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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

Thu, 03 Dec 2009 10:32:57 -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/03/t1259861735eq6i07r6g1wb4dc.htm/, Retrieved Thu, 25 Apr 2024 05:03:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62964, Retrieved Thu, 25 Apr 2024 05:03:00 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

128

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       [Standard Deviation-Mean Plot] [Identifying Integ...] [2009-11-22 12:50:05] [b98453cac15ba1066b407e146608df68]
-    D        [Standard Deviation-Mean Plot] [] [2009-11-26 10:43:35] [d181e5359f7da6c8509e4702d1229fb0]
- RMP             [(Partial) Autocorrelation Function] [] [2009-12-03 17:32:57] [b4088cbf8335906ce53a9289ed6fac01] [Current]
-   P               [(Partial) Autocorrelation Function] [] [2009-12-04 13:09:20] [d181e5359f7da6c8509e4702d1229fb0] 
-   P                 [(Partial) Autocorrelation Function] [] [2009-12-18 14:18:09] [d181e5359f7da6c8509e4702d1229fb0] 

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8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.4
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8.00
8.2
8.1
8.1
8.00
7.9
7.9
8.00
8.00
7.9
8.00
7.7
7.2
7.5
7.3
7.00
7.00
7.00
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8.00
8.00
7.7
7.3
7.4
8.1
8.3
8.2

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=62964&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=62964&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62964&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	0.278552	2.1396	0.018267
2	-0.210316	-1.6155	0.055773
3	-0.465593	-3.5763	0.000352
4	-0.447296	-3.4357	0.000544
5	-0.051765	-0.3976	0.346174
6	0.188151	1.4452	0.076844
7	0.304139	2.3361	0.011451
8	0.211579	1.6252	0.054729
9	-0.130828	-1.0049	0.159523
10	-0.096428	-0.7407	0.230913
11	-0.043966	-0.3377	0.368391
12	-0.132791	-1.02	0.15595
13	0.013904	0.1068	0.457656
14	0.098083	0.7534	0.227106
15	0.074559	0.5727	0.284512
16	-0.000948	-0.0073	0.497107
17	-0.06075	-0.4666	0.321242
18	0.018408	0.1414	0.444019

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.278552 & 2.1396 & 0.018267 \tabularnewline
2 & -0.210316 & -1.6155 & 0.055773 \tabularnewline
3 & -0.465593 & -3.5763 & 0.000352 \tabularnewline
4 & -0.447296 & -3.4357 & 0.000544 \tabularnewline
5 & -0.051765 & -0.3976 & 0.346174 \tabularnewline
6 & 0.188151 & 1.4452 & 0.076844 \tabularnewline
7 & 0.304139 & 2.3361 & 0.011451 \tabularnewline
8 & 0.211579 & 1.6252 & 0.054729 \tabularnewline
9 & -0.130828 & -1.0049 & 0.159523 \tabularnewline
10 & -0.096428 & -0.7407 & 0.230913 \tabularnewline
11 & -0.043966 & -0.3377 & 0.368391 \tabularnewline
12 & -0.132791 & -1.02 & 0.15595 \tabularnewline
13 & 0.013904 & 0.1068 & 0.457656 \tabularnewline
14 & 0.098083 & 0.7534 & 0.227106 \tabularnewline
15 & 0.074559 & 0.5727 & 0.284512 \tabularnewline
16 & -0.000948 & -0.0073 & 0.497107 \tabularnewline
17 & -0.06075 & -0.4666 & 0.321242 \tabularnewline
18 & 0.018408 & 0.1414 & 0.444019 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62964&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]0.278552[/C][C]2.1396[/C][C]0.018267[/C][/ROW]
[ROW][C]2[/C][C]-0.210316[/C][C]-1.6155[/C][C]0.055773[/C][/ROW]
[ROW][C]3[/C][C]-0.465593[/C][C]-3.5763[/C][C]0.000352[/C][/ROW]
[ROW][C]4[/C][C]-0.447296[/C][C]-3.4357[/C][C]0.000544[/C][/ROW]
[ROW][C]5[/C][C]-0.051765[/C][C]-0.3976[/C][C]0.346174[/C][/ROW]
[ROW][C]6[/C][C]0.188151[/C][C]1.4452[/C][C]0.076844[/C][/ROW]
[ROW][C]7[/C][C]0.304139[/C][C]2.3361[/C][C]0.011451[/C][/ROW]
[ROW][C]8[/C][C]0.211579[/C][C]1.6252[/C][C]0.054729[/C][/ROW]
[ROW][C]9[/C][C]-0.130828[/C][C]-1.0049[/C][C]0.159523[/C][/ROW]
[ROW][C]10[/C][C]-0.096428[/C][C]-0.7407[/C][C]0.230913[/C][/ROW]
[ROW][C]11[/C][C]-0.043966[/C][C]-0.3377[/C][C]0.368391[/C][/ROW]
[ROW][C]12[/C][C]-0.132791[/C][C]-1.02[/C][C]0.15595[/C][/ROW]
[ROW][C]13[/C][C]0.013904[/C][C]0.1068[/C][C]0.457656[/C][/ROW]
[ROW][C]14[/C][C]0.098083[/C][C]0.7534[/C][C]0.227106[/C][/ROW]
[ROW][C]15[/C][C]0.074559[/C][C]0.5727[/C][C]0.284512[/C][/ROW]
[ROW][C]16[/C][C]-0.000948[/C][C]-0.0073[/C][C]0.497107[/C][/ROW]
[ROW][C]17[/C][C]-0.06075[/C][C]-0.4666[/C][C]0.321242[/C][/ROW]
[ROW][C]18[/C][C]0.018408[/C][C]0.1414[/C][C]0.444019[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62964&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62964&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	0.278552	2.1396	0.018267
2	-0.210316	-1.6155	0.055773
3	-0.465593	-3.5763	0.000352
4	-0.447296	-3.4357	0.000544
5	-0.051765	-0.3976	0.346174
6	0.188151	1.4452	0.076844
7	0.304139	2.3361	0.011451
8	0.211579	1.6252	0.054729
9	-0.130828	-1.0049	0.159523
10	-0.096428	-0.7407	0.230913
11	-0.043966	-0.3377	0.368391
12	-0.132791	-1.02	0.15595
13	0.013904	0.1068	0.457656
14	0.098083	0.7534	0.227106
15	0.074559	0.5727	0.284512
16	-0.000948	-0.0073	0.497107
17	-0.06075	-0.4666	0.321242
18	0.018408	0.1414	0.444019

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.278552	2.1396	0.018267
2	-0.312125	-2.3975	0.009846
3	-0.362479	-2.7843	0.0036
4	-0.368679	-2.8319	0.00316
5	-0.107399	-0.8249	0.206362
6	-0.183532	-1.4097	0.081934
7	-0.065135	-0.5003	0.309359
8	-0.037661	-0.2893	0.386689
9	-0.227022	-1.7438	0.043202
10	0.103751	0.7969	0.214345
11	0.083314	0.6399	0.262342
12	-0.193442	-1.4859	0.071321
13	0.015291	0.1175	0.45345
14	0.112355	0.863	0.195812
15	-0.040437	-0.3106	0.3786
16	-0.078729	-0.6047	0.27384
17	0.026505	0.2036	0.419688
18	0.045324	0.3481	0.364487

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.278552 & 2.1396 & 0.018267 \tabularnewline
2 & -0.312125 & -2.3975 & 0.009846 \tabularnewline
3 & -0.362479 & -2.7843 & 0.0036 \tabularnewline
4 & -0.368679 & -2.8319 & 0.00316 \tabularnewline
5 & -0.107399 & -0.8249 & 0.206362 \tabularnewline
6 & -0.183532 & -1.4097 & 0.081934 \tabularnewline
7 & -0.065135 & -0.5003 & 0.309359 \tabularnewline
8 & -0.037661 & -0.2893 & 0.386689 \tabularnewline
9 & -0.227022 & -1.7438 & 0.043202 \tabularnewline
10 & 0.103751 & 0.7969 & 0.214345 \tabularnewline
11 & 0.083314 & 0.6399 & 0.262342 \tabularnewline
12 & -0.193442 & -1.4859 & 0.071321 \tabularnewline
13 & 0.015291 & 0.1175 & 0.45345 \tabularnewline
14 & 0.112355 & 0.863 & 0.195812 \tabularnewline
15 & -0.040437 & -0.3106 & 0.3786 \tabularnewline
16 & -0.078729 & -0.6047 & 0.27384 \tabularnewline
17 & 0.026505 & 0.2036 & 0.419688 \tabularnewline
18 & 0.045324 & 0.3481 & 0.364487 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62964&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]0.278552[/C][C]2.1396[/C][C]0.018267[/C][/ROW]
[ROW][C]2[/C][C]-0.312125[/C][C]-2.3975[/C][C]0.009846[/C][/ROW]
[ROW][C]3[/C][C]-0.362479[/C][C]-2.7843[/C][C]0.0036[/C][/ROW]
[ROW][C]4[/C][C]-0.368679[/C][C]-2.8319[/C][C]0.00316[/C][/ROW]
[ROW][C]5[/C][C]-0.107399[/C][C]-0.8249[/C][C]0.206362[/C][/ROW]
[ROW][C]6[/C][C]-0.183532[/C][C]-1.4097[/C][C]0.081934[/C][/ROW]
[ROW][C]7[/C][C]-0.065135[/C][C]-0.5003[/C][C]0.309359[/C][/ROW]
[ROW][C]8[/C][C]-0.037661[/C][C]-0.2893[/C][C]0.386689[/C][/ROW]
[ROW][C]9[/C][C]-0.227022[/C][C]-1.7438[/C][C]0.043202[/C][/ROW]
[ROW][C]10[/C][C]0.103751[/C][C]0.7969[/C][C]0.214345[/C][/ROW]
[ROW][C]11[/C][C]0.083314[/C][C]0.6399[/C][C]0.262342[/C][/ROW]
[ROW][C]12[/C][C]-0.193442[/C][C]-1.4859[/C][C]0.071321[/C][/ROW]
[ROW][C]13[/C][C]0.015291[/C][C]0.1175[/C][C]0.45345[/C][/ROW]
[ROW][C]14[/C][C]0.112355[/C][C]0.863[/C][C]0.195812[/C][/ROW]
[ROW][C]15[/C][C]-0.040437[/C][C]-0.3106[/C][C]0.3786[/C][/ROW]
[ROW][C]16[/C][C]-0.078729[/C][C]-0.6047[/C][C]0.27384[/C][/ROW]
[ROW][C]17[/C][C]0.026505[/C][C]0.2036[/C][C]0.419688[/C][/ROW]
[ROW][C]18[/C][C]0.045324[/C][C]0.3481[/C][C]0.364487[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62964&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62964&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	0.278552	2.1396	0.018267
2	-0.312125	-2.3975	0.009846
3	-0.362479	-2.7843	0.0036
4	-0.368679	-2.8319	0.00316
5	-0.107399	-0.8249	0.206362
6	-0.183532	-1.4097	0.081934
7	-0.065135	-0.5003	0.309359
8	-0.037661	-0.2893	0.386689
9	-0.227022	-1.7438	0.043202
10	0.103751	0.7969	0.214345
11	0.083314	0.6399	0.262342
12	-0.193442	-1.4859	0.071321
13	0.015291	0.1175	0.45345
14	0.112355	0.863	0.195812
15	-0.040437	-0.3106	0.3786
16	-0.078729	-0.6047	0.27384
17	0.026505	0.2036	0.419688
18	0.045324	0.3481	0.364487

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 1 ; 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