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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, 27 Nov 2009 05:34:11 -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/Nov/27/t1259325282f9hkp2tc3mo85kz.htm/, Retrieved Mon, 29 Apr 2024 01:16:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60648, Retrieved Mon, 29 Apr 2024 01:16:12 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

ACF101

Estimated Impact

131

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       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:16:10] [b98453cac15ba1066b407e146608df68]
-   PD        [(Partial) Autocorrelation Function] [] [2009-11-27 12:26:17] [4f76e114ed5e444b1133aad392380aad]
-   P           [(Partial) Autocorrelation Function] [] [2009-11-27 12:31:03] [4f76e114ed5e444b1133aad392380aad]
-   P               [(Partial) Autocorrelation Function] [] [2009-11-27 12:34:11] [9002751dd674b8c934bf183fdf4510e9] [Current]
-   P                 [(Partial) Autocorrelation Function] [] [2009-11-27 12:36:50] [4f76e114ed5e444b1133aad392380aad] 

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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	3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60648&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]3 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=60648&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60648&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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.599642	5.5609	0
2	0.536191	4.9724	2e-06
3	0.446659	4.1421	4e-05
4	0.335905	3.1151	0.00125
5	0.290126	2.6905	0.004285
6	0.234315	2.173	0.016267
7	0.21978	2.0382	0.022304
8	0.163971	1.5206	0.066014
9	0.140898	1.3066	0.097411
10	0.065113	0.6038	0.273771
11	0.018235	0.1691	0.433057
12	0.001289	0.012	0.495245
13	-0.005366	-0.0498	0.480213
14	0.014947	0.1386	0.445042
15	-0.006736	-0.0625	0.475167
16	-0.033689	-0.3124	0.377739
17	-0.033283	-0.3087	0.379164
18	-0.044134	-0.4093	0.341676
19	-0.070269	-0.6516	0.258183

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.599642 & 5.5609 & 0 \tabularnewline
2 & 0.536191 & 4.9724 & 2e-06 \tabularnewline
3 & 0.446659 & 4.1421 & 4e-05 \tabularnewline
4 & 0.335905 & 3.1151 & 0.00125 \tabularnewline
5 & 0.290126 & 2.6905 & 0.004285 \tabularnewline
6 & 0.234315 & 2.173 & 0.016267 \tabularnewline
7 & 0.21978 & 2.0382 & 0.022304 \tabularnewline
8 & 0.163971 & 1.5206 & 0.066014 \tabularnewline
9 & 0.140898 & 1.3066 & 0.097411 \tabularnewline
10 & 0.065113 & 0.6038 & 0.273771 \tabularnewline
11 & 0.018235 & 0.1691 & 0.433057 \tabularnewline
12 & 0.001289 & 0.012 & 0.495245 \tabularnewline
13 & -0.005366 & -0.0498 & 0.480213 \tabularnewline
14 & 0.014947 & 0.1386 & 0.445042 \tabularnewline
15 & -0.006736 & -0.0625 & 0.475167 \tabularnewline
16 & -0.033689 & -0.3124 & 0.377739 \tabularnewline
17 & -0.033283 & -0.3087 & 0.379164 \tabularnewline
18 & -0.044134 & -0.4093 & 0.341676 \tabularnewline
19 & -0.070269 & -0.6516 & 0.258183 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60648&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]0.599642[/C][C]5.5609[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.536191[/C][C]4.9724[/C][C]2e-06[/C][/ROW]
[ROW][C]3[/C][C]0.446659[/C][C]4.1421[/C][C]4e-05[/C][/ROW]
[ROW][C]4[/C][C]0.335905[/C][C]3.1151[/C][C]0.00125[/C][/ROW]
[ROW][C]5[/C][C]0.290126[/C][C]2.6905[/C][C]0.004285[/C][/ROW]
[ROW][C]6[/C][C]0.234315[/C][C]2.173[/C][C]0.016267[/C][/ROW]
[ROW][C]7[/C][C]0.21978[/C][C]2.0382[/C][C]0.022304[/C][/ROW]
[ROW][C]8[/C][C]0.163971[/C][C]1.5206[/C][C]0.066014[/C][/ROW]
[ROW][C]9[/C][C]0.140898[/C][C]1.3066[/C][C]0.097411[/C][/ROW]
[ROW][C]10[/C][C]0.065113[/C][C]0.6038[/C][C]0.273771[/C][/ROW]
[ROW][C]11[/C][C]0.018235[/C][C]0.1691[/C][C]0.433057[/C][/ROW]
[ROW][C]12[/C][C]0.001289[/C][C]0.012[/C][C]0.495245[/C][/ROW]
[ROW][C]13[/C][C]-0.005366[/C][C]-0.0498[/C][C]0.480213[/C][/ROW]
[ROW][C]14[/C][C]0.014947[/C][C]0.1386[/C][C]0.445042[/C][/ROW]
[ROW][C]15[/C][C]-0.006736[/C][C]-0.0625[/C][C]0.475167[/C][/ROW]
[ROW][C]16[/C][C]-0.033689[/C][C]-0.3124[/C][C]0.377739[/C][/ROW]
[ROW][C]17[/C][C]-0.033283[/C][C]-0.3087[/C][C]0.379164[/C][/ROW]
[ROW][C]18[/C][C]-0.044134[/C][C]-0.4093[/C][C]0.341676[/C][/ROW]
[ROW][C]19[/C][C]-0.070269[/C][C]-0.6516[/C][C]0.258183[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60648&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60648&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	0.599642	5.5609	0
2	0.536191	4.9724	2e-06
3	0.446659	4.1421	4e-05
4	0.335905	3.1151	0.00125
5	0.290126	2.6905	0.004285
6	0.234315	2.173	0.016267
7	0.21978	2.0382	0.022304
8	0.163971	1.5206	0.066014
9	0.140898	1.3066	0.097411
10	0.065113	0.6038	0.273771
11	0.018235	0.1691	0.433057
12	0.001289	0.012	0.495245
13	-0.005366	-0.0498	0.480213
14	0.014947	0.1386	0.445042
15	-0.006736	-0.0625	0.475167
16	-0.033689	-0.3124	0.377739
17	-0.033283	-0.3087	0.379164
18	-0.044134	-0.4093	0.341676
19	-0.070269	-0.6516	0.258183

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.599642	5.5609	0
2	0.275785	2.5575	0.006148
3	0.081855	0.7591	0.224936
4	-0.044033	-0.4083	0.342019
5	0.019416	0.1801	0.428766
6	0.006459	0.0599	0.47619
7	0.050134	0.4649	0.321581
8	-0.031443	-0.2916	0.385652
9	-0.0032	-0.0297	0.488199
10	-0.08915	-0.8267	0.205334
11	-0.053582	-0.4969	0.310263
12	0.002098	0.0195	0.492261
13	0.032745	0.3037	0.381057
14	0.050621	0.4694	0.319973
15	-0.025071	-0.2325	0.408352
16	-0.062153	-0.5764	0.282931
17	0.00087	0.0081	0.496791
18	0.005737	0.0532	0.478845
19	-0.034125	-0.3165	0.376208

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.599642 & 5.5609 & 0 \tabularnewline
2 & 0.275785 & 2.5575 & 0.006148 \tabularnewline
3 & 0.081855 & 0.7591 & 0.224936 \tabularnewline
4 & -0.044033 & -0.4083 & 0.342019 \tabularnewline
5 & 0.019416 & 0.1801 & 0.428766 \tabularnewline
6 & 0.006459 & 0.0599 & 0.47619 \tabularnewline
7 & 0.050134 & 0.4649 & 0.321581 \tabularnewline
8 & -0.031443 & -0.2916 & 0.385652 \tabularnewline
9 & -0.0032 & -0.0297 & 0.488199 \tabularnewline
10 & -0.08915 & -0.8267 & 0.205334 \tabularnewline
11 & -0.053582 & -0.4969 & 0.310263 \tabularnewline
12 & 0.002098 & 0.0195 & 0.492261 \tabularnewline
13 & 0.032745 & 0.3037 & 0.381057 \tabularnewline
14 & 0.050621 & 0.4694 & 0.319973 \tabularnewline
15 & -0.025071 & -0.2325 & 0.408352 \tabularnewline
16 & -0.062153 & -0.5764 & 0.282931 \tabularnewline
17 & 0.00087 & 0.0081 & 0.496791 \tabularnewline
18 & 0.005737 & 0.0532 & 0.478845 \tabularnewline
19 & -0.034125 & -0.3165 & 0.376208 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60648&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]0.599642[/C][C]5.5609[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.275785[/C][C]2.5575[/C][C]0.006148[/C][/ROW]
[ROW][C]3[/C][C]0.081855[/C][C]0.7591[/C][C]0.224936[/C][/ROW]
[ROW][C]4[/C][C]-0.044033[/C][C]-0.4083[/C][C]0.342019[/C][/ROW]
[ROW][C]5[/C][C]0.019416[/C][C]0.1801[/C][C]0.428766[/C][/ROW]
[ROW][C]6[/C][C]0.006459[/C][C]0.0599[/C][C]0.47619[/C][/ROW]
[ROW][C]7[/C][C]0.050134[/C][C]0.4649[/C][C]0.321581[/C][/ROW]
[ROW][C]8[/C][C]-0.031443[/C][C]-0.2916[/C][C]0.385652[/C][/ROW]
[ROW][C]9[/C][C]-0.0032[/C][C]-0.0297[/C][C]0.488199[/C][/ROW]
[ROW][C]10[/C][C]-0.08915[/C][C]-0.8267[/C][C]0.205334[/C][/ROW]
[ROW][C]11[/C][C]-0.053582[/C][C]-0.4969[/C][C]0.310263[/C][/ROW]
[ROW][C]12[/C][C]0.002098[/C][C]0.0195[/C][C]0.492261[/C][/ROW]
[ROW][C]13[/C][C]0.032745[/C][C]0.3037[/C][C]0.381057[/C][/ROW]
[ROW][C]14[/C][C]0.050621[/C][C]0.4694[/C][C]0.319973[/C][/ROW]
[ROW][C]15[/C][C]-0.025071[/C][C]-0.2325[/C][C]0.408352[/C][/ROW]
[ROW][C]16[/C][C]-0.062153[/C][C]-0.5764[/C][C]0.282931[/C][/ROW]
[ROW][C]17[/C][C]0.00087[/C][C]0.0081[/C][C]0.496791[/C][/ROW]
[ROW][C]18[/C][C]0.005737[/C][C]0.0532[/C][C]0.478845[/C][/ROW]
[ROW][C]19[/C][C]-0.034125[/C][C]-0.3165[/C][C]0.376208[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60648&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60648&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	0.599642	5.5609	0
2	0.275785	2.5575	0.006148
3	0.081855	0.7591	0.224936
4	-0.044033	-0.4083	0.342019
5	0.019416	0.1801	0.428766
6	0.006459	0.0599	0.47619
7	0.050134	0.4649	0.321581
8	-0.031443	-0.2916	0.385652
9	-0.0032	-0.0297	0.488199
10	-0.08915	-0.8267	0.205334
11	-0.053582	-0.4969	0.310263
12	0.002098	0.0195	0.492261
13	0.032745	0.3037	0.381057
14	0.050621	0.4694	0.319973
15	-0.025071	-0.2325	0.408352
16	-0.062153	-0.5764	0.282931
17	0.00087	0.0081	0.496791
18	0.005737	0.0532	0.478845
19	-0.034125	-0.3165	0.376208

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 = 1 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 4 ; 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