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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 20 Aug 2010 08:08:59 +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/Aug/20/t1282291739kohzpg1x6xt0cfj.htm/, Retrieved Wed, 08 May 2024 15:13:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79446, Retrieved Wed, 08 May 2024 15:13:29 +0000

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User-defined keywords

Willem Van Tendeloo MAR 201 A

Estimated Impact

155

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

-       [(Partial) Autocorrelation Function] [Tijdreeks A Stap 21] [2010-08-20 08:08:59] [6b796205aa6c71fffca3ea7e892beea1] [Current]

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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	9 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 9 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79446&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]9 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79446&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79446&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	9 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.667687	-6.0462	0
2	0.343264	3.1084	0.001293
3	-0.234445	-2.123	0.018385
4	0.301248	2.7279	0.003897
5	-0.370583	-3.3558	0.000601
6	0.289387	2.6205	0.00523
7	-0.258716	-2.3428	0.010782
8	0.177831	1.6103	0.055585
9	-0.201137	-1.8214	0.036099
10	0.354242	3.2078	0.000954
11	-0.593229	-5.3719	0
12	0.7088	6.4185	0
13	-0.487191	-4.4117	1.5e-05
14	0.289026	2.6172	0.005276
15	-0.243616	-2.206	0.01509
16	0.298283	2.7011	0.004198
17	-0.273916	-2.4804	0.007584
18	0.158486	1.4352	0.077523
19	-0.146906	-1.3303	0.093556

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.667687 & -6.0462 & 0 \tabularnewline
2 & 0.343264 & 3.1084 & 0.001293 \tabularnewline
3 & -0.234445 & -2.123 & 0.018385 \tabularnewline
4 & 0.301248 & 2.7279 & 0.003897 \tabularnewline
5 & -0.370583 & -3.3558 & 0.000601 \tabularnewline
6 & 0.289387 & 2.6205 & 0.00523 \tabularnewline
7 & -0.258716 & -2.3428 & 0.010782 \tabularnewline
8 & 0.177831 & 1.6103 & 0.055585 \tabularnewline
9 & -0.201137 & -1.8214 & 0.036099 \tabularnewline
10 & 0.354242 & 3.2078 & 0.000954 \tabularnewline
11 & -0.593229 & -5.3719 & 0 \tabularnewline
12 & 0.7088 & 6.4185 & 0 \tabularnewline
13 & -0.487191 & -4.4117 & 1.5e-05 \tabularnewline
14 & 0.289026 & 2.6172 & 0.005276 \tabularnewline
15 & -0.243616 & -2.206 & 0.01509 \tabularnewline
16 & 0.298283 & 2.7011 & 0.004198 \tabularnewline
17 & -0.273916 & -2.4804 & 0.007584 \tabularnewline
18 & 0.158486 & 1.4352 & 0.077523 \tabularnewline
19 & -0.146906 & -1.3303 & 0.093556 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79446&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]-0.667687[/C][C]-6.0462[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.343264[/C][C]3.1084[/C][C]0.001293[/C][/ROW]
[ROW][C]3[/C][C]-0.234445[/C][C]-2.123[/C][C]0.018385[/C][/ROW]
[ROW][C]4[/C][C]0.301248[/C][C]2.7279[/C][C]0.003897[/C][/ROW]
[ROW][C]5[/C][C]-0.370583[/C][C]-3.3558[/C][C]0.000601[/C][/ROW]
[ROW][C]6[/C][C]0.289387[/C][C]2.6205[/C][C]0.00523[/C][/ROW]
[ROW][C]7[/C][C]-0.258716[/C][C]-2.3428[/C][C]0.010782[/C][/ROW]
[ROW][C]8[/C][C]0.177831[/C][C]1.6103[/C][C]0.055585[/C][/ROW]
[ROW][C]9[/C][C]-0.201137[/C][C]-1.8214[/C][C]0.036099[/C][/ROW]
[ROW][C]10[/C][C]0.354242[/C][C]3.2078[/C][C]0.000954[/C][/ROW]
[ROW][C]11[/C][C]-0.593229[/C][C]-5.3719[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.7088[/C][C]6.4185[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.487191[/C][C]-4.4117[/C][C]1.5e-05[/C][/ROW]
[ROW][C]14[/C][C]0.289026[/C][C]2.6172[/C][C]0.005276[/C][/ROW]
[ROW][C]15[/C][C]-0.243616[/C][C]-2.206[/C][C]0.01509[/C][/ROW]
[ROW][C]16[/C][C]0.298283[/C][C]2.7011[/C][C]0.004198[/C][/ROW]
[ROW][C]17[/C][C]-0.273916[/C][C]-2.4804[/C][C]0.007584[/C][/ROW]
[ROW][C]18[/C][C]0.158486[/C][C]1.4352[/C][C]0.077523[/C][/ROW]
[ROW][C]19[/C][C]-0.146906[/C][C]-1.3303[/C][C]0.093556[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79446&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79446&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	-0.667687	-6.0462	0
2	0.343264	3.1084	0.001293
3	-0.234445	-2.123	0.018385
4	0.301248	2.7279	0.003897
5	-0.370583	-3.3558	0.000601
6	0.289387	2.6205	0.00523
7	-0.258716	-2.3428	0.010782
8	0.177831	1.6103	0.055585
9	-0.201137	-1.8214	0.036099
10	0.354242	3.2078	0.000954
11	-0.593229	-5.3719	0
12	0.7088	6.4185	0
13	-0.487191	-4.4117	1.5e-05
14	0.289026	2.6172	0.005276
15	-0.243616	-2.206	0.01509
16	0.298283	2.7011	0.004198
17	-0.273916	-2.4804	0.007584
18	0.158486	1.4352	0.077523
19	-0.146906	-1.3303	0.093556

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.667687	-6.0462	0
2	-0.185029	-1.6755	0.048822
3	-0.161403	-1.4616	0.073841
4	0.207819	1.8819	0.0317
5	-0.111936	-1.0136	0.156873
6	-0.080556	-0.7295	0.233898
7	-0.179021	-1.6211	0.054417
8	-0.154396	-1.3981	0.082925
9	-0.170044	-1.5398	0.063728
10	0.261178	2.3651	0.010194
11	-0.442525	-4.0072	6.7e-05
12	0.265387	2.4032	0.009255
13	0.118415	1.0723	0.143366
14	-0.01797	-0.1627	0.435569
15	0.061907	0.5606	0.288301
16	-0.122598	-1.1102	0.135086
17	0.150132	1.3595	0.088857
18	-0.074246	-0.6723	0.251634
19	-0.124737	-1.1295	0.130981

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.667687 & -6.0462 & 0 \tabularnewline
2 & -0.185029 & -1.6755 & 0.048822 \tabularnewline
3 & -0.161403 & -1.4616 & 0.073841 \tabularnewline
4 & 0.207819 & 1.8819 & 0.0317 \tabularnewline
5 & -0.111936 & -1.0136 & 0.156873 \tabularnewline
6 & -0.080556 & -0.7295 & 0.233898 \tabularnewline
7 & -0.179021 & -1.6211 & 0.054417 \tabularnewline
8 & -0.154396 & -1.3981 & 0.082925 \tabularnewline
9 & -0.170044 & -1.5398 & 0.063728 \tabularnewline
10 & 0.261178 & 2.3651 & 0.010194 \tabularnewline
11 & -0.442525 & -4.0072 & 6.7e-05 \tabularnewline
12 & 0.265387 & 2.4032 & 0.009255 \tabularnewline
13 & 0.118415 & 1.0723 & 0.143366 \tabularnewline
14 & -0.01797 & -0.1627 & 0.435569 \tabularnewline
15 & 0.061907 & 0.5606 & 0.288301 \tabularnewline
16 & -0.122598 & -1.1102 & 0.135086 \tabularnewline
17 & 0.150132 & 1.3595 & 0.088857 \tabularnewline
18 & -0.074246 & -0.6723 & 0.251634 \tabularnewline
19 & -0.124737 & -1.1295 & 0.130981 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79446&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]-0.667687[/C][C]-6.0462[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.185029[/C][C]-1.6755[/C][C]0.048822[/C][/ROW]
[ROW][C]3[/C][C]-0.161403[/C][C]-1.4616[/C][C]0.073841[/C][/ROW]
[ROW][C]4[/C][C]0.207819[/C][C]1.8819[/C][C]0.0317[/C][/ROW]
[ROW][C]5[/C][C]-0.111936[/C][C]-1.0136[/C][C]0.156873[/C][/ROW]
[ROW][C]6[/C][C]-0.080556[/C][C]-0.7295[/C][C]0.233898[/C][/ROW]
[ROW][C]7[/C][C]-0.179021[/C][C]-1.6211[/C][C]0.054417[/C][/ROW]
[ROW][C]8[/C][C]-0.154396[/C][C]-1.3981[/C][C]0.082925[/C][/ROW]
[ROW][C]9[/C][C]-0.170044[/C][C]-1.5398[/C][C]0.063728[/C][/ROW]
[ROW][C]10[/C][C]0.261178[/C][C]2.3651[/C][C]0.010194[/C][/ROW]
[ROW][C]11[/C][C]-0.442525[/C][C]-4.0072[/C][C]6.7e-05[/C][/ROW]
[ROW][C]12[/C][C]0.265387[/C][C]2.4032[/C][C]0.009255[/C][/ROW]
[ROW][C]13[/C][C]0.118415[/C][C]1.0723[/C][C]0.143366[/C][/ROW]
[ROW][C]14[/C][C]-0.01797[/C][C]-0.1627[/C][C]0.435569[/C][/ROW]
[ROW][C]15[/C][C]0.061907[/C][C]0.5606[/C][C]0.288301[/C][/ROW]
[ROW][C]16[/C][C]-0.122598[/C][C]-1.1102[/C][C]0.135086[/C][/ROW]
[ROW][C]17[/C][C]0.150132[/C][C]1.3595[/C][C]0.088857[/C][/ROW]
[ROW][C]18[/C][C]-0.074246[/C][C]-0.6723[/C][C]0.251634[/C][/ROW]
[ROW][C]19[/C][C]-0.124737[/C][C]-1.1295[/C][C]0.130981[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79446&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79446&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	-0.667687	-6.0462	0
2	-0.185029	-1.6755	0.048822
3	-0.161403	-1.4616	0.073841
4	0.207819	1.8819	0.0317
5	-0.111936	-1.0136	0.156873
6	-0.080556	-0.7295	0.233898
7	-0.179021	-1.6211	0.054417
8	-0.154396	-1.3981	0.082925
9	-0.170044	-1.5398	0.063728
10	0.261178	2.3651	0.010194
11	-0.442525	-4.0072	6.7e-05
12	0.265387	2.4032	0.009255
13	0.118415	1.0723	0.143366
14	-0.01797	-0.1627	0.435569
15	0.061907	0.5606	0.288301
16	-0.122598	-1.1102	0.135086
17	0.150132	1.3595	0.088857
18	-0.074246	-0.6723	0.251634
19	-0.124737	-1.1295	0.130981

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; 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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code