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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 17 Aug 2010 11:13:42 +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/17/t12820436092fmi11r7n9f60gr.htm/, Retrieved Sat, 27 Apr 2024 10:08:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79084, Retrieved Sat, 27 Apr 2024 10:08:51 +0000

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No (this computation is public)

User-defined keywords

mattias debbaut

Estimated Impact

146

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

-       [(Partial) Autocorrelation Function] [autocorrelation F...] [2010-08-17 11:13:42] [59fa324537f53fb6459bc6951db20f7b] [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	'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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79084&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79084&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79084&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.303351	-2.747	0.003696
2	-0.134916	-1.2217	0.112658
3	-0.111397	-1.0087	0.158033
4	0.362867	3.2859	0.000749
5	-0.21361	-1.9343	0.028261
6	-0.047105	-0.4266	0.335412
7	-0.214576	-1.9431	0.02772
8	0.296271	2.6828	0.004414
9	-0.081372	-0.7369	0.231658
10	-0.147814	-1.3385	0.092214
11	-0.15483	-1.402	0.082338
12	0.570136	5.1628	1e-06
13	-0.168899	-1.5294	0.065001
14	-0.145505	-1.3176	0.095654
15	0.002968	0.0269	0.489311
16	0.264479	2.395	0.009451
17	-0.152877	-1.3844	0.085002
18	-0.128043	-1.1595	0.124813
19	-0.025485	-0.2308	0.409031

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.303351 & -2.747 & 0.003696 \tabularnewline
2 & -0.134916 & -1.2217 & 0.112658 \tabularnewline
3 & -0.111397 & -1.0087 & 0.158033 \tabularnewline
4 & 0.362867 & 3.2859 & 0.000749 \tabularnewline
5 & -0.21361 & -1.9343 & 0.028261 \tabularnewline
6 & -0.047105 & -0.4266 & 0.335412 \tabularnewline
7 & -0.214576 & -1.9431 & 0.02772 \tabularnewline
8 & 0.296271 & 2.6828 & 0.004414 \tabularnewline
9 & -0.081372 & -0.7369 & 0.231658 \tabularnewline
10 & -0.147814 & -1.3385 & 0.092214 \tabularnewline
11 & -0.15483 & -1.402 & 0.082338 \tabularnewline
12 & 0.570136 & 5.1628 & 1e-06 \tabularnewline
13 & -0.168899 & -1.5294 & 0.065001 \tabularnewline
14 & -0.145505 & -1.3176 & 0.095654 \tabularnewline
15 & 0.002968 & 0.0269 & 0.489311 \tabularnewline
16 & 0.264479 & 2.395 & 0.009451 \tabularnewline
17 & -0.152877 & -1.3844 & 0.085002 \tabularnewline
18 & -0.128043 & -1.1595 & 0.124813 \tabularnewline
19 & -0.025485 & -0.2308 & 0.409031 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79084&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]-0.303351[/C][C]-2.747[/C][C]0.003696[/C][/ROW]
[ROW][C]2[/C][C]-0.134916[/C][C]-1.2217[/C][C]0.112658[/C][/ROW]
[ROW][C]3[/C][C]-0.111397[/C][C]-1.0087[/C][C]0.158033[/C][/ROW]
[ROW][C]4[/C][C]0.362867[/C][C]3.2859[/C][C]0.000749[/C][/ROW]
[ROW][C]5[/C][C]-0.21361[/C][C]-1.9343[/C][C]0.028261[/C][/ROW]
[ROW][C]6[/C][C]-0.047105[/C][C]-0.4266[/C][C]0.335412[/C][/ROW]
[ROW][C]7[/C][C]-0.214576[/C][C]-1.9431[/C][C]0.02772[/C][/ROW]
[ROW][C]8[/C][C]0.296271[/C][C]2.6828[/C][C]0.004414[/C][/ROW]
[ROW][C]9[/C][C]-0.081372[/C][C]-0.7369[/C][C]0.231658[/C][/ROW]
[ROW][C]10[/C][C]-0.147814[/C][C]-1.3385[/C][C]0.092214[/C][/ROW]
[ROW][C]11[/C][C]-0.15483[/C][C]-1.402[/C][C]0.082338[/C][/ROW]
[ROW][C]12[/C][C]0.570136[/C][C]5.1628[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.168899[/C][C]-1.5294[/C][C]0.065001[/C][/ROW]
[ROW][C]14[/C][C]-0.145505[/C][C]-1.3176[/C][C]0.095654[/C][/ROW]
[ROW][C]15[/C][C]0.002968[/C][C]0.0269[/C][C]0.489311[/C][/ROW]
[ROW][C]16[/C][C]0.264479[/C][C]2.395[/C][C]0.009451[/C][/ROW]
[ROW][C]17[/C][C]-0.152877[/C][C]-1.3844[/C][C]0.085002[/C][/ROW]
[ROW][C]18[/C][C]-0.128043[/C][C]-1.1595[/C][C]0.124813[/C][/ROW]
[ROW][C]19[/C][C]-0.025485[/C][C]-0.2308[/C][C]0.409031[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79084&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79084&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	-0.303351	-2.747	0.003696
2	-0.134916	-1.2217	0.112658
3	-0.111397	-1.0087	0.158033
4	0.362867	3.2859	0.000749
5	-0.21361	-1.9343	0.028261
6	-0.047105	-0.4266	0.335412
7	-0.214576	-1.9431	0.02772
8	0.296271	2.6828	0.004414
9	-0.081372	-0.7369	0.231658
10	-0.147814	-1.3385	0.092214
11	-0.15483	-1.402	0.082338
12	0.570136	5.1628	1e-06
13	-0.168899	-1.5294	0.065001
14	-0.145505	-1.3176	0.095654
15	0.002968	0.0269	0.489311
16	0.264479	2.395	0.009451
17	-0.152877	-1.3844	0.085002
18	-0.128043	-1.1595	0.124813
19	-0.025485	-0.2308	0.409031

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.303351	-2.747	0.003696
2	-0.249937	-2.2633	0.013131
3	-0.280022	-2.5357	0.00656
4	0.229241	2.0759	0.02052
5	-0.079166	-0.7169	0.237743
6	-0.054315	-0.4918	0.312073
7	-0.305216	-2.7639	0.003526
8	-0.019707	-0.1785	0.429403
9	-0.019018	-0.1722	0.431847
10	-0.202435	-1.8331	0.035206
11	-0.243921	-2.2088	0.01499
12	0.354414	3.2094	0.00095
13	0.10683	0.9674	0.168097
14	-0.029262	-0.265	0.395846
15	0.108628	0.9837	0.164087
16	0.010568	0.0957	0.461997
17	-0.015026	-0.1361	0.446051
18	-0.116738	-1.0571	0.146783
19	0.092033	0.8334	0.203523

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.303351 & -2.747 & 0.003696 \tabularnewline
2 & -0.249937 & -2.2633 & 0.013131 \tabularnewline
3 & -0.280022 & -2.5357 & 0.00656 \tabularnewline
4 & 0.229241 & 2.0759 & 0.02052 \tabularnewline
5 & -0.079166 & -0.7169 & 0.237743 \tabularnewline
6 & -0.054315 & -0.4918 & 0.312073 \tabularnewline
7 & -0.305216 & -2.7639 & 0.003526 \tabularnewline
8 & -0.019707 & -0.1785 & 0.429403 \tabularnewline
9 & -0.019018 & -0.1722 & 0.431847 \tabularnewline
10 & -0.202435 & -1.8331 & 0.035206 \tabularnewline
11 & -0.243921 & -2.2088 & 0.01499 \tabularnewline
12 & 0.354414 & 3.2094 & 0.00095 \tabularnewline
13 & 0.10683 & 0.9674 & 0.168097 \tabularnewline
14 & -0.029262 & -0.265 & 0.395846 \tabularnewline
15 & 0.108628 & 0.9837 & 0.164087 \tabularnewline
16 & 0.010568 & 0.0957 & 0.461997 \tabularnewline
17 & -0.015026 & -0.1361 & 0.446051 \tabularnewline
18 & -0.116738 & -1.0571 & 0.146783 \tabularnewline
19 & 0.092033 & 0.8334 & 0.203523 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79084&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]-0.303351[/C][C]-2.747[/C][C]0.003696[/C][/ROW]
[ROW][C]2[/C][C]-0.249937[/C][C]-2.2633[/C][C]0.013131[/C][/ROW]
[ROW][C]3[/C][C]-0.280022[/C][C]-2.5357[/C][C]0.00656[/C][/ROW]
[ROW][C]4[/C][C]0.229241[/C][C]2.0759[/C][C]0.02052[/C][/ROW]
[ROW][C]5[/C][C]-0.079166[/C][C]-0.7169[/C][C]0.237743[/C][/ROW]
[ROW][C]6[/C][C]-0.054315[/C][C]-0.4918[/C][C]0.312073[/C][/ROW]
[ROW][C]7[/C][C]-0.305216[/C][C]-2.7639[/C][C]0.003526[/C][/ROW]
[ROW][C]8[/C][C]-0.019707[/C][C]-0.1785[/C][C]0.429403[/C][/ROW]
[ROW][C]9[/C][C]-0.019018[/C][C]-0.1722[/C][C]0.431847[/C][/ROW]
[ROW][C]10[/C][C]-0.202435[/C][C]-1.8331[/C][C]0.035206[/C][/ROW]
[ROW][C]11[/C][C]-0.243921[/C][C]-2.2088[/C][C]0.01499[/C][/ROW]
[ROW][C]12[/C][C]0.354414[/C][C]3.2094[/C][C]0.00095[/C][/ROW]
[ROW][C]13[/C][C]0.10683[/C][C]0.9674[/C][C]0.168097[/C][/ROW]
[ROW][C]14[/C][C]-0.029262[/C][C]-0.265[/C][C]0.395846[/C][/ROW]
[ROW][C]15[/C][C]0.108628[/C][C]0.9837[/C][C]0.164087[/C][/ROW]
[ROW][C]16[/C][C]0.010568[/C][C]0.0957[/C][C]0.461997[/C][/ROW]
[ROW][C]17[/C][C]-0.015026[/C][C]-0.1361[/C][C]0.446051[/C][/ROW]
[ROW][C]18[/C][C]-0.116738[/C][C]-1.0571[/C][C]0.146783[/C][/ROW]
[ROW][C]19[/C][C]0.092033[/C][C]0.8334[/C][C]0.203523[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79084&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79084&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	-0.303351	-2.747	0.003696
2	-0.249937	-2.2633	0.013131
3	-0.280022	-2.5357	0.00656
4	0.229241	2.0759	0.02052
5	-0.079166	-0.7169	0.237743
6	-0.054315	-0.4918	0.312073
7	-0.305216	-2.7639	0.003526
8	-0.019707	-0.1785	0.429403
9	-0.019018	-0.1722	0.431847
10	-0.202435	-1.8331	0.035206
11	-0.243921	-2.2088	0.01499
12	0.354414	3.2094	0.00095
13	0.10683	0.9674	0.168097
14	-0.029262	-0.265	0.395846
15	0.108628	0.9837	0.164087
16	0.010568	0.0957	0.461997
17	-0.015026	-0.1361	0.446051
18	-0.116738	-1.0571	0.146783
19	0.092033	0.8334	0.203523

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code