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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 12 Dec 2009 08:27:57 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/12/t1260631719kxbacka9ca4pp5l.htm/, Retrieved Mon, 29 Apr 2024 13:51:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67017, Retrieved Mon, 29 Apr 2024 13:51:05 +0000

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

-       [(Partial) Autocorrelation Function] [ACF] [2009-12-12 15:27:57] [5d37783481a916b2505b66314b556267] [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	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=67017&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=67017&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67017&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	-0.383634	-2.9716	0.002129
2	-0.217114	-1.6818	0.048907
3	0.341651	2.6464	0.005187
4	-0.170056	-1.3172	0.096382
5	-0.096885	-0.7505	0.227953
6	0.267723	2.0738	0.0212
7	-0.217538	-1.685	0.048588
8	-0.001218	-0.0094	0.496252
9	0.17685	1.3699	0.087916
10	-0.249235	-1.9306	0.029133
11	-0.114883	-0.8899	0.188542
12	0.461002	3.5709	0.000354
13	-0.240321	-1.8615	0.033786
14	-0.117076	-0.9069	0.184052
15	0.125239	0.9701	0.167946
16	-0.032188	-0.2493	0.401981
17	-0.039003	-0.3021	0.381803

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.383634 & -2.9716 & 0.002129 \tabularnewline
2 & -0.217114 & -1.6818 & 0.048907 \tabularnewline
3 & 0.341651 & 2.6464 & 0.005187 \tabularnewline
4 & -0.170056 & -1.3172 & 0.096382 \tabularnewline
5 & -0.096885 & -0.7505 & 0.227953 \tabularnewline
6 & 0.267723 & 2.0738 & 0.0212 \tabularnewline
7 & -0.217538 & -1.685 & 0.048588 \tabularnewline
8 & -0.001218 & -0.0094 & 0.496252 \tabularnewline
9 & 0.17685 & 1.3699 & 0.087916 \tabularnewline
10 & -0.249235 & -1.9306 & 0.029133 \tabularnewline
11 & -0.114883 & -0.8899 & 0.188542 \tabularnewline
12 & 0.461002 & 3.5709 & 0.000354 \tabularnewline
13 & -0.240321 & -1.8615 & 0.033786 \tabularnewline
14 & -0.117076 & -0.9069 & 0.184052 \tabularnewline
15 & 0.125239 & 0.9701 & 0.167946 \tabularnewline
16 & -0.032188 & -0.2493 & 0.401981 \tabularnewline
17 & -0.039003 & -0.3021 & 0.381803 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67017&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]-0.383634[/C][C]-2.9716[/C][C]0.002129[/C][/ROW]
[ROW][C]2[/C][C]-0.217114[/C][C]-1.6818[/C][C]0.048907[/C][/ROW]
[ROW][C]3[/C][C]0.341651[/C][C]2.6464[/C][C]0.005187[/C][/ROW]
[ROW][C]4[/C][C]-0.170056[/C][C]-1.3172[/C][C]0.096382[/C][/ROW]
[ROW][C]5[/C][C]-0.096885[/C][C]-0.7505[/C][C]0.227953[/C][/ROW]
[ROW][C]6[/C][C]0.267723[/C][C]2.0738[/C][C]0.0212[/C][/ROW]
[ROW][C]7[/C][C]-0.217538[/C][C]-1.685[/C][C]0.048588[/C][/ROW]
[ROW][C]8[/C][C]-0.001218[/C][C]-0.0094[/C][C]0.496252[/C][/ROW]
[ROW][C]9[/C][C]0.17685[/C][C]1.3699[/C][C]0.087916[/C][/ROW]
[ROW][C]10[/C][C]-0.249235[/C][C]-1.9306[/C][C]0.029133[/C][/ROW]
[ROW][C]11[/C][C]-0.114883[/C][C]-0.8899[/C][C]0.188542[/C][/ROW]
[ROW][C]12[/C][C]0.461002[/C][C]3.5709[/C][C]0.000354[/C][/ROW]
[ROW][C]13[/C][C]-0.240321[/C][C]-1.8615[/C][C]0.033786[/C][/ROW]
[ROW][C]14[/C][C]-0.117076[/C][C]-0.9069[/C][C]0.184052[/C][/ROW]
[ROW][C]15[/C][C]0.125239[/C][C]0.9701[/C][C]0.167946[/C][/ROW]
[ROW][C]16[/C][C]-0.032188[/C][C]-0.2493[/C][C]0.401981[/C][/ROW]
[ROW][C]17[/C][C]-0.039003[/C][C]-0.3021[/C][C]0.381803[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67017&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67017&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	-0.383634	-2.9716	0.002129
2	-0.217114	-1.6818	0.048907
3	0.341651	2.6464	0.005187
4	-0.170056	-1.3172	0.096382
5	-0.096885	-0.7505	0.227953
6	0.267723	2.0738	0.0212
7	-0.217538	-1.685	0.048588
8	-0.001218	-0.0094	0.496252
9	0.17685	1.3699	0.087916
10	-0.249235	-1.9306	0.029133
11	-0.114883	-0.8899	0.188542
12	0.461002	3.5709	0.000354
13	-0.240321	-1.8615	0.033786
14	-0.117076	-0.9069	0.184052
15	0.125239	0.9701	0.167946
16	-0.032188	-0.2493	0.401981
17	-0.039003	-0.3021	0.381803

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.383634	-2.9716	0.002129
2	-0.427156	-3.3087	0.000794
3	0.084491	0.6545	0.257658
4	-0.065894	-0.5104	0.305817
5	-0.084804	-0.6569	0.256881
6	0.128778	0.9975	0.161262
7	-0.080079	-0.6203	0.268707
8	-0.009895	-0.0766	0.46958
9	0.036105	0.2797	0.390346
10	-0.145956	-1.1306	0.131368
11	-0.327671	-2.5381	0.006879
12	0.221238	1.7137	0.045873
13	0.111708	0.8653	0.195165
14	0.007427	0.0575	0.477156
15	-0.225626	-1.7477	0.042816
16	0.008197	0.0635	0.474792
17	0.026231	0.2032	0.41984

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.383634 & -2.9716 & 0.002129 \tabularnewline
2 & -0.427156 & -3.3087 & 0.000794 \tabularnewline
3 & 0.084491 & 0.6545 & 0.257658 \tabularnewline
4 & -0.065894 & -0.5104 & 0.305817 \tabularnewline
5 & -0.084804 & -0.6569 & 0.256881 \tabularnewline
6 & 0.128778 & 0.9975 & 0.161262 \tabularnewline
7 & -0.080079 & -0.6203 & 0.268707 \tabularnewline
8 & -0.009895 & -0.0766 & 0.46958 \tabularnewline
9 & 0.036105 & 0.2797 & 0.390346 \tabularnewline
10 & -0.145956 & -1.1306 & 0.131368 \tabularnewline
11 & -0.327671 & -2.5381 & 0.006879 \tabularnewline
12 & 0.221238 & 1.7137 & 0.045873 \tabularnewline
13 & 0.111708 & 0.8653 & 0.195165 \tabularnewline
14 & 0.007427 & 0.0575 & 0.477156 \tabularnewline
15 & -0.225626 & -1.7477 & 0.042816 \tabularnewline
16 & 0.008197 & 0.0635 & 0.474792 \tabularnewline
17 & 0.026231 & 0.2032 & 0.41984 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67017&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]-0.383634[/C][C]-2.9716[/C][C]0.002129[/C][/ROW]
[ROW][C]2[/C][C]-0.427156[/C][C]-3.3087[/C][C]0.000794[/C][/ROW]
[ROW][C]3[/C][C]0.084491[/C][C]0.6545[/C][C]0.257658[/C][/ROW]
[ROW][C]4[/C][C]-0.065894[/C][C]-0.5104[/C][C]0.305817[/C][/ROW]
[ROW][C]5[/C][C]-0.084804[/C][C]-0.6569[/C][C]0.256881[/C][/ROW]
[ROW][C]6[/C][C]0.128778[/C][C]0.9975[/C][C]0.161262[/C][/ROW]
[ROW][C]7[/C][C]-0.080079[/C][C]-0.6203[/C][C]0.268707[/C][/ROW]
[ROW][C]8[/C][C]-0.009895[/C][C]-0.0766[/C][C]0.46958[/C][/ROW]
[ROW][C]9[/C][C]0.036105[/C][C]0.2797[/C][C]0.390346[/C][/ROW]
[ROW][C]10[/C][C]-0.145956[/C][C]-1.1306[/C][C]0.131368[/C][/ROW]
[ROW][C]11[/C][C]-0.327671[/C][C]-2.5381[/C][C]0.006879[/C][/ROW]
[ROW][C]12[/C][C]0.221238[/C][C]1.7137[/C][C]0.045873[/C][/ROW]
[ROW][C]13[/C][C]0.111708[/C][C]0.8653[/C][C]0.195165[/C][/ROW]
[ROW][C]14[/C][C]0.007427[/C][C]0.0575[/C][C]0.477156[/C][/ROW]
[ROW][C]15[/C][C]-0.225626[/C][C]-1.7477[/C][C]0.042816[/C][/ROW]
[ROW][C]16[/C][C]0.008197[/C][C]0.0635[/C][C]0.474792[/C][/ROW]
[ROW][C]17[/C][C]0.026231[/C][C]0.2032[/C][C]0.41984[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67017&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67017&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	-0.383634	-2.9716	0.002129
2	-0.427156	-3.3087	0.000794
3	0.084491	0.6545	0.257658
4	-0.065894	-0.5104	0.305817
5	-0.084804	-0.6569	0.256881
6	0.128778	0.9975	0.161262
7	-0.080079	-0.6203	0.268707
8	-0.009895	-0.0766	0.46958
9	0.036105	0.2797	0.390346
10	-0.145956	-1.1306	0.131368
11	-0.327671	-2.5381	0.006879
12	0.221238	1.7137	0.045873
13	0.111708	0.8653	0.195165
14	0.007427	0.0575	0.477156
15	-0.225626	-1.7477	0.042816
16	0.008197	0.0635	0.474792
17	0.026231	0.2032	0.41984

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')

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Tables (Output of Computation)

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Input Parameters & R Code