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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

Tue, 20 Dec 2011 08:35:21 -0500

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/2011/Dec/20/t13243881445asmtf8h29820qc.htm/, Retrieved Sun, 05 May 2024 22:14:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157957, Retrieved Sun, 05 May 2024 22:14:09 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

113

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

-     [(Partial) Autocorrelation Function] [] [2011-12-05 11:42:22] [aba4febe8a2e49e81bdc61a6c01f5c21]
-    D    [(Partial) Autocorrelation Function] [ACF pageviews] [2011-12-20 13:35:21] [3627de22d386f4cb93d383ef7c1ade7f] [Current]
- R         [(Partial) Autocorrelation Function] [ACF pageviews Fixed] [2011-12-20 14:13:44] [aba4febe8a2e49e81bdc61a6c01f5c21] 

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Dataseries X:

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Boxplots

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	'AstonUniversity' @ aston.wessa.net

\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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157957&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157957&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157957&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	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.209057	3.554	0.000222
2	0.264246	4.4922	5e-06
3	0.284382	4.8345	1e-06
4	0.236127	4.0142	3.8e-05
5	0.257951	4.3852	8e-06
6	0.240433	4.0874	2.8e-05
7	0.324268	5.5126	0
8	0.235304	4.0002	4e-05
9	0.25495	4.3342	1e-05
10	0.316281	5.3768	0
11	0.221823	3.771	9.9e-05
12	0.248509	4.2247	1.6e-05
13	0.212158	3.6067	0.000183
14	0.176414	2.999	0.001472
15	0.218934	3.7219	0.000119
16	0.187484	3.1872	0.000797
17	0.178726	3.0383	0.001298
18	0.275321	4.6805	2e-06
19	0.227158	3.8617	7e-05
20	0.249704	4.245	1.5e-05
21	0.159171	2.7059	0.003608
22	0.180235	3.064	0.001195
23	0.06272	1.0662	0.143601
24	0.172682	2.9356	0.001798

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.209057 & 3.554 & 0.000222 \tabularnewline
2 & 0.264246 & 4.4922 & 5e-06 \tabularnewline
3 & 0.284382 & 4.8345 & 1e-06 \tabularnewline
4 & 0.236127 & 4.0142 & 3.8e-05 \tabularnewline
5 & 0.257951 & 4.3852 & 8e-06 \tabularnewline
6 & 0.240433 & 4.0874 & 2.8e-05 \tabularnewline
7 & 0.324268 & 5.5126 & 0 \tabularnewline
8 & 0.235304 & 4.0002 & 4e-05 \tabularnewline
9 & 0.25495 & 4.3342 & 1e-05 \tabularnewline
10 & 0.316281 & 5.3768 & 0 \tabularnewline
11 & 0.221823 & 3.771 & 9.9e-05 \tabularnewline
12 & 0.248509 & 4.2247 & 1.6e-05 \tabularnewline
13 & 0.212158 & 3.6067 & 0.000183 \tabularnewline
14 & 0.176414 & 2.999 & 0.001472 \tabularnewline
15 & 0.218934 & 3.7219 & 0.000119 \tabularnewline
16 & 0.187484 & 3.1872 & 0.000797 \tabularnewline
17 & 0.178726 & 3.0383 & 0.001298 \tabularnewline
18 & 0.275321 & 4.6805 & 2e-06 \tabularnewline
19 & 0.227158 & 3.8617 & 7e-05 \tabularnewline
20 & 0.249704 & 4.245 & 1.5e-05 \tabularnewline
21 & 0.159171 & 2.7059 & 0.003608 \tabularnewline
22 & 0.180235 & 3.064 & 0.001195 \tabularnewline
23 & 0.06272 & 1.0662 & 0.143601 \tabularnewline
24 & 0.172682 & 2.9356 & 0.001798 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157957&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]0.209057[/C][C]3.554[/C][C]0.000222[/C][/ROW]
[ROW][C]2[/C][C]0.264246[/C][C]4.4922[/C][C]5e-06[/C][/ROW]
[ROW][C]3[/C][C]0.284382[/C][C]4.8345[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]0.236127[/C][C]4.0142[/C][C]3.8e-05[/C][/ROW]
[ROW][C]5[/C][C]0.257951[/C][C]4.3852[/C][C]8e-06[/C][/ROW]
[ROW][C]6[/C][C]0.240433[/C][C]4.0874[/C][C]2.8e-05[/C][/ROW]
[ROW][C]7[/C][C]0.324268[/C][C]5.5126[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.235304[/C][C]4.0002[/C][C]4e-05[/C][/ROW]
[ROW][C]9[/C][C]0.25495[/C][C]4.3342[/C][C]1e-05[/C][/ROW]
[ROW][C]10[/C][C]0.316281[/C][C]5.3768[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.221823[/C][C]3.771[/C][C]9.9e-05[/C][/ROW]
[ROW][C]12[/C][C]0.248509[/C][C]4.2247[/C][C]1.6e-05[/C][/ROW]
[ROW][C]13[/C][C]0.212158[/C][C]3.6067[/C][C]0.000183[/C][/ROW]
[ROW][C]14[/C][C]0.176414[/C][C]2.999[/C][C]0.001472[/C][/ROW]
[ROW][C]15[/C][C]0.218934[/C][C]3.7219[/C][C]0.000119[/C][/ROW]
[ROW][C]16[/C][C]0.187484[/C][C]3.1872[/C][C]0.000797[/C][/ROW]
[ROW][C]17[/C][C]0.178726[/C][C]3.0383[/C][C]0.001298[/C][/ROW]
[ROW][C]18[/C][C]0.275321[/C][C]4.6805[/C][C]2e-06[/C][/ROW]
[ROW][C]19[/C][C]0.227158[/C][C]3.8617[/C][C]7e-05[/C][/ROW]
[ROW][C]20[/C][C]0.249704[/C][C]4.245[/C][C]1.5e-05[/C][/ROW]
[ROW][C]21[/C][C]0.159171[/C][C]2.7059[/C][C]0.003608[/C][/ROW]
[ROW][C]22[/C][C]0.180235[/C][C]3.064[/C][C]0.001195[/C][/ROW]
[ROW][C]23[/C][C]0.06272[/C][C]1.0662[/C][C]0.143601[/C][/ROW]
[ROW][C]24[/C][C]0.172682[/C][C]2.9356[/C][C]0.001798[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157957&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157957&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	0.209057	3.554	0.000222
2	0.264246	4.4922	5e-06
3	0.284382	4.8345	1e-06
4	0.236127	4.0142	3.8e-05
5	0.257951	4.3852	8e-06
6	0.240433	4.0874	2.8e-05
7	0.324268	5.5126	0
8	0.235304	4.0002	4e-05
9	0.25495	4.3342	1e-05
10	0.316281	5.3768	0
11	0.221823	3.771	9.9e-05
12	0.248509	4.2247	1.6e-05
13	0.212158	3.6067	0.000183
14	0.176414	2.999	0.001472
15	0.218934	3.7219	0.000119
16	0.187484	3.1872	0.000797
17	0.178726	3.0383	0.001298
18	0.275321	4.6805	2e-06
19	0.227158	3.8617	7e-05
20	0.249704	4.245	1.5e-05
21	0.159171	2.7059	0.003608
22	0.180235	3.064	0.001195
23	0.06272	1.0662	0.143601
24	0.172682	2.9356	0.001798

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.209057	3.554	0.000222
2	0.230621	3.9206	5.5e-05
3	0.213894	3.6362	0.000164
4	0.124823	2.122	0.017345
5	0.129505	2.2016	0.014242
6	0.096367	1.6382	0.05123
7	0.189563	3.2226	0.000708
8	0.066741	1.1346	0.128742
9	0.07433	1.2636	0.103694
10	0.142094	2.4156	0.008165
11	0.03046	0.5178	0.30249
12	0.042711	0.7261	0.234184
13	-0.001606	-0.0273	0.489116
14	-0.049528	-0.842	0.200247
15	0.016073	0.2732	0.392432
16	-0.012061	-0.205	0.418847
17	-0.037898	-0.6443	0.259957
18	0.114085	1.9395	0.02671
19	0.054244	0.9221	0.178612
20	0.075142	1.2774	0.10124
21	-0.033301	-0.5661	0.285875
22	-0.021143	-0.3594	0.359765
23	-0.15299	-2.6008	0.004889
24	0.016662	0.2832	0.388595

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.209057 & 3.554 & 0.000222 \tabularnewline
2 & 0.230621 & 3.9206 & 5.5e-05 \tabularnewline
3 & 0.213894 & 3.6362 & 0.000164 \tabularnewline
4 & 0.124823 & 2.122 & 0.017345 \tabularnewline
5 & 0.129505 & 2.2016 & 0.014242 \tabularnewline
6 & 0.096367 & 1.6382 & 0.05123 \tabularnewline
7 & 0.189563 & 3.2226 & 0.000708 \tabularnewline
8 & 0.066741 & 1.1346 & 0.128742 \tabularnewline
9 & 0.07433 & 1.2636 & 0.103694 \tabularnewline
10 & 0.142094 & 2.4156 & 0.008165 \tabularnewline
11 & 0.03046 & 0.5178 & 0.30249 \tabularnewline
12 & 0.042711 & 0.7261 & 0.234184 \tabularnewline
13 & -0.001606 & -0.0273 & 0.489116 \tabularnewline
14 & -0.049528 & -0.842 & 0.200247 \tabularnewline
15 & 0.016073 & 0.2732 & 0.392432 \tabularnewline
16 & -0.012061 & -0.205 & 0.418847 \tabularnewline
17 & -0.037898 & -0.6443 & 0.259957 \tabularnewline
18 & 0.114085 & 1.9395 & 0.02671 \tabularnewline
19 & 0.054244 & 0.9221 & 0.178612 \tabularnewline
20 & 0.075142 & 1.2774 & 0.10124 \tabularnewline
21 & -0.033301 & -0.5661 & 0.285875 \tabularnewline
22 & -0.021143 & -0.3594 & 0.359765 \tabularnewline
23 & -0.15299 & -2.6008 & 0.004889 \tabularnewline
24 & 0.016662 & 0.2832 & 0.388595 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157957&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]0.209057[/C][C]3.554[/C][C]0.000222[/C][/ROW]
[ROW][C]2[/C][C]0.230621[/C][C]3.9206[/C][C]5.5e-05[/C][/ROW]
[ROW][C]3[/C][C]0.213894[/C][C]3.6362[/C][C]0.000164[/C][/ROW]
[ROW][C]4[/C][C]0.124823[/C][C]2.122[/C][C]0.017345[/C][/ROW]
[ROW][C]5[/C][C]0.129505[/C][C]2.2016[/C][C]0.014242[/C][/ROW]
[ROW][C]6[/C][C]0.096367[/C][C]1.6382[/C][C]0.05123[/C][/ROW]
[ROW][C]7[/C][C]0.189563[/C][C]3.2226[/C][C]0.000708[/C][/ROW]
[ROW][C]8[/C][C]0.066741[/C][C]1.1346[/C][C]0.128742[/C][/ROW]
[ROW][C]9[/C][C]0.07433[/C][C]1.2636[/C][C]0.103694[/C][/ROW]
[ROW][C]10[/C][C]0.142094[/C][C]2.4156[/C][C]0.008165[/C][/ROW]
[ROW][C]11[/C][C]0.03046[/C][C]0.5178[/C][C]0.30249[/C][/ROW]
[ROW][C]12[/C][C]0.042711[/C][C]0.7261[/C][C]0.234184[/C][/ROW]
[ROW][C]13[/C][C]-0.001606[/C][C]-0.0273[/C][C]0.489116[/C][/ROW]
[ROW][C]14[/C][C]-0.049528[/C][C]-0.842[/C][C]0.200247[/C][/ROW]
[ROW][C]15[/C][C]0.016073[/C][C]0.2732[/C][C]0.392432[/C][/ROW]
[ROW][C]16[/C][C]-0.012061[/C][C]-0.205[/C][C]0.418847[/C][/ROW]
[ROW][C]17[/C][C]-0.037898[/C][C]-0.6443[/C][C]0.259957[/C][/ROW]
[ROW][C]18[/C][C]0.114085[/C][C]1.9395[/C][C]0.02671[/C][/ROW]
[ROW][C]19[/C][C]0.054244[/C][C]0.9221[/C][C]0.178612[/C][/ROW]
[ROW][C]20[/C][C]0.075142[/C][C]1.2774[/C][C]0.10124[/C][/ROW]
[ROW][C]21[/C][C]-0.033301[/C][C]-0.5661[/C][C]0.285875[/C][/ROW]
[ROW][C]22[/C][C]-0.021143[/C][C]-0.3594[/C][C]0.359765[/C][/ROW]
[ROW][C]23[/C][C]-0.15299[/C][C]-2.6008[/C][C]0.004889[/C][/ROW]
[ROW][C]24[/C][C]0.016662[/C][C]0.2832[/C][C]0.388595[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157957&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157957&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	0.209057	3.554	0.000222
2	0.230621	3.9206	5.5e-05
3	0.213894	3.6362	0.000164
4	0.124823	2.122	0.017345
5	0.129505	2.2016	0.014242
6	0.096367	1.6382	0.05123
7	0.189563	3.2226	0.000708
8	0.066741	1.1346	0.128742
9	0.07433	1.2636	0.103694
10	0.142094	2.4156	0.008165
11	0.03046	0.5178	0.30249
12	0.042711	0.7261	0.234184
13	-0.001606	-0.0273	0.489116
14	-0.049528	-0.842	0.200247
15	0.016073	0.2732	0.392432
16	-0.012061	-0.205	0.418847
17	-0.037898	-0.6443	0.259957
18	0.114085	1.9395	0.02671
19	0.054244	0.9221	0.178612
20	0.075142	1.2774	0.10124
21	-0.033301	-0.5661	0.285875
22	-0.021143	-0.3594	0.359765
23	-0.15299	-2.6008	0.004889
24	0.016662	0.2832	0.388595

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

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 ; par8 = ;

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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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