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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 15 Dec 2009 01:39:30 -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/2009/Dec/15/t12608664284hj2tgmc4zmls00.htm/, Retrieved Wed, 08 May 2024 22:31:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67765, Retrieved Wed, 08 May 2024 22:31:07 +0000

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Estimated Impact

126

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

-       [(Partial) Autocorrelation Function] [Autocorrelation (...] [2009-12-15 08:39:30] [91da2e1ebdd83187f2515f461585cbee] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67765&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]2 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=67765&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67765&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.279767	-3.2021	0.000856
2	-0.356958	-4.0856	3.8e-05
3	0.128567	1.4715	0.071775
4	0.064961	0.7435	0.22925
5	-0.083218	-0.9525	0.171306
6	0.182776	2.092	0.019186
7	-0.173697	-1.988	0.024446
8	0.189441	2.1682	0.015973
9	-0.006451	-0.0738	0.470625
10	-0.356049	-4.0752	4e-05
11	-0.112716	-1.2901	0.099646
12	0.696041	7.9666	0
13	-0.200545	-2.2953	0.011652
14	-0.274295	-3.1395	0.001046
15	0.030855	0.3532	0.36227
16	0.072705	0.8322	0.203419
17	-0.05023	-0.5749	0.283171
18	0.122916	1.4068	0.080922
19	-0.10135	-1.16	0.124078
20	0.171311	1.9607	0.026015
21	-0.069361	-0.7939	0.214352

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.279767 & -3.2021 & 0.000856 \tabularnewline
2 & -0.356958 & -4.0856 & 3.8e-05 \tabularnewline
3 & 0.128567 & 1.4715 & 0.071775 \tabularnewline
4 & 0.064961 & 0.7435 & 0.22925 \tabularnewline
5 & -0.083218 & -0.9525 & 0.171306 \tabularnewline
6 & 0.182776 & 2.092 & 0.019186 \tabularnewline
7 & -0.173697 & -1.988 & 0.024446 \tabularnewline
8 & 0.189441 & 2.1682 & 0.015973 \tabularnewline
9 & -0.006451 & -0.0738 & 0.470625 \tabularnewline
10 & -0.356049 & -4.0752 & 4e-05 \tabularnewline
11 & -0.112716 & -1.2901 & 0.099646 \tabularnewline
12 & 0.696041 & 7.9666 & 0 \tabularnewline
13 & -0.200545 & -2.2953 & 0.011652 \tabularnewline
14 & -0.274295 & -3.1395 & 0.001046 \tabularnewline
15 & 0.030855 & 0.3532 & 0.36227 \tabularnewline
16 & 0.072705 & 0.8322 & 0.203419 \tabularnewline
17 & -0.05023 & -0.5749 & 0.283171 \tabularnewline
18 & 0.122916 & 1.4068 & 0.080922 \tabularnewline
19 & -0.10135 & -1.16 & 0.124078 \tabularnewline
20 & 0.171311 & 1.9607 & 0.026015 \tabularnewline
21 & -0.069361 & -0.7939 & 0.214352 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67765&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]-0.279767[/C][C]-3.2021[/C][C]0.000856[/C][/ROW]
[ROW][C]2[/C][C]-0.356958[/C][C]-4.0856[/C][C]3.8e-05[/C][/ROW]
[ROW][C]3[/C][C]0.128567[/C][C]1.4715[/C][C]0.071775[/C][/ROW]
[ROW][C]4[/C][C]0.064961[/C][C]0.7435[/C][C]0.22925[/C][/ROW]
[ROW][C]5[/C][C]-0.083218[/C][C]-0.9525[/C][C]0.171306[/C][/ROW]
[ROW][C]6[/C][C]0.182776[/C][C]2.092[/C][C]0.019186[/C][/ROW]
[ROW][C]7[/C][C]-0.173697[/C][C]-1.988[/C][C]0.024446[/C][/ROW]
[ROW][C]8[/C][C]0.189441[/C][C]2.1682[/C][C]0.015973[/C][/ROW]
[ROW][C]9[/C][C]-0.006451[/C][C]-0.0738[/C][C]0.470625[/C][/ROW]
[ROW][C]10[/C][C]-0.356049[/C][C]-4.0752[/C][C]4e-05[/C][/ROW]
[ROW][C]11[/C][C]-0.112716[/C][C]-1.2901[/C][C]0.099646[/C][/ROW]
[ROW][C]12[/C][C]0.696041[/C][C]7.9666[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.200545[/C][C]-2.2953[/C][C]0.011652[/C][/ROW]
[ROW][C]14[/C][C]-0.274295[/C][C]-3.1395[/C][C]0.001046[/C][/ROW]
[ROW][C]15[/C][C]0.030855[/C][C]0.3532[/C][C]0.36227[/C][/ROW]
[ROW][C]16[/C][C]0.072705[/C][C]0.8322[/C][C]0.203419[/C][/ROW]
[ROW][C]17[/C][C]-0.05023[/C][C]-0.5749[/C][C]0.283171[/C][/ROW]
[ROW][C]18[/C][C]0.122916[/C][C]1.4068[/C][C]0.080922[/C][/ROW]
[ROW][C]19[/C][C]-0.10135[/C][C]-1.16[/C][C]0.124078[/C][/ROW]
[ROW][C]20[/C][C]0.171311[/C][C]1.9607[/C][C]0.026015[/C][/ROW]
[ROW][C]21[/C][C]-0.069361[/C][C]-0.7939[/C][C]0.214352[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67765&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67765&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	-0.279767	-3.2021	0.000856
2	-0.356958	-4.0856	3.8e-05
3	0.128567	1.4715	0.071775
4	0.064961	0.7435	0.22925
5	-0.083218	-0.9525	0.171306
6	0.182776	2.092	0.019186
7	-0.173697	-1.988	0.024446
8	0.189441	2.1682	0.015973
9	-0.006451	-0.0738	0.470625
10	-0.356049	-4.0752	4e-05
11	-0.112716	-1.2901	0.099646
12	0.696041	7.9666	0
13	-0.200545	-2.2953	0.011652
14	-0.274295	-3.1395	0.001046
15	0.030855	0.3532	0.36227
16	0.072705	0.8322	0.203419
17	-0.05023	-0.5749	0.283171
18	0.122916	1.4068	0.080922
19	-0.10135	-1.16	0.124078
20	0.171311	1.9607	0.026015
21	-0.069361	-0.7939	0.214352

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.279767	-3.2021	0.000856
2	-0.472185	-5.4044	0
3	-0.210207	-2.4059	0.008764
4	-0.186377	-2.1332	0.017387
5	-0.186781	-2.1378	0.017195
6	0.126339	1.446	0.07528
7	-0.132308	-1.5143	0.066176
8	0.345225	3.9513	6.3e-05
9	0.172534	1.9747	0.0252
10	-0.203898	-2.3337	0.010566
11	-0.586434	-6.712	0
12	0.229184	2.6231	0.004873
13	0.163258	1.8686	0.031958
14	0.164668	1.8847	0.030842
15	-0.076823	-0.8793	0.190428
16	-0.05715	-0.6541	0.257093
17	-0.105766	-1.2105	0.114124
18	-0.094138	-1.0775	0.141627
19	0.072127	0.8255	0.205284
20	-0.008859	-0.1014	0.459694
21	-0.014183	-0.1623	0.435648

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.279767 & -3.2021 & 0.000856 \tabularnewline
2 & -0.472185 & -5.4044 & 0 \tabularnewline
3 & -0.210207 & -2.4059 & 0.008764 \tabularnewline
4 & -0.186377 & -2.1332 & 0.017387 \tabularnewline
5 & -0.186781 & -2.1378 & 0.017195 \tabularnewline
6 & 0.126339 & 1.446 & 0.07528 \tabularnewline
7 & -0.132308 & -1.5143 & 0.066176 \tabularnewline
8 & 0.345225 & 3.9513 & 6.3e-05 \tabularnewline
9 & 0.172534 & 1.9747 & 0.0252 \tabularnewline
10 & -0.203898 & -2.3337 & 0.010566 \tabularnewline
11 & -0.586434 & -6.712 & 0 \tabularnewline
12 & 0.229184 & 2.6231 & 0.004873 \tabularnewline
13 & 0.163258 & 1.8686 & 0.031958 \tabularnewline
14 & 0.164668 & 1.8847 & 0.030842 \tabularnewline
15 & -0.076823 & -0.8793 & 0.190428 \tabularnewline
16 & -0.05715 & -0.6541 & 0.257093 \tabularnewline
17 & -0.105766 & -1.2105 & 0.114124 \tabularnewline
18 & -0.094138 & -1.0775 & 0.141627 \tabularnewline
19 & 0.072127 & 0.8255 & 0.205284 \tabularnewline
20 & -0.008859 & -0.1014 & 0.459694 \tabularnewline
21 & -0.014183 & -0.1623 & 0.435648 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67765&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]-0.279767[/C][C]-3.2021[/C][C]0.000856[/C][/ROW]
[ROW][C]2[/C][C]-0.472185[/C][C]-5.4044[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.210207[/C][C]-2.4059[/C][C]0.008764[/C][/ROW]
[ROW][C]4[/C][C]-0.186377[/C][C]-2.1332[/C][C]0.017387[/C][/ROW]
[ROW][C]5[/C][C]-0.186781[/C][C]-2.1378[/C][C]0.017195[/C][/ROW]
[ROW][C]6[/C][C]0.126339[/C][C]1.446[/C][C]0.07528[/C][/ROW]
[ROW][C]7[/C][C]-0.132308[/C][C]-1.5143[/C][C]0.066176[/C][/ROW]
[ROW][C]8[/C][C]0.345225[/C][C]3.9513[/C][C]6.3e-05[/C][/ROW]
[ROW][C]9[/C][C]0.172534[/C][C]1.9747[/C][C]0.0252[/C][/ROW]
[ROW][C]10[/C][C]-0.203898[/C][C]-2.3337[/C][C]0.010566[/C][/ROW]
[ROW][C]11[/C][C]-0.586434[/C][C]-6.712[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.229184[/C][C]2.6231[/C][C]0.004873[/C][/ROW]
[ROW][C]13[/C][C]0.163258[/C][C]1.8686[/C][C]0.031958[/C][/ROW]
[ROW][C]14[/C][C]0.164668[/C][C]1.8847[/C][C]0.030842[/C][/ROW]
[ROW][C]15[/C][C]-0.076823[/C][C]-0.8793[/C][C]0.190428[/C][/ROW]
[ROW][C]16[/C][C]-0.05715[/C][C]-0.6541[/C][C]0.257093[/C][/ROW]
[ROW][C]17[/C][C]-0.105766[/C][C]-1.2105[/C][C]0.114124[/C][/ROW]
[ROW][C]18[/C][C]-0.094138[/C][C]-1.0775[/C][C]0.141627[/C][/ROW]
[ROW][C]19[/C][C]0.072127[/C][C]0.8255[/C][C]0.205284[/C][/ROW]
[ROW][C]20[/C][C]-0.008859[/C][C]-0.1014[/C][C]0.459694[/C][/ROW]
[ROW][C]21[/C][C]-0.014183[/C][C]-0.1623[/C][C]0.435648[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67765&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67765&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	-0.279767	-3.2021	0.000856
2	-0.472185	-5.4044	0
3	-0.210207	-2.4059	0.008764
4	-0.186377	-2.1332	0.017387
5	-0.186781	-2.1378	0.017195
6	0.126339	1.446	0.07528
7	-0.132308	-1.5143	0.066176
8	0.345225	3.9513	6.3e-05
9	0.172534	1.9747	0.0252
10	-0.203898	-2.3337	0.010566
11	-0.586434	-6.712	0
12	0.229184	2.6231	0.004873
13	0.163258	1.8686	0.031958
14	0.164668	1.8847	0.030842
15	-0.076823	-0.8793	0.190428
16	-0.05715	-0.6541	0.257093
17	-0.105766	-1.2105	0.114124
18	-0.094138	-1.0775	0.141627
19	0.072127	0.8255	0.205284
20	-0.008859	-0.1014	0.459694
21	-0.014183	-0.1623	0.435648

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code