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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 05 Dec 2010 13:53:50 +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/05/t12915571429jhbo2l1y6mo3gr.htm/, Retrieved Wed, 01 May 2024 20:52:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105401, Retrieved Wed, 01 May 2024 20:52:14 +0000

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Estimated Impact

106

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]
-    D      [(Partial) Autocorrelation Function] [WS 9 ACF] [2010-12-05 13:53:50] [b47314d83d48c7bf812ec2bcd743b159] [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	4 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105401&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105401&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105401&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	4 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.921082	6.954	0
2	0.815602	6.1577	0
3	0.72041	5.439	1e-06
4	0.62231	4.6983	8e-06
5	0.532699	4.0218	8.6e-05
6	0.411692	3.1082	0.001467
7	0.267063	2.0163	0.024246
8	0.153128	1.1561	0.126233
9	0.064744	0.4888	0.313427
10	-0.017236	-0.1301	0.448462
11	-0.090664	-0.6845	0.248217
12	-0.168583	-1.2728	0.104133
13	-0.226519	-1.7102	0.046336
14	-0.244314	-1.8445	0.035152
15	-0.260664	-1.968	0.026971
16	-0.2977	-2.2476	0.014245
17	-0.351818	-2.6562	0.005116

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.921082 & 6.954 & 0 \tabularnewline
2 & 0.815602 & 6.1577 & 0 \tabularnewline
3 & 0.72041 & 5.439 & 1e-06 \tabularnewline
4 & 0.62231 & 4.6983 & 8e-06 \tabularnewline
5 & 0.532699 & 4.0218 & 8.6e-05 \tabularnewline
6 & 0.411692 & 3.1082 & 0.001467 \tabularnewline
7 & 0.267063 & 2.0163 & 0.024246 \tabularnewline
8 & 0.153128 & 1.1561 & 0.126233 \tabularnewline
9 & 0.064744 & 0.4888 & 0.313427 \tabularnewline
10 & -0.017236 & -0.1301 & 0.448462 \tabularnewline
11 & -0.090664 & -0.6845 & 0.248217 \tabularnewline
12 & -0.168583 & -1.2728 & 0.104133 \tabularnewline
13 & -0.226519 & -1.7102 & 0.046336 \tabularnewline
14 & -0.244314 & -1.8445 & 0.035152 \tabularnewline
15 & -0.260664 & -1.968 & 0.026971 \tabularnewline
16 & -0.2977 & -2.2476 & 0.014245 \tabularnewline
17 & -0.351818 & -2.6562 & 0.005116 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105401&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]0.921082[/C][C]6.954[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.815602[/C][C]6.1577[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.72041[/C][C]5.439[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]0.62231[/C][C]4.6983[/C][C]8e-06[/C][/ROW]
[ROW][C]5[/C][C]0.532699[/C][C]4.0218[/C][C]8.6e-05[/C][/ROW]
[ROW][C]6[/C][C]0.411692[/C][C]3.1082[/C][C]0.001467[/C][/ROW]
[ROW][C]7[/C][C]0.267063[/C][C]2.0163[/C][C]0.024246[/C][/ROW]
[ROW][C]8[/C][C]0.153128[/C][C]1.1561[/C][C]0.126233[/C][/ROW]
[ROW][C]9[/C][C]0.064744[/C][C]0.4888[/C][C]0.313427[/C][/ROW]
[ROW][C]10[/C][C]-0.017236[/C][C]-0.1301[/C][C]0.448462[/C][/ROW]
[ROW][C]11[/C][C]-0.090664[/C][C]-0.6845[/C][C]0.248217[/C][/ROW]
[ROW][C]12[/C][C]-0.168583[/C][C]-1.2728[/C][C]0.104133[/C][/ROW]
[ROW][C]13[/C][C]-0.226519[/C][C]-1.7102[/C][C]0.046336[/C][/ROW]
[ROW][C]14[/C][C]-0.244314[/C][C]-1.8445[/C][C]0.035152[/C][/ROW]
[ROW][C]15[/C][C]-0.260664[/C][C]-1.968[/C][C]0.026971[/C][/ROW]
[ROW][C]16[/C][C]-0.2977[/C][C]-2.2476[/C][C]0.014245[/C][/ROW]
[ROW][C]17[/C][C]-0.351818[/C][C]-2.6562[/C][C]0.005116[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105401&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105401&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	0.921082	6.954	0
2	0.815602	6.1577	0
3	0.72041	5.439	1e-06
4	0.62231	4.6983	8e-06
5	0.532699	4.0218	8.6e-05
6	0.411692	3.1082	0.001467
7	0.267063	2.0163	0.024246
8	0.153128	1.1561	0.126233
9	0.064744	0.4888	0.313427
10	-0.017236	-0.1301	0.448462
11	-0.090664	-0.6845	0.248217
12	-0.168583	-1.2728	0.104133
13	-0.226519	-1.7102	0.046336
14	-0.244314	-1.8445	0.035152
15	-0.260664	-1.968	0.026971
16	-0.2977	-2.2476	0.014245
17	-0.351818	-2.6562	0.005116

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.921082	6.954	0
2	-0.216278	-1.6329	0.054005
3	0.04088	0.3086	0.37936
4	-0.104196	-0.7867	0.21737
5	0.017703	0.1337	0.447074
6	-0.308922	-2.3323	0.01162
7	-0.163861	-1.2371	0.110557
8	0.108144	0.8165	0.208816
9	0.022468	0.1696	0.432952
10	-0.081557	-0.6157	0.270258
11	-0.003933	-0.0297	0.488209
12	-0.059869	-0.452	0.326491
13	0.031299	0.2363	0.407023
14	0.068137	0.5144	0.304474
15	-0.102592	-0.7746	0.220903
16	-0.192432	-1.4528	0.075878
17	-0.176468	-1.3323	0.094031

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.921082 & 6.954 & 0 \tabularnewline
2 & -0.216278 & -1.6329 & 0.054005 \tabularnewline
3 & 0.04088 & 0.3086 & 0.37936 \tabularnewline
4 & -0.104196 & -0.7867 & 0.21737 \tabularnewline
5 & 0.017703 & 0.1337 & 0.447074 \tabularnewline
6 & -0.308922 & -2.3323 & 0.01162 \tabularnewline
7 & -0.163861 & -1.2371 & 0.110557 \tabularnewline
8 & 0.108144 & 0.8165 & 0.208816 \tabularnewline
9 & 0.022468 & 0.1696 & 0.432952 \tabularnewline
10 & -0.081557 & -0.6157 & 0.270258 \tabularnewline
11 & -0.003933 & -0.0297 & 0.488209 \tabularnewline
12 & -0.059869 & -0.452 & 0.326491 \tabularnewline
13 & 0.031299 & 0.2363 & 0.407023 \tabularnewline
14 & 0.068137 & 0.5144 & 0.304474 \tabularnewline
15 & -0.102592 & -0.7746 & 0.220903 \tabularnewline
16 & -0.192432 & -1.4528 & 0.075878 \tabularnewline
17 & -0.176468 & -1.3323 & 0.094031 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105401&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]0.921082[/C][C]6.954[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.216278[/C][C]-1.6329[/C][C]0.054005[/C][/ROW]
[ROW][C]3[/C][C]0.04088[/C][C]0.3086[/C][C]0.37936[/C][/ROW]
[ROW][C]4[/C][C]-0.104196[/C][C]-0.7867[/C][C]0.21737[/C][/ROW]
[ROW][C]5[/C][C]0.017703[/C][C]0.1337[/C][C]0.447074[/C][/ROW]
[ROW][C]6[/C][C]-0.308922[/C][C]-2.3323[/C][C]0.01162[/C][/ROW]
[ROW][C]7[/C][C]-0.163861[/C][C]-1.2371[/C][C]0.110557[/C][/ROW]
[ROW][C]8[/C][C]0.108144[/C][C]0.8165[/C][C]0.208816[/C][/ROW]
[ROW][C]9[/C][C]0.022468[/C][C]0.1696[/C][C]0.432952[/C][/ROW]
[ROW][C]10[/C][C]-0.081557[/C][C]-0.6157[/C][C]0.270258[/C][/ROW]
[ROW][C]11[/C][C]-0.003933[/C][C]-0.0297[/C][C]0.488209[/C][/ROW]
[ROW][C]12[/C][C]-0.059869[/C][C]-0.452[/C][C]0.326491[/C][/ROW]
[ROW][C]13[/C][C]0.031299[/C][C]0.2363[/C][C]0.407023[/C][/ROW]
[ROW][C]14[/C][C]0.068137[/C][C]0.5144[/C][C]0.304474[/C][/ROW]
[ROW][C]15[/C][C]-0.102592[/C][C]-0.7746[/C][C]0.220903[/C][/ROW]
[ROW][C]16[/C][C]-0.192432[/C][C]-1.4528[/C][C]0.075878[/C][/ROW]
[ROW][C]17[/C][C]-0.176468[/C][C]-1.3323[/C][C]0.094031[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105401&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105401&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	0.921082	6.954	0
2	-0.216278	-1.6329	0.054005
3	0.04088	0.3086	0.37936
4	-0.104196	-0.7867	0.21737
5	0.017703	0.1337	0.447074
6	-0.308922	-2.3323	0.01162
7	-0.163861	-1.2371	0.110557
8	0.108144	0.8165	0.208816
9	0.022468	0.1696	0.432952
10	-0.081557	-0.6157	0.270258
11	-0.003933	-0.0297	0.488209
12	-0.059869	-0.452	0.326491
13	0.031299	0.2363	0.407023
14	0.068137	0.5144	0.304474
15	-0.102592	-0.7746	0.220903
16	-0.192432	-1.4528	0.075878
17	-0.176468	-1.3323	0.094031

Figure 1

PNG link

Postscript link

PDF link

Figure 2

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 ;

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