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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 03 Dec 2010 17:10:35 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/03/t12913961639fq0joeiadbl9sm.htm/, Retrieved Tue, 07 May 2024 04:58:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=104927, Retrieved Tue, 07 May 2024 04:58:22 +0000

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User-defined keywords

Estimated Impact

114

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-   PD      [(Partial) Autocorrelation Function] [ws9] [2010-12-03 17:10:35] [0cadca125c925bcc9e6efbdd1941e458] [Current]
-             [(Partial) Autocorrelation Function] [ws9] [2010-12-03 17:12:55] [c7506ced21a6c0dca45d37c8a93c80e0] 

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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	'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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104927&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104927&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104927&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.934186	7.8716	0
2	0.870551	7.3354	0
3	0.808013	6.8084	0
4	0.747986	6.3026	0
5	0.685031	5.7722	0
6	0.611051	5.1488	1e-06
7	0.544512	4.5881	9e-06
8	0.493343	4.157	4.4e-05
9	0.450359	3.7948	0.000154
10	0.411082	3.4638	0.000453
11	0.376699	3.1741	0.001111
12	0.343607	2.8953	0.002515
13	0.312752	2.6353	0.005158
14	0.28981	2.442	0.00855
15	0.270162	2.2764	0.012919
16	0.253233	2.1338	0.018158
17	0.235608	1.9853	0.025489
18	0.21077	1.776	0.04001

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.934186 & 7.8716 & 0 \tabularnewline
2 & 0.870551 & 7.3354 & 0 \tabularnewline
3 & 0.808013 & 6.8084 & 0 \tabularnewline
4 & 0.747986 & 6.3026 & 0 \tabularnewline
5 & 0.685031 & 5.7722 & 0 \tabularnewline
6 & 0.611051 & 5.1488 & 1e-06 \tabularnewline
7 & 0.544512 & 4.5881 & 9e-06 \tabularnewline
8 & 0.493343 & 4.157 & 4.4e-05 \tabularnewline
9 & 0.450359 & 3.7948 & 0.000154 \tabularnewline
10 & 0.411082 & 3.4638 & 0.000453 \tabularnewline
11 & 0.376699 & 3.1741 & 0.001111 \tabularnewline
12 & 0.343607 & 2.8953 & 0.002515 \tabularnewline
13 & 0.312752 & 2.6353 & 0.005158 \tabularnewline
14 & 0.28981 & 2.442 & 0.00855 \tabularnewline
15 & 0.270162 & 2.2764 & 0.012919 \tabularnewline
16 & 0.253233 & 2.1338 & 0.018158 \tabularnewline
17 & 0.235608 & 1.9853 & 0.025489 \tabularnewline
18 & 0.21077 & 1.776 & 0.04001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104927&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]0.934186[/C][C]7.8716[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.870551[/C][C]7.3354[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.808013[/C][C]6.8084[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.747986[/C][C]6.3026[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.685031[/C][C]5.7722[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.611051[/C][C]5.1488[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.544512[/C][C]4.5881[/C][C]9e-06[/C][/ROW]
[ROW][C]8[/C][C]0.493343[/C][C]4.157[/C][C]4.4e-05[/C][/ROW]
[ROW][C]9[/C][C]0.450359[/C][C]3.7948[/C][C]0.000154[/C][/ROW]
[ROW][C]10[/C][C]0.411082[/C][C]3.4638[/C][C]0.000453[/C][/ROW]
[ROW][C]11[/C][C]0.376699[/C][C]3.1741[/C][C]0.001111[/C][/ROW]
[ROW][C]12[/C][C]0.343607[/C][C]2.8953[/C][C]0.002515[/C][/ROW]
[ROW][C]13[/C][C]0.312752[/C][C]2.6353[/C][C]0.005158[/C][/ROW]
[ROW][C]14[/C][C]0.28981[/C][C]2.442[/C][C]0.00855[/C][/ROW]
[ROW][C]15[/C][C]0.270162[/C][C]2.2764[/C][C]0.012919[/C][/ROW]
[ROW][C]16[/C][C]0.253233[/C][C]2.1338[/C][C]0.018158[/C][/ROW]
[ROW][C]17[/C][C]0.235608[/C][C]1.9853[/C][C]0.025489[/C][/ROW]
[ROW][C]18[/C][C]0.21077[/C][C]1.776[/C][C]0.04001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104927&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104927&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	0.934186	7.8716	0
2	0.870551	7.3354	0
3	0.808013	6.8084	0
4	0.747986	6.3026	0
5	0.685031	5.7722	0
6	0.611051	5.1488	1e-06
7	0.544512	4.5881	9e-06
8	0.493343	4.157	4.4e-05
9	0.450359	3.7948	0.000154
10	0.411082	3.4638	0.000453
11	0.376699	3.1741	0.001111
12	0.343607	2.8953	0.002515
13	0.312752	2.6353	0.005158
14	0.28981	2.442	0.00855
15	0.270162	2.2764	0.012919
16	0.253233	2.1338	0.018158
17	0.235608	1.9853	0.025489
18	0.21077	1.776	0.04001

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.934186	7.8716	0
2	-0.0169	-0.1424	0.443581
3	-0.025144	-0.2119	0.416408
4	-0.014574	-0.1228	0.451304
5	-0.056734	-0.478	0.317043
6	-0.124714	-1.0509	0.148444
7	0.010344	0.0872	0.465394
8	0.079535	0.6702	0.252462
9	0.032797	0.2764	0.391541
10	0.007629	0.0643	0.474463
11	0.020038	0.1688	0.433199
12	-0.028302	-0.2385	0.406099
13	-0.029884	-0.2518	0.40096
14	0.036923	0.3111	0.378309
15	0.018413	0.1552	0.438571
16	0.012519	0.1055	0.458145
17	-0.007668	-0.0646	0.474331
18	-0.068138	-0.5741	0.283842

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.934186 & 7.8716 & 0 \tabularnewline
2 & -0.0169 & -0.1424 & 0.443581 \tabularnewline
3 & -0.025144 & -0.2119 & 0.416408 \tabularnewline
4 & -0.014574 & -0.1228 & 0.451304 \tabularnewline
5 & -0.056734 & -0.478 & 0.317043 \tabularnewline
6 & -0.124714 & -1.0509 & 0.148444 \tabularnewline
7 & 0.010344 & 0.0872 & 0.465394 \tabularnewline
8 & 0.079535 & 0.6702 & 0.252462 \tabularnewline
9 & 0.032797 & 0.2764 & 0.391541 \tabularnewline
10 & 0.007629 & 0.0643 & 0.474463 \tabularnewline
11 & 0.020038 & 0.1688 & 0.433199 \tabularnewline
12 & -0.028302 & -0.2385 & 0.406099 \tabularnewline
13 & -0.029884 & -0.2518 & 0.40096 \tabularnewline
14 & 0.036923 & 0.3111 & 0.378309 \tabularnewline
15 & 0.018413 & 0.1552 & 0.438571 \tabularnewline
16 & 0.012519 & 0.1055 & 0.458145 \tabularnewline
17 & -0.007668 & -0.0646 & 0.474331 \tabularnewline
18 & -0.068138 & -0.5741 & 0.283842 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104927&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]0.934186[/C][C]7.8716[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.0169[/C][C]-0.1424[/C][C]0.443581[/C][/ROW]
[ROW][C]3[/C][C]-0.025144[/C][C]-0.2119[/C][C]0.416408[/C][/ROW]
[ROW][C]4[/C][C]-0.014574[/C][C]-0.1228[/C][C]0.451304[/C][/ROW]
[ROW][C]5[/C][C]-0.056734[/C][C]-0.478[/C][C]0.317043[/C][/ROW]
[ROW][C]6[/C][C]-0.124714[/C][C]-1.0509[/C][C]0.148444[/C][/ROW]
[ROW][C]7[/C][C]0.010344[/C][C]0.0872[/C][C]0.465394[/C][/ROW]
[ROW][C]8[/C][C]0.079535[/C][C]0.6702[/C][C]0.252462[/C][/ROW]
[ROW][C]9[/C][C]0.032797[/C][C]0.2764[/C][C]0.391541[/C][/ROW]
[ROW][C]10[/C][C]0.007629[/C][C]0.0643[/C][C]0.474463[/C][/ROW]
[ROW][C]11[/C][C]0.020038[/C][C]0.1688[/C][C]0.433199[/C][/ROW]
[ROW][C]12[/C][C]-0.028302[/C][C]-0.2385[/C][C]0.406099[/C][/ROW]
[ROW][C]13[/C][C]-0.029884[/C][C]-0.2518[/C][C]0.40096[/C][/ROW]
[ROW][C]14[/C][C]0.036923[/C][C]0.3111[/C][C]0.378309[/C][/ROW]
[ROW][C]15[/C][C]0.018413[/C][C]0.1552[/C][C]0.438571[/C][/ROW]
[ROW][C]16[/C][C]0.012519[/C][C]0.1055[/C][C]0.458145[/C][/ROW]
[ROW][C]17[/C][C]-0.007668[/C][C]-0.0646[/C][C]0.474331[/C][/ROW]
[ROW][C]18[/C][C]-0.068138[/C][C]-0.5741[/C][C]0.283842[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104927&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104927&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	0.934186	7.8716	0
2	-0.0169	-0.1424	0.443581
3	-0.025144	-0.2119	0.416408
4	-0.014574	-0.1228	0.451304
5	-0.056734	-0.478	0.317043
6	-0.124714	-1.0509	0.148444
7	0.010344	0.0872	0.465394
8	0.079535	0.6702	0.252462
9	0.032797	0.2764	0.391541
10	0.007629	0.0643	0.474463
11	0.020038	0.1688	0.433199
12	-0.028302	-0.2385	0.406099
13	-0.029884	-0.2518	0.40096
14	0.036923	0.3111	0.378309
15	0.018413	0.1552	0.438571
16	0.012519	0.1055	0.458145
17	-0.007668	-0.0646	0.474331
18	-0.068138	-0.5741	0.283842

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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