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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

Mon, 01 Dec 2008 07:18:51 -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/01/t1228141170lhxnb1luqc8vw3v.htm/, Retrieved Sun, 05 May 2024 18:25:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26929, Retrieved Sun, 05 May 2024 18:25:22 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

219

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

F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
- RMPD    [(Partial) Autocorrelation Function] [question 6] [2008-12-01 14:18:51] [490fee4f334e2e025c95681783e3fd0b] [Current]
-           [(Partial) Autocorrelation Function] [Q6] [2008-12-02 14:34:33] [d811f621c525a990f9b60f1ae1e2e8fd] 
F R P       [(Partial) Autocorrelation Function] [] [2008-12-03 10:10:36] [74be16979710d4c4e7c6647856088456] 
F RMP       [Variance Reduction Matrix] [] [2008-12-03 10:18:57] [03c8f0b5f6fe0fafd3d60ad5379ae7bd] 
F RMP       [Spectral Analysis] [] [2008-12-03 10:18:50] [03c8f0b5f6fe0fafd3d60ad5379ae7bd] 

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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	'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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26929&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26929&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26929&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.332039	-3.8004	0.00011
2	0.08344	0.955	0.170664
3	-0.210458	-2.4088	0.008698
4	0.039154	0.4481	0.327398
5	0.049915	0.5713	0.284388
6	0.044082	0.5045	0.307362
7	-0.062545	-0.7159	0.237675
8	-0.001067	-0.0122	0.495139
9	0.162718	1.8624	0.032394
10	-0.05311	-0.6079	0.272161
11	0.076485	0.8754	0.191476
12	-0.410552	-4.699	3e-06
13	0.169668	1.9419	0.027145
14	-0.070911	-0.8116	0.209242
15	0.144806	1.6574	0.049917
16	-0.148873	-1.7039	0.045382
17	0.094144	1.0775	0.141611
18	0.008722	0.0998	0.460318
19	0.002456	0.0281	0.48881
20	-0.112715	-1.2901	0.099646
21	0.022384	0.2562	0.399102

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.332039 & -3.8004 & 0.00011 \tabularnewline
2 & 0.08344 & 0.955 & 0.170664 \tabularnewline
3 & -0.210458 & -2.4088 & 0.008698 \tabularnewline
4 & 0.039154 & 0.4481 & 0.327398 \tabularnewline
5 & 0.049915 & 0.5713 & 0.284388 \tabularnewline
6 & 0.044082 & 0.5045 & 0.307362 \tabularnewline
7 & -0.062545 & -0.7159 & 0.237675 \tabularnewline
8 & -0.001067 & -0.0122 & 0.495139 \tabularnewline
9 & 0.162718 & 1.8624 & 0.032394 \tabularnewline
10 & -0.05311 & -0.6079 & 0.272161 \tabularnewline
11 & 0.076485 & 0.8754 & 0.191476 \tabularnewline
12 & -0.410552 & -4.699 & 3e-06 \tabularnewline
13 & 0.169668 & 1.9419 & 0.027145 \tabularnewline
14 & -0.070911 & -0.8116 & 0.209242 \tabularnewline
15 & 0.144806 & 1.6574 & 0.049917 \tabularnewline
16 & -0.148873 & -1.7039 & 0.045382 \tabularnewline
17 & 0.094144 & 1.0775 & 0.141611 \tabularnewline
18 & 0.008722 & 0.0998 & 0.460318 \tabularnewline
19 & 0.002456 & 0.0281 & 0.48881 \tabularnewline
20 & -0.112715 & -1.2901 & 0.099646 \tabularnewline
21 & 0.022384 & 0.2562 & 0.399102 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26929&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]-0.332039[/C][C]-3.8004[/C][C]0.00011[/C][/ROW]
[ROW][C]2[/C][C]0.08344[/C][C]0.955[/C][C]0.170664[/C][/ROW]
[ROW][C]3[/C][C]-0.210458[/C][C]-2.4088[/C][C]0.008698[/C][/ROW]
[ROW][C]4[/C][C]0.039154[/C][C]0.4481[/C][C]0.327398[/C][/ROW]
[ROW][C]5[/C][C]0.049915[/C][C]0.5713[/C][C]0.284388[/C][/ROW]
[ROW][C]6[/C][C]0.044082[/C][C]0.5045[/C][C]0.307362[/C][/ROW]
[ROW][C]7[/C][C]-0.062545[/C][C]-0.7159[/C][C]0.237675[/C][/ROW]
[ROW][C]8[/C][C]-0.001067[/C][C]-0.0122[/C][C]0.495139[/C][/ROW]
[ROW][C]9[/C][C]0.162718[/C][C]1.8624[/C][C]0.032394[/C][/ROW]
[ROW][C]10[/C][C]-0.05311[/C][C]-0.6079[/C][C]0.272161[/C][/ROW]
[ROW][C]11[/C][C]0.076485[/C][C]0.8754[/C][C]0.191476[/C][/ROW]
[ROW][C]12[/C][C]-0.410552[/C][C]-4.699[/C][C]3e-06[/C][/ROW]
[ROW][C]13[/C][C]0.169668[/C][C]1.9419[/C][C]0.027145[/C][/ROW]
[ROW][C]14[/C][C]-0.070911[/C][C]-0.8116[/C][C]0.209242[/C][/ROW]
[ROW][C]15[/C][C]0.144806[/C][C]1.6574[/C][C]0.049917[/C][/ROW]
[ROW][C]16[/C][C]-0.148873[/C][C]-1.7039[/C][C]0.045382[/C][/ROW]
[ROW][C]17[/C][C]0.094144[/C][C]1.0775[/C][C]0.141611[/C][/ROW]
[ROW][C]18[/C][C]0.008722[/C][C]0.0998[/C][C]0.460318[/C][/ROW]
[ROW][C]19[/C][C]0.002456[/C][C]0.0281[/C][C]0.48881[/C][/ROW]
[ROW][C]20[/C][C]-0.112715[/C][C]-1.2901[/C][C]0.099646[/C][/ROW]
[ROW][C]21[/C][C]0.022384[/C][C]0.2562[/C][C]0.399102[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26929&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26929&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	-0.332039	-3.8004	0.00011
2	0.08344	0.955	0.170664
3	-0.210458	-2.4088	0.008698
4	0.039154	0.4481	0.327398
5	0.049915	0.5713	0.284388
6	0.044082	0.5045	0.307362
7	-0.062545	-0.7159	0.237675
8	-0.001067	-0.0122	0.495139
9	0.162718	1.8624	0.032394
10	-0.05311	-0.6079	0.272161
11	0.076485	0.8754	0.191476
12	-0.410552	-4.699	3e-06
13	0.169668	1.9419	0.027145
14	-0.070911	-0.8116	0.209242
15	0.144806	1.6574	0.049917
16	-0.148873	-1.7039	0.045382
17	0.094144	1.0775	0.141611
18	0.008722	0.0998	0.460318
19	0.002456	0.0281	0.48881
20	-0.112715	-1.2901	0.099646
21	0.022384	0.2562	0.399102

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.332039	-3.8004	0.00011
2	-0.030132	-0.3449	0.365372
3	-0.215899	-2.4711	0.007377
4	-0.114704	-1.3128	0.095766
5	0.027982	0.3203	0.374638
6	0.037855	0.4333	0.332767
7	-0.052061	-0.5959	0.276146
8	-0.016784	-0.1921	0.423981
9	0.209284	2.3954	0.009009
10	0.059397	0.6798	0.248906
11	0.091528	1.0476	0.14838
12	-0.351236	-4.0201	4.9e-05
13	-0.09691	-1.1092	0.134691
14	-0.088253	-1.0101	0.157154
15	-0.063526	-0.7271	0.234235
16	-0.170035	-1.9461	0.026889
17	0.039763	0.4551	0.32489
18	0.132132	1.5123	0.06643
19	-0.003849	-0.0441	0.482464
20	-0.127537	-1.4597	0.07338
21	0.134073	1.5345	0.063655

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.332039 & -3.8004 & 0.00011 \tabularnewline
2 & -0.030132 & -0.3449 & 0.365372 \tabularnewline
3 & -0.215899 & -2.4711 & 0.007377 \tabularnewline
4 & -0.114704 & -1.3128 & 0.095766 \tabularnewline
5 & 0.027982 & 0.3203 & 0.374638 \tabularnewline
6 & 0.037855 & 0.4333 & 0.332767 \tabularnewline
7 & -0.052061 & -0.5959 & 0.276146 \tabularnewline
8 & -0.016784 & -0.1921 & 0.423981 \tabularnewline
9 & 0.209284 & 2.3954 & 0.009009 \tabularnewline
10 & 0.059397 & 0.6798 & 0.248906 \tabularnewline
11 & 0.091528 & 1.0476 & 0.14838 \tabularnewline
12 & -0.351236 & -4.0201 & 4.9e-05 \tabularnewline
13 & -0.09691 & -1.1092 & 0.134691 \tabularnewline
14 & -0.088253 & -1.0101 & 0.157154 \tabularnewline
15 & -0.063526 & -0.7271 & 0.234235 \tabularnewline
16 & -0.170035 & -1.9461 & 0.026889 \tabularnewline
17 & 0.039763 & 0.4551 & 0.32489 \tabularnewline
18 & 0.132132 & 1.5123 & 0.06643 \tabularnewline
19 & -0.003849 & -0.0441 & 0.482464 \tabularnewline
20 & -0.127537 & -1.4597 & 0.07338 \tabularnewline
21 & 0.134073 & 1.5345 & 0.063655 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26929&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]-0.332039[/C][C]-3.8004[/C][C]0.00011[/C][/ROW]
[ROW][C]2[/C][C]-0.030132[/C][C]-0.3449[/C][C]0.365372[/C][/ROW]
[ROW][C]3[/C][C]-0.215899[/C][C]-2.4711[/C][C]0.007377[/C][/ROW]
[ROW][C]4[/C][C]-0.114704[/C][C]-1.3128[/C][C]0.095766[/C][/ROW]
[ROW][C]5[/C][C]0.027982[/C][C]0.3203[/C][C]0.374638[/C][/ROW]
[ROW][C]6[/C][C]0.037855[/C][C]0.4333[/C][C]0.332767[/C][/ROW]
[ROW][C]7[/C][C]-0.052061[/C][C]-0.5959[/C][C]0.276146[/C][/ROW]
[ROW][C]8[/C][C]-0.016784[/C][C]-0.1921[/C][C]0.423981[/C][/ROW]
[ROW][C]9[/C][C]0.209284[/C][C]2.3954[/C][C]0.009009[/C][/ROW]
[ROW][C]10[/C][C]0.059397[/C][C]0.6798[/C][C]0.248906[/C][/ROW]
[ROW][C]11[/C][C]0.091528[/C][C]1.0476[/C][C]0.14838[/C][/ROW]
[ROW][C]12[/C][C]-0.351236[/C][C]-4.0201[/C][C]4.9e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.09691[/C][C]-1.1092[/C][C]0.134691[/C][/ROW]
[ROW][C]14[/C][C]-0.088253[/C][C]-1.0101[/C][C]0.157154[/C][/ROW]
[ROW][C]15[/C][C]-0.063526[/C][C]-0.7271[/C][C]0.234235[/C][/ROW]
[ROW][C]16[/C][C]-0.170035[/C][C]-1.9461[/C][C]0.026889[/C][/ROW]
[ROW][C]17[/C][C]0.039763[/C][C]0.4551[/C][C]0.32489[/C][/ROW]
[ROW][C]18[/C][C]0.132132[/C][C]1.5123[/C][C]0.06643[/C][/ROW]
[ROW][C]19[/C][C]-0.003849[/C][C]-0.0441[/C][C]0.482464[/C][/ROW]
[ROW][C]20[/C][C]-0.127537[/C][C]-1.4597[/C][C]0.07338[/C][/ROW]
[ROW][C]21[/C][C]0.134073[/C][C]1.5345[/C][C]0.063655[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26929&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26929&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	-0.332039	-3.8004	0.00011
2	-0.030132	-0.3449	0.365372
3	-0.215899	-2.4711	0.007377
4	-0.114704	-1.3128	0.095766
5	0.027982	0.3203	0.374638
6	0.037855	0.4333	0.332767
7	-0.052061	-0.5959	0.276146
8	-0.016784	-0.1921	0.423981
9	0.209284	2.3954	0.009009
10	0.059397	0.6798	0.248906
11	0.091528	1.0476	0.14838
12	-0.351236	-4.0201	4.9e-05
13	-0.09691	-1.1092	0.134691
14	-0.088253	-1.0101	0.157154
15	-0.063526	-0.7271	0.234235
16	-0.170035	-1.9461	0.026889
17	0.039763	0.4551	0.32489
18	0.132132	1.5123	0.06643
19	-0.003849	-0.0441	0.482464
20	-0.127537	-1.4597	0.07338
21	0.134073	1.5345	0.063655

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = -0.3 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = -0.3 ; par3 = 1 ; par4 = 1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code