	0.401222
7	0.00263	0.0223	0.491128
8	0.237534	2.0155	0.02379
9	-0.068014	-0.5771	0.282831
10	-0.205634	-1.7449	0.042638
11	0.313915	2.6637	0.004766
12	0.479743	4.0708	5.9e-05
13	-0.146859	-1.2461	0.108376
14	-0.123656	-1.0493	0.148784
15	-0.176841	-1.5005	0.068923
16	0.065916	0.5593	0.28884
17	-0.069209	-0.5873	0.279434
18	-0.178375	-1.5136	0.067258

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.140289 & 1.1904 & 0.118902 \tabularnewline
2 & -0.298514 & -2.533 & 0.006745 \tabularnewline
3 & 0.295909 & 2.5109 & 0.007145 \tabularnewline
4 & -0.224346 & -1.9036 & 0.030477 \tabularnewline
5 & 0.217541 & 1.8459 & 0.034509 \tabularnewline
6 & 0.029594 & 0.2511 & 0.401222 \tabularnewline
7 & 0.00263 & 0.0223 & 0.491128 \tabularnewline
8 & 0.237534 & 2.0155 & 0.02379 \tabularnewline
9 & -0.068014 & -0.5771 & 0.282831 \tabularnewline
10 & -0.205634 & -1.7449 & 0.042638 \tabularnewline
11 & 0.313915 & 2.6637 & 0.004766 \tabularnewline
12 & 0.479743 & 4.0708 & 5.9e-05 \tabularnewline
13 & -0.146859 & -1.2461 & 0.108376 \tabularnewline
14 & -0.123656 & -1.0493 & 0.148784 \tabularnewline
15 & -0.176841 & -1.5005 & 0.068923 \tabularnewline
16 & 0.065916 & 0.5593 & 0.28884 \tabularnewline
17 & -0.069209 & -0.5873 & 0.279434 \tabularnewline
18 & -0.178375 & -1.5136 & 0.067258 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106844&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]0.140289[/C][C]1.1904[/C][C]0.118902[/C][/ROW]
[ROW][C]2[/C][C]-0.298514[/C][C]-2.533[/C][C]0.006745[/C][/ROW]
[ROW][C]3[/C][C]0.295909[/C][C]2.5109[/C][C]0.007145[/C][/ROW]
[ROW][C]4[/C][C]-0.224346[/C][C]-1.9036[/C][C]0.030477[/C][/ROW]
[ROW][C]5[/C][C]0.217541[/C][C]1.8459[/C][C]0.034509[/C][/ROW]
[ROW][C]6[/C][C]0.029594[/C][C]0.2511[/C][C]0.401222[/C][/ROW]
[ROW][C]7[/C][C]0.00263[/C][C]0.0223[/C][C]0.491128[/C][/ROW]
[ROW][C]8[/C][C]0.237534[/C][C]2.0155[/C][C]0.02379[/C][/ROW]
[ROW][C]9[/C][C]-0.068014[/C][C]-0.5771[/C][C]0.282831[/C][/ROW]
[ROW][C]10[/C][C]-0.205634[/C][C]-1.7449[/C][C]0.042638[/C][/ROW]
[ROW][C]11[/C][C]0.313915[/C][C]2.6637[/C][C]0.004766[/C][/ROW]
[ROW][C]12[/C][C]0.479743[/C][C]4.0708[/C][C]5.9e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.146859[/C][C]-1.2461[/C][C]0.108376[/C][/ROW]
[ROW][C]14[/C][C]-0.123656[/C][C]-1.0493[/C][C]0.148784[/C][/ROW]
[ROW][C]15[/C][C]-0.176841[/C][C]-1.5005[/C][C]0.068923[/C][/ROW]
[ROW][C]16[/C][C]0.065916[/C][C]0.5593[/C][C]0.28884[/C][/ROW]
[ROW][C]17[/C][C]-0.069209[/C][C]-0.5873[/C][C]0.279434[/C][/ROW]
[ROW][C]18[/C][C]-0.178375[/C][C]-1.5136[/C][C]0.067258[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106844&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106844&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	0.140289	1.1904	0.118902
2	-0.298514	-2.533	0.006745
3	0.295909	2.5109	0.007145
4	-0.224346	-1.9036	0.030477
5	0.217541	1.8459	0.034509
6	0.029594	0.2511	0.401222
7	0.00263	0.0223	0.491128
8	0.237534	2.0155	0.02379
9	-0.068014	-0.5771	0.282831
10	-0.205634	-1.7449	0.042638
11	0.313915	2.6637	0.004766
12	0.479743	4.0708	5.9e-05
13	-0.146859	-1.2461	0.108376
14	-0.123656	-1.0493	0.148784
15	-0.176841	-1.5005	0.068923
16	0.065916	0.5593	0.28884
17	-0.069209	-0.5873	0.279434
18	-0.178375	-1.5136	0.067258

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 ;

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