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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 26 Jan 2010 07:56:44 -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/2010/Jan/26/t1264518046klrbo4k680nk8u8.htm/, Retrieved Thu, 02 May 2024 17:00:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72635, Retrieved Thu, 02 May 2024 17:00:04 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W21

Estimated Impact

102

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

-       [(Partial) Autocorrelation Function] [Autocorrelation g...] [2010-01-26 14:56:44] [91b501704ec53ded4f914c1fb409b978] [Current]

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Dataseries X:

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Histogram

Boxplots

1,14
1,15
1,15
1,14
1,14
1,14
1,15
1,14
1,14
1,15
1,15
1,14
1,15
1,17
1,17
1,17
1,17
1,17
1,17
1,17
1,17
1,17
1,17
1,17
1,17
1,18
1,19
1,19
1,19
1,19
1,18
1,19
1,19
1,2
1,21
1,21
1,2
1,21
1,21
1,21
1,21
1,21
1,21
1,2
1,21
1,22
1,22
1,23
1,22
1,23
1,23
1,23
1,23
1,23
1,22
1,22
1,23
1,24
1,24
1,25
1,25
1,25
1,26
1,26
1,26
1,26
1,27
1,27
1,29
1,31
1,32
1,32
1,33
1,33
1,32
1,32
1,31
1,3
1,31
1,29
1,3
1,3
1,32
1,31
1,35
1,35
1,36
1,37
1,37
1,37
1,32
1,32
1,31
1,31
1,34
1,31
1,26
1,27
1,24
1,25
1,27
1,25
1,26
1,27
1,26
1,26
1,28
1,27
1,28
1,27
1,26
1,27
1,27
1,28
1,27
1,26
1,3
1,31
1,28
1,29
1,31
1,29
1,29
1,32
1,3
1,29
1,31
1,29
1,33
1,35
1,32
1,33

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=72635&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=72635&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72635&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	-0.178627	-2.0445	0.021455
2	-0.141954	-1.6247	0.05331
3	0.269674	3.0866	0.001236
4	-0.20081	-2.2984	0.011562
5	-0.032934	-0.3769	0.353412
6	0.195367	2.2361	0.013519
7	-0.124759	-1.4279	0.077845
8	-0.064474	-0.7379	0.230936
9	0.056793	0.65	0.258406
10	-0.166155	-1.9017	0.029701
11	-0.014206	-0.1626	0.435544
12	0.079606	0.9111	0.181949
13	0.046614	0.5335	0.297287
14	-0.016619	-0.1902	0.424718
15	-0.023828	-0.2727	0.392749
16	0.035959	0.4116	0.340664
17	0.077589	0.888	0.188073
18	-0.076751	-0.8785	0.190652
19	0.054372	0.6223	0.267409
20	0.042763	0.4894	0.312672
21	-0.156573	-1.7921	0.037716

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.178627 & -2.0445 & 0.021455 \tabularnewline
2 & -0.141954 & -1.6247 & 0.05331 \tabularnewline
3 & 0.269674 & 3.0866 & 0.001236 \tabularnewline
4 & -0.20081 & -2.2984 & 0.011562 \tabularnewline
5 & -0.032934 & -0.3769 & 0.353412 \tabularnewline
6 & 0.195367 & 2.2361 & 0.013519 \tabularnewline
7 & -0.124759 & -1.4279 & 0.077845 \tabularnewline
8 & -0.064474 & -0.7379 & 0.230936 \tabularnewline
9 & 0.056793 & 0.65 & 0.258406 \tabularnewline
10 & -0.166155 & -1.9017 & 0.029701 \tabularnewline
11 & -0.014206 & -0.1626 & 0.435544 \tabularnewline
12 & 0.079606 & 0.9111 & 0.181949 \tabularnewline
13 & 0.046614 & 0.5335 & 0.297287 \tabularnewline
14 & -0.016619 & -0.1902 & 0.424718 \tabularnewline
15 & -0.023828 & -0.2727 & 0.392749 \tabularnewline
16 & 0.035959 & 0.4116 & 0.340664 \tabularnewline
17 & 0.077589 & 0.888 & 0.188073 \tabularnewline
18 & -0.076751 & -0.8785 & 0.190652 \tabularnewline
19 & 0.054372 & 0.6223 & 0.267409 \tabularnewline
20 & 0.042763 & 0.4894 & 0.312672 \tabularnewline
21 & -0.156573 & -1.7921 & 0.037716 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72635&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]-0.178627[/C][C]-2.0445[/C][C]0.021455[/C][/ROW]
[ROW][C]2[/C][C]-0.141954[/C][C]-1.6247[/C][C]0.05331[/C][/ROW]
[ROW][C]3[/C][C]0.269674[/C][C]3.0866[/C][C]0.001236[/C][/ROW]
[ROW][C]4[/C][C]-0.20081[/C][C]-2.2984[/C][C]0.011562[/C][/ROW]
[ROW][C]5[/C][C]-0.032934[/C][C]-0.3769[/C][C]0.353412[/C][/ROW]
[ROW][C]6[/C][C]0.195367[/C][C]2.2361[/C][C]0.013519[/C][/ROW]
[ROW][C]7[/C][C]-0.124759[/C][C]-1.4279[/C][C]0.077845[/C][/ROW]
[ROW][C]8[/C][C]-0.064474[/C][C]-0.7379[/C][C]0.230936[/C][/ROW]
[ROW][C]9[/C][C]0.056793[/C][C]0.65[/C][C]0.258406[/C][/ROW]
[ROW][C]10[/C][C]-0.166155[/C][C]-1.9017[/C][C]0.029701[/C][/ROW]
[ROW][C]11[/C][C]-0.014206[/C][C]-0.1626[/C][C]0.435544[/C][/ROW]
[ROW][C]12[/C][C]0.079606[/C][C]0.9111[/C][C]0.181949[/C][/ROW]
[ROW][C]13[/C][C]0.046614[/C][C]0.5335[/C][C]0.297287[/C][/ROW]
[ROW][C]14[/C][C]-0.016619[/C][C]-0.1902[/C][C]0.424718[/C][/ROW]
[ROW][C]15[/C][C]-0.023828[/C][C]-0.2727[/C][C]0.392749[/C][/ROW]
[ROW][C]16[/C][C]0.035959[/C][C]0.4116[/C][C]0.340664[/C][/ROW]
[ROW][C]17[/C][C]0.077589[/C][C]0.888[/C][C]0.188073[/C][/ROW]
[ROW][C]18[/C][C]-0.076751[/C][C]-0.8785[/C][C]0.190652[/C][/ROW]
[ROW][C]19[/C][C]0.054372[/C][C]0.6223[/C][C]0.267409[/C][/ROW]
[ROW][C]20[/C][C]0.042763[/C][C]0.4894[/C][C]0.312672[/C][/ROW]
[ROW][C]21[/C][C]-0.156573[/C][C]-1.7921[/C][C]0.037716[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72635&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72635&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	-0.178627	-2.0445	0.021455
2	-0.141954	-1.6247	0.05331
3	0.269674	3.0866	0.001236
4	-0.20081	-2.2984	0.011562
5	-0.032934	-0.3769	0.353412
6	0.195367	2.2361	0.013519
7	-0.124759	-1.4279	0.077845
8	-0.064474	-0.7379	0.230936
9	0.056793	0.65	0.258406
10	-0.166155	-1.9017	0.029701
11	-0.014206	-0.1626	0.435544
12	0.079606	0.9111	0.181949
13	0.046614	0.5335	0.297287
14	-0.016619	-0.1902	0.424718
15	-0.023828	-0.2727	0.392749
16	0.035959	0.4116	0.340664
17	0.077589	0.888	0.188073
18	-0.076751	-0.8785	0.190652
19	0.054372	0.6223	0.267409
20	0.042763	0.4894	0.312672
21	-0.156573	-1.7921	0.037716

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.178627	-2.0445	0.021455
2	-0.179592	-2.0555	0.020907
3	0.221678	2.5372	0.006173
4	-0.15041	-1.7215	0.043758
5	-0.021108	-0.2416	0.404735
6	0.095776	1.0962	0.1375
7	-0.015712	-0.1798	0.428781
8	-0.074217	-0.8495	0.19859
9	-0.052702	-0.6032	0.27371
10	-0.128184	-1.4671	0.072368
11	-0.049795	-0.5699	0.284849
12	-0.005613	-0.0642	0.474439
13	0.136948	1.5674	0.059712
14	0.003709	0.0425	0.483101
15	-0.044299	-0.507	0.306495
16	0.028688	0.3283	0.371587
17	0.120889	1.3836	0.08441
18	-0.076947	-0.8807	0.190048
19	0.002449	0.028	0.488842
20	0.013496	0.1545	0.438737
21	-0.085394	-0.9774	0.165093

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.178627 & -2.0445 & 0.021455 \tabularnewline
2 & -0.179592 & -2.0555 & 0.020907 \tabularnewline
3 & 0.221678 & 2.5372 & 0.006173 \tabularnewline
4 & -0.15041 & -1.7215 & 0.043758 \tabularnewline
5 & -0.021108 & -0.2416 & 0.404735 \tabularnewline
6 & 0.095776 & 1.0962 & 0.1375 \tabularnewline
7 & -0.015712 & -0.1798 & 0.428781 \tabularnewline
8 & -0.074217 & -0.8495 & 0.19859 \tabularnewline
9 & -0.052702 & -0.6032 & 0.27371 \tabularnewline
10 & -0.128184 & -1.4671 & 0.072368 \tabularnewline
11 & -0.049795 & -0.5699 & 0.284849 \tabularnewline
12 & -0.005613 & -0.0642 & 0.474439 \tabularnewline
13 & 0.136948 & 1.5674 & 0.059712 \tabularnewline
14 & 0.003709 & 0.0425 & 0.483101 \tabularnewline
15 & -0.044299 & -0.507 & 0.306495 \tabularnewline
16 & 0.028688 & 0.3283 & 0.371587 \tabularnewline
17 & 0.120889 & 1.3836 & 0.08441 \tabularnewline
18 & -0.076947 & -0.8807 & 0.190048 \tabularnewline
19 & 0.002449 & 0.028 & 0.488842 \tabularnewline
20 & 0.013496 & 0.1545 & 0.438737 \tabularnewline
21 & -0.085394 & -0.9774 & 0.165093 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72635&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]-0.178627[/C][C]-2.0445[/C][C]0.021455[/C][/ROW]
[ROW][C]2[/C][C]-0.179592[/C][C]-2.0555[/C][C]0.020907[/C][/ROW]
[ROW][C]3[/C][C]0.221678[/C][C]2.5372[/C][C]0.006173[/C][/ROW]
[ROW][C]4[/C][C]-0.15041[/C][C]-1.7215[/C][C]0.043758[/C][/ROW]
[ROW][C]5[/C][C]-0.021108[/C][C]-0.2416[/C][C]0.404735[/C][/ROW]
[ROW][C]6[/C][C]0.095776[/C][C]1.0962[/C][C]0.1375[/C][/ROW]
[ROW][C]7[/C][C]-0.015712[/C][C]-0.1798[/C][C]0.428781[/C][/ROW]
[ROW][C]8[/C][C]-0.074217[/C][C]-0.8495[/C][C]0.19859[/C][/ROW]
[ROW][C]9[/C][C]-0.052702[/C][C]-0.6032[/C][C]0.27371[/C][/ROW]
[ROW][C]10[/C][C]-0.128184[/C][C]-1.4671[/C][C]0.072368[/C][/ROW]
[ROW][C]11[/C][C]-0.049795[/C][C]-0.5699[/C][C]0.284849[/C][/ROW]
[ROW][C]12[/C][C]-0.005613[/C][C]-0.0642[/C][C]0.474439[/C][/ROW]
[ROW][C]13[/C][C]0.136948[/C][C]1.5674[/C][C]0.059712[/C][/ROW]
[ROW][C]14[/C][C]0.003709[/C][C]0.0425[/C][C]0.483101[/C][/ROW]
[ROW][C]15[/C][C]-0.044299[/C][C]-0.507[/C][C]0.306495[/C][/ROW]
[ROW][C]16[/C][C]0.028688[/C][C]0.3283[/C][C]0.371587[/C][/ROW]
[ROW][C]17[/C][C]0.120889[/C][C]1.3836[/C][C]0.08441[/C][/ROW]
[ROW][C]18[/C][C]-0.076947[/C][C]-0.8807[/C][C]0.190048[/C][/ROW]
[ROW][C]19[/C][C]0.002449[/C][C]0.028[/C][C]0.488842[/C][/ROW]
[ROW][C]20[/C][C]0.013496[/C][C]0.1545[/C][C]0.438737[/C][/ROW]
[ROW][C]21[/C][C]-0.085394[/C][C]-0.9774[/C][C]0.165093[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72635&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72635&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	-0.178627	-2.0445	0.021455
2	-0.179592	-2.0555	0.020907
3	0.221678	2.5372	0.006173
4	-0.15041	-1.7215	0.043758
5	-0.021108	-0.2416	0.404735
6	0.095776	1.0962	0.1375
7	-0.015712	-0.1798	0.428781
8	-0.074217	-0.8495	0.19859
9	-0.052702	-0.6032	0.27371
10	-0.128184	-1.4671	0.072368
11	-0.049795	-0.5699	0.284849
12	-0.005613	-0.0642	0.474439
13	0.136948	1.5674	0.059712
14	0.003709	0.0425	0.483101
15	-0.044299	-0.507	0.306495
16	0.028688	0.3283	0.371587
17	0.120889	1.3836	0.08441
18	-0.076947	-0.8807	0.190048
19	0.002449	0.028	0.488842
20	0.013496	0.1545	0.438737
21	-0.085394	-0.9774	0.165093

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; 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