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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

Sun, 27 Dec 2009 03:10:23 -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/27/t1261908728hmfdskx1jna4jp7.htm/, Retrieved Thu, 02 May 2024 17:42:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70810, Retrieved Thu, 02 May 2024 17:42:17 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

188

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

-     [Spectral Analysis] [Spectraalanalyse ...] [2008-12-11 17:29:14] [12d343c4448a5f9e527bb31caeac580b]
- RMPD    [(Partial) Autocorrelation Function] [Paper PACF d=1] [2009-12-27 10:10:23] [eba9f01697e64705b70041e6f338cb22] [Current]
-   PD      [(Partial) Autocorrelation Function] [paper lambda 1] [2010-12-18 12:54:47] [d87a19cd5db53e12ea62bda70b3bb267] 

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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	'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70810&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70810&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70810&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.380144	5.574	0
2	0.490766	7.196	0
3	0.446181	6.5423	0
4	0.301625	4.4227	8e-06
5	0.305303	4.4766	6e-06
6	0.215745	3.1634	0.000892
7	0.277701	4.0719	3.3e-05
8	0.241243	3.5373	0.000248
9	0.32494	4.7646	2e-06
10	0.351151	5.1489	0
11	0.372806	5.4664	0
12	0.381855	5.5991	0
13	0.351326	5.1514	0
14	0.266466	3.9072	6.3e-05
15	0.171457	2.5141	0.006334
16	0.177668	2.6051	0.004913
17	0.06903	1.0122	0.156294
18	0.050409	0.7391	0.230312
19	0.090927	1.3332	0.091931
20	0.109238	1.6017	0.055341
21	0.151562	2.2223	0.013651
22	0.217947	3.1957	0.000802
23	0.225301	3.3036	0.000559

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.380144 & 5.574 & 0 \tabularnewline
2 & 0.490766 & 7.196 & 0 \tabularnewline
3 & 0.446181 & 6.5423 & 0 \tabularnewline
4 & 0.301625 & 4.4227 & 8e-06 \tabularnewline
5 & 0.305303 & 4.4766 & 6e-06 \tabularnewline
6 & 0.215745 & 3.1634 & 0.000892 \tabularnewline
7 & 0.277701 & 4.0719 & 3.3e-05 \tabularnewline
8 & 0.241243 & 3.5373 & 0.000248 \tabularnewline
9 & 0.32494 & 4.7646 & 2e-06 \tabularnewline
10 & 0.351151 & 5.1489 & 0 \tabularnewline
11 & 0.372806 & 5.4664 & 0 \tabularnewline
12 & 0.381855 & 5.5991 & 0 \tabularnewline
13 & 0.351326 & 5.1514 & 0 \tabularnewline
14 & 0.266466 & 3.9072 & 6.3e-05 \tabularnewline
15 & 0.171457 & 2.5141 & 0.006334 \tabularnewline
16 & 0.177668 & 2.6051 & 0.004913 \tabularnewline
17 & 0.06903 & 1.0122 & 0.156294 \tabularnewline
18 & 0.050409 & 0.7391 & 0.230312 \tabularnewline
19 & 0.090927 & 1.3332 & 0.091931 \tabularnewline
20 & 0.109238 & 1.6017 & 0.055341 \tabularnewline
21 & 0.151562 & 2.2223 & 0.013651 \tabularnewline
22 & 0.217947 & 3.1957 & 0.000802 \tabularnewline
23 & 0.225301 & 3.3036 & 0.000559 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70810&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]0.380144[/C][C]5.574[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.490766[/C][C]7.196[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.446181[/C][C]6.5423[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.301625[/C][C]4.4227[/C][C]8e-06[/C][/ROW]
[ROW][C]5[/C][C]0.305303[/C][C]4.4766[/C][C]6e-06[/C][/ROW]
[ROW][C]6[/C][C]0.215745[/C][C]3.1634[/C][C]0.000892[/C][/ROW]
[ROW][C]7[/C][C]0.277701[/C][C]4.0719[/C][C]3.3e-05[/C][/ROW]
[ROW][C]8[/C][C]0.241243[/C][C]3.5373[/C][C]0.000248[/C][/ROW]
[ROW][C]9[/C][C]0.32494[/C][C]4.7646[/C][C]2e-06[/C][/ROW]
[ROW][C]10[/C][C]0.351151[/C][C]5.1489[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.372806[/C][C]5.4664[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.381855[/C][C]5.5991[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.351326[/C][C]5.1514[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.266466[/C][C]3.9072[/C][C]6.3e-05[/C][/ROW]
[ROW][C]15[/C][C]0.171457[/C][C]2.5141[/C][C]0.006334[/C][/ROW]
[ROW][C]16[/C][C]0.177668[/C][C]2.6051[/C][C]0.004913[/C][/ROW]
[ROW][C]17[/C][C]0.06903[/C][C]1.0122[/C][C]0.156294[/C][/ROW]
[ROW][C]18[/C][C]0.050409[/C][C]0.7391[/C][C]0.230312[/C][/ROW]
[ROW][C]19[/C][C]0.090927[/C][C]1.3332[/C][C]0.091931[/C][/ROW]
[ROW][C]20[/C][C]0.109238[/C][C]1.6017[/C][C]0.055341[/C][/ROW]
[ROW][C]21[/C][C]0.151562[/C][C]2.2223[/C][C]0.013651[/C][/ROW]
[ROW][C]22[/C][C]0.217947[/C][C]3.1957[/C][C]0.000802[/C][/ROW]
[ROW][C]23[/C][C]0.225301[/C][C]3.3036[/C][C]0.000559[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70810&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70810&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	0.380144	5.574	0
2	0.490766	7.196	0
3	0.446181	6.5423	0
4	0.301625	4.4227	8e-06
5	0.305303	4.4766	6e-06
6	0.215745	3.1634	0.000892
7	0.277701	4.0719	3.3e-05
8	0.241243	3.5373	0.000248
9	0.32494	4.7646	2e-06
10	0.351151	5.1489	0
11	0.372806	5.4664	0
12	0.381855	5.5991	0
13	0.351326	5.1514	0
14	0.266466	3.9072	6.3e-05
15	0.171457	2.5141	0.006334
16	0.177668	2.6051	0.004913
17	0.06903	1.0122	0.156294
18	0.050409	0.7391	0.230312
19	0.090927	1.3332	0.091931
20	0.109238	1.6017	0.055341
21	0.151562	2.2223	0.013651
22	0.217947	3.1957	0.000802
23	0.225301	3.3036	0.000559

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.380144	5.574	0
2	0.404746	5.9347	0
3	0.253399	3.7156	0.000129
4	-0.030474	-0.4468	0.327721
5	-0.013006	-0.1907	0.42447
6	-0.046379	-0.68	0.248603
7	0.124993	1.8328	0.034111
8	0.094118	1.38	0.084504
9	0.186087	2.7286	0.003444
10	0.154557	2.2662	0.012216
11	0.122607	1.7978	0.036808
12	0.047152	0.6914	0.245033
13	0.000411	0.006	0.497598
14	-0.126469	-1.8544	0.032526
15	-0.191186	-2.8033	0.00276
16	-0.05155	-0.7559	0.225276
17	-0.069561	-1.02	0.154447
18	-0.066616	-0.9768	0.164886
19	0.020566	0.3016	0.381639
20	0.068198	1	0.159221
21	0.05612	0.8229	0.205742
22	0.095735	1.4037	0.080919
23	0.040329	0.5913	0.277456

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.380144 & 5.574 & 0 \tabularnewline
2 & 0.404746 & 5.9347 & 0 \tabularnewline
3 & 0.253399 & 3.7156 & 0.000129 \tabularnewline
4 & -0.030474 & -0.4468 & 0.327721 \tabularnewline
5 & -0.013006 & -0.1907 & 0.42447 \tabularnewline
6 & -0.046379 & -0.68 & 0.248603 \tabularnewline
7 & 0.124993 & 1.8328 & 0.034111 \tabularnewline
8 & 0.094118 & 1.38 & 0.084504 \tabularnewline
9 & 0.186087 & 2.7286 & 0.003444 \tabularnewline
10 & 0.154557 & 2.2662 & 0.012216 \tabularnewline
11 & 0.122607 & 1.7978 & 0.036808 \tabularnewline
12 & 0.047152 & 0.6914 & 0.245033 \tabularnewline
13 & 0.000411 & 0.006 & 0.497598 \tabularnewline
14 & -0.126469 & -1.8544 & 0.032526 \tabularnewline
15 & -0.191186 & -2.8033 & 0.00276 \tabularnewline
16 & -0.05155 & -0.7559 & 0.225276 \tabularnewline
17 & -0.069561 & -1.02 & 0.154447 \tabularnewline
18 & -0.066616 & -0.9768 & 0.164886 \tabularnewline
19 & 0.020566 & 0.3016 & 0.381639 \tabularnewline
20 & 0.068198 & 1 & 0.159221 \tabularnewline
21 & 0.05612 & 0.8229 & 0.205742 \tabularnewline
22 & 0.095735 & 1.4037 & 0.080919 \tabularnewline
23 & 0.040329 & 0.5913 & 0.277456 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70810&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]0.380144[/C][C]5.574[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.404746[/C][C]5.9347[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.253399[/C][C]3.7156[/C][C]0.000129[/C][/ROW]
[ROW][C]4[/C][C]-0.030474[/C][C]-0.4468[/C][C]0.327721[/C][/ROW]
[ROW][C]5[/C][C]-0.013006[/C][C]-0.1907[/C][C]0.42447[/C][/ROW]
[ROW][C]6[/C][C]-0.046379[/C][C]-0.68[/C][C]0.248603[/C][/ROW]
[ROW][C]7[/C][C]0.124993[/C][C]1.8328[/C][C]0.034111[/C][/ROW]
[ROW][C]8[/C][C]0.094118[/C][C]1.38[/C][C]0.084504[/C][/ROW]
[ROW][C]9[/C][C]0.186087[/C][C]2.7286[/C][C]0.003444[/C][/ROW]
[ROW][C]10[/C][C]0.154557[/C][C]2.2662[/C][C]0.012216[/C][/ROW]
[ROW][C]11[/C][C]0.122607[/C][C]1.7978[/C][C]0.036808[/C][/ROW]
[ROW][C]12[/C][C]0.047152[/C][C]0.6914[/C][C]0.245033[/C][/ROW]
[ROW][C]13[/C][C]0.000411[/C][C]0.006[/C][C]0.497598[/C][/ROW]
[ROW][C]14[/C][C]-0.126469[/C][C]-1.8544[/C][C]0.032526[/C][/ROW]
[ROW][C]15[/C][C]-0.191186[/C][C]-2.8033[/C][C]0.00276[/C][/ROW]
[ROW][C]16[/C][C]-0.05155[/C][C]-0.7559[/C][C]0.225276[/C][/ROW]
[ROW][C]17[/C][C]-0.069561[/C][C]-1.02[/C][C]0.154447[/C][/ROW]
[ROW][C]18[/C][C]-0.066616[/C][C]-0.9768[/C][C]0.164886[/C][/ROW]
[ROW][C]19[/C][C]0.020566[/C][C]0.3016[/C][C]0.381639[/C][/ROW]
[ROW][C]20[/C][C]0.068198[/C][C]1[/C][C]0.159221[/C][/ROW]
[ROW][C]21[/C][C]0.05612[/C][C]0.8229[/C][C]0.205742[/C][/ROW]
[ROW][C]22[/C][C]0.095735[/C][C]1.4037[/C][C]0.080919[/C][/ROW]
[ROW][C]23[/C][C]0.040329[/C][C]0.5913[/C][C]0.277456[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70810&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70810&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	0.380144	5.574	0
2	0.404746	5.9347	0
3	0.253399	3.7156	0.000129
4	-0.030474	-0.4468	0.327721
5	-0.013006	-0.1907	0.42447
6	-0.046379	-0.68	0.248603
7	0.124993	1.8328	0.034111
8	0.094118	1.38	0.084504
9	0.186087	2.7286	0.003444
10	0.154557	2.2662	0.012216
11	0.122607	1.7978	0.036808
12	0.047152	0.6914	0.245033
13	0.000411	0.006	0.497598
14	-0.126469	-1.8544	0.032526
15	-0.191186	-2.8033	0.00276
16	-0.05155	-0.7559	0.225276
17	-0.069561	-1.02	0.154447
18	-0.066616	-0.9768	0.164886
19	0.020566	0.3016	0.381639
20	0.068198	1	0.159221
21	0.05612	0.8229	0.205742
22	0.095735	1.4037	0.080919
23	0.040329	0.5913	0.277456

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = -1.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = -1.0 ; par3 = 1 ; 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