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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 21 Dec 2008 15:34:36 -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/2008/Dec/21/t1229898894b6fed7uukqobexc.htm/, Retrieved Sun, 19 May 2024 08:51:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35892, Retrieved Sun, 19 May 2024 08:51:04 +0000

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Estimated Impact

129

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-       [(Partial) Autocorrelation Function] [fsqd] [2008-12-21 22:34:36] [7a2afff08a618fdf6611a1bb6e1c3da4] [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=35892&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=35892&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35892&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	0.415867	4.032	5.6e-05
2	0.244952	2.3749	0.009793
3	0.506949	4.9151	2e-06
4	0.243085	2.3568	0.010254
5	0.329823	3.1977	0.000944
6	0.562241	5.4511	0
7	0.253367	2.4565	0.007933
8	0.222398	2.1562	0.016809
9	0.400913	3.887	9.5e-05
10	0.166229	1.6116	0.055196
11	0.341402	3.31	0.000662
12	0.653099	6.332	0
13	0.258935	2.5105	0.006883
14	0.145477	1.4104	0.080854
15	0.29922	2.901	0.002316
16	0.092719	0.8989	0.185489
17	0.179032	1.7358	0.042939
18	0.326398	3.1645	0.001047
19	0.083278	0.8074	0.210734

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.415867 & 4.032 & 5.6e-05 \tabularnewline
2 & 0.244952 & 2.3749 & 0.009793 \tabularnewline
3 & 0.506949 & 4.9151 & 2e-06 \tabularnewline
4 & 0.243085 & 2.3568 & 0.010254 \tabularnewline
5 & 0.329823 & 3.1977 & 0.000944 \tabularnewline
6 & 0.562241 & 5.4511 & 0 \tabularnewline
7 & 0.253367 & 2.4565 & 0.007933 \tabularnewline
8 & 0.222398 & 2.1562 & 0.016809 \tabularnewline
9 & 0.400913 & 3.887 & 9.5e-05 \tabularnewline
10 & 0.166229 & 1.6116 & 0.055196 \tabularnewline
11 & 0.341402 & 3.31 & 0.000662 \tabularnewline
12 & 0.653099 & 6.332 & 0 \tabularnewline
13 & 0.258935 & 2.5105 & 0.006883 \tabularnewline
14 & 0.145477 & 1.4104 & 0.080854 \tabularnewline
15 & 0.29922 & 2.901 & 0.002316 \tabularnewline
16 & 0.092719 & 0.8989 & 0.185489 \tabularnewline
17 & 0.179032 & 1.7358 & 0.042939 \tabularnewline
18 & 0.326398 & 3.1645 & 0.001047 \tabularnewline
19 & 0.083278 & 0.8074 & 0.210734 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35892&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]0.415867[/C][C]4.032[/C][C]5.6e-05[/C][/ROW]
[ROW][C]2[/C][C]0.244952[/C][C]2.3749[/C][C]0.009793[/C][/ROW]
[ROW][C]3[/C][C]0.506949[/C][C]4.9151[/C][C]2e-06[/C][/ROW]
[ROW][C]4[/C][C]0.243085[/C][C]2.3568[/C][C]0.010254[/C][/ROW]
[ROW][C]5[/C][C]0.329823[/C][C]3.1977[/C][C]0.000944[/C][/ROW]
[ROW][C]6[/C][C]0.562241[/C][C]5.4511[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.253367[/C][C]2.4565[/C][C]0.007933[/C][/ROW]
[ROW][C]8[/C][C]0.222398[/C][C]2.1562[/C][C]0.016809[/C][/ROW]
[ROW][C]9[/C][C]0.400913[/C][C]3.887[/C][C]9.5e-05[/C][/ROW]
[ROW][C]10[/C][C]0.166229[/C][C]1.6116[/C][C]0.055196[/C][/ROW]
[ROW][C]11[/C][C]0.341402[/C][C]3.31[/C][C]0.000662[/C][/ROW]
[ROW][C]12[/C][C]0.653099[/C][C]6.332[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.258935[/C][C]2.5105[/C][C]0.006883[/C][/ROW]
[ROW][C]14[/C][C]0.145477[/C][C]1.4104[/C][C]0.080854[/C][/ROW]
[ROW][C]15[/C][C]0.29922[/C][C]2.901[/C][C]0.002316[/C][/ROW]
[ROW][C]16[/C][C]0.092719[/C][C]0.8989[/C][C]0.185489[/C][/ROW]
[ROW][C]17[/C][C]0.179032[/C][C]1.7358[/C][C]0.042939[/C][/ROW]
[ROW][C]18[/C][C]0.326398[/C][C]3.1645[/C][C]0.001047[/C][/ROW]
[ROW][C]19[/C][C]0.083278[/C][C]0.8074[/C][C]0.210734[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35892&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35892&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	0.415867	4.032	5.6e-05
2	0.244952	2.3749	0.009793
3	0.506949	4.9151	2e-06
4	0.243085	2.3568	0.010254
5	0.329823	3.1977	0.000944
6	0.562241	5.4511	0
7	0.253367	2.4565	0.007933
8	0.222398	2.1562	0.016809
9	0.400913	3.887	9.5e-05
10	0.166229	1.6116	0.055196
11	0.341402	3.31	0.000662
12	0.653099	6.332	0
13	0.258935	2.5105	0.006883
14	0.145477	1.4104	0.080854
15	0.29922	2.901	0.002316
16	0.092719	0.8989	0.185489
17	0.179032	1.7358	0.042939
18	0.326398	3.1645	0.001047
19	0.083278	0.8074	0.210734

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.415867	4.032	5.6e-05
2	0.087064	0.8441	0.200374
3	0.460222	4.462	1.1e-05
4	-0.153009	-1.4835	0.070646
5	0.347531	3.3694	0.000547
6	0.229906	2.229	0.014097
7	-0.061442	-0.5957	0.276404
8	-0.008483	-0.0822	0.467312
9	0.06475	0.6278	0.265836
10	-0.10813	-1.0484	0.14858
11	0.279021	2.7052	0.004053
12	0.37305	3.6169	0.000241
13	-0.112377	-1.0895	0.139352
14	-0.208718	-2.0236	0.022926
15	-0.180988	-1.7547	0.041281
16	-0.114043	-1.1057	0.135842
17	-0.099979	-0.9693	0.167434
18	-0.082995	-0.8047	0.211521
19	0.035257	0.3418	0.36662

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.415867 & 4.032 & 5.6e-05 \tabularnewline
2 & 0.087064 & 0.8441 & 0.200374 \tabularnewline
3 & 0.460222 & 4.462 & 1.1e-05 \tabularnewline
4 & -0.153009 & -1.4835 & 0.070646 \tabularnewline
5 & 0.347531 & 3.3694 & 0.000547 \tabularnewline
6 & 0.229906 & 2.229 & 0.014097 \tabularnewline
7 & -0.061442 & -0.5957 & 0.276404 \tabularnewline
8 & -0.008483 & -0.0822 & 0.467312 \tabularnewline
9 & 0.06475 & 0.6278 & 0.265836 \tabularnewline
10 & -0.10813 & -1.0484 & 0.14858 \tabularnewline
11 & 0.279021 & 2.7052 & 0.004053 \tabularnewline
12 & 0.37305 & 3.6169 & 0.000241 \tabularnewline
13 & -0.112377 & -1.0895 & 0.139352 \tabularnewline
14 & -0.208718 & -2.0236 & 0.022926 \tabularnewline
15 & -0.180988 & -1.7547 & 0.041281 \tabularnewline
16 & -0.114043 & -1.1057 & 0.135842 \tabularnewline
17 & -0.099979 & -0.9693 & 0.167434 \tabularnewline
18 & -0.082995 & -0.8047 & 0.211521 \tabularnewline
19 & 0.035257 & 0.3418 & 0.36662 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35892&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]0.415867[/C][C]4.032[/C][C]5.6e-05[/C][/ROW]
[ROW][C]2[/C][C]0.087064[/C][C]0.8441[/C][C]0.200374[/C][/ROW]
[ROW][C]3[/C][C]0.460222[/C][C]4.462[/C][C]1.1e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.153009[/C][C]-1.4835[/C][C]0.070646[/C][/ROW]
[ROW][C]5[/C][C]0.347531[/C][C]3.3694[/C][C]0.000547[/C][/ROW]
[ROW][C]6[/C][C]0.229906[/C][C]2.229[/C][C]0.014097[/C][/ROW]
[ROW][C]7[/C][C]-0.061442[/C][C]-0.5957[/C][C]0.276404[/C][/ROW]
[ROW][C]8[/C][C]-0.008483[/C][C]-0.0822[/C][C]0.467312[/C][/ROW]
[ROW][C]9[/C][C]0.06475[/C][C]0.6278[/C][C]0.265836[/C][/ROW]
[ROW][C]10[/C][C]-0.10813[/C][C]-1.0484[/C][C]0.14858[/C][/ROW]
[ROW][C]11[/C][C]0.279021[/C][C]2.7052[/C][C]0.004053[/C][/ROW]
[ROW][C]12[/C][C]0.37305[/C][C]3.6169[/C][C]0.000241[/C][/ROW]
[ROW][C]13[/C][C]-0.112377[/C][C]-1.0895[/C][C]0.139352[/C][/ROW]
[ROW][C]14[/C][C]-0.208718[/C][C]-2.0236[/C][C]0.022926[/C][/ROW]
[ROW][C]15[/C][C]-0.180988[/C][C]-1.7547[/C][C]0.041281[/C][/ROW]
[ROW][C]16[/C][C]-0.114043[/C][C]-1.1057[/C][C]0.135842[/C][/ROW]
[ROW][C]17[/C][C]-0.099979[/C][C]-0.9693[/C][C]0.167434[/C][/ROW]
[ROW][C]18[/C][C]-0.082995[/C][C]-0.8047[/C][C]0.211521[/C][/ROW]
[ROW][C]19[/C][C]0.035257[/C][C]0.3418[/C][C]0.36662[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35892&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35892&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	0.415867	4.032	5.6e-05
2	0.087064	0.8441	0.200374
3	0.460222	4.462	1.1e-05
4	-0.153009	-1.4835	0.070646
5	0.347531	3.3694	0.000547
6	0.229906	2.229	0.014097
7	-0.061442	-0.5957	0.276404
8	-0.008483	-0.0822	0.467312
9	0.06475	0.6278	0.265836
10	-0.10813	-1.0484	0.14858
11	0.279021	2.7052	0.004053
12	0.37305	3.6169	0.000241
13	-0.112377	-1.0895	0.139352
14	-0.208718	-2.0236	0.022926
15	-0.180988	-1.7547	0.041281
16	-0.114043	-1.1057	0.135842
17	-0.099979	-0.9693	0.167434
18	-0.082995	-0.8047	0.211521
19	0.035257	0.3418	0.36662

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 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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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