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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

Sun, 19 Dec 2010 14:18:56 +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/Dec/19/t1292768271mr1gf3mpq3bxj0d.htm/, Retrieved Sun, 05 May 2024 01:52:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112414, Retrieved Sun, 05 May 2024 01:52:02 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

129

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] [Workshop 9, Stati...] [2010-12-03 13:18:27] [d946de7cca328fbcf207448a112523ab]
-    D        [(Partial) Autocorrelation Function] [Autocorrelatie Fu...] [2010-12-19 14:18:56] [99c051a77087383325372ff23bc64341] [Current]
- R PD          [(Partial) Autocorrelation Function] [Paper ACF] [2010-12-19 14:22:07] [3635fb7041b1998c5a1332cf9de22bce] 
-                 [(Partial) Autocorrelation Function] [Paper ACF werklozen] [2010-12-19 14:32:52] [d946de7cca328fbcf207448a112523ab] 
-   PD            [(Partial) Autocorrelation Function] [Paper ACF D=1 d=1] [2010-12-19 14:47:59] [3635fb7041b1998c5a1332cf9de22bce] 
-                   [(Partial) Autocorrelation Function] [Paper ACF D=1 d=1...] [2010-12-19 14:54:07] [d946de7cca328fbcf207448a112523ab] 
-   PD            [(Partial) Autocorrelation Function] [Paper ACF poging 2] [2010-12-19 21:25:36] [3635fb7041b1998c5a1332cf9de22bce] 
-   P               [(Partial) Autocorrelation Function] [Autocorrelationfu...] [2010-12-22 08:46:14] [8081b8996d5947580de3eb171e82db4f] 
-   P               [(Partial) Autocorrelation Function] [Paper Autocorrela...] [2010-12-22 09:08:40] [d946de7cca328fbcf207448a112523ab] 
-   P               [(Partial) Autocorrelation Function] [Paper Autocorrela...] [2010-12-22 09:08:40] [d946de7cca328fbcf207448a112523ab] 
-   P               [(Partial) Autocorrelation Function] [Paper Autocorrela...] [2010-12-22 09:08:40] [d946de7cca328fbcf207448a112523ab] 
-   P               [(Partial) Autocorrelation Function] [Paper ACF poging 3] [2010-12-22 09:12:13] [3635fb7041b1998c5a1332cf9de22bce] 
-   PD            [(Partial) Autocorrelation Function] [Paper ACF D=1 d=1...] [2010-12-19 21:28:57] [3635fb7041b1998c5a1332cf9de22bce] 
-   P               [(Partial) Autocorrelation Function] [ACF d=D=1] [2010-12-22 08:48:35] [8081b8996d5947580de3eb171e82db4f] 
-                     [(Partial) Autocorrelation Function] [ACF d=D=1] [2010-12-22 09:14:48] [8081b8996d5947580de3eb171e82db4f] 
-                     [(Partial) Autocorrelation Function] [ACF d=D=1] [2010-12-22 09:14:48] [8081b8996d5947580de3eb171e82db4f] 
-   P               [(Partial) Autocorrelation Function] [Paper ACF D=1 d=1] [2010-12-22 09:16:52] [d946de7cca328fbcf207448a112523ab] 

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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=112414&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=112414&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112414&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	0.471632	4.3226	2.1e-05
2	0.435323	3.9898	7e-05
3	0.425968	3.9041	9.5e-05
4	0.06033	0.5529	0.290888
5	0.139573	1.2792	0.102174
6	0.096826	0.8874	0.188693
7	-0.042997	-0.3941	0.347263
8	-0.009589	-0.0879	0.465089
9	0.037341	0.3422	0.366515
10	-0.052043	-0.477	0.317306
11	0.087265	0.7998	0.213043
12	0.251864	2.3084	0.011718
13	-0.023008	-0.2109	0.416751
14	0.050764	0.4653	0.321475
15	-0.077946	-0.7144	0.238485
16	-0.245162	-2.247	0.013633
17	-0.129931	-1.1908	0.118537
18	-0.222404	-2.0384	0.02233
19	-0.261056	-2.3926	0.00948

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.471632 & 4.3226 & 2.1e-05 \tabularnewline
2 & 0.435323 & 3.9898 & 7e-05 \tabularnewline
3 & 0.425968 & 3.9041 & 9.5e-05 \tabularnewline
4 & 0.06033 & 0.5529 & 0.290888 \tabularnewline
5 & 0.139573 & 1.2792 & 0.102174 \tabularnewline
6 & 0.096826 & 0.8874 & 0.188693 \tabularnewline
7 & -0.042997 & -0.3941 & 0.347263 \tabularnewline
8 & -0.009589 & -0.0879 & 0.465089 \tabularnewline
9 & 0.037341 & 0.3422 & 0.366515 \tabularnewline
10 & -0.052043 & -0.477 & 0.317306 \tabularnewline
11 & 0.087265 & 0.7998 & 0.213043 \tabularnewline
12 & 0.251864 & 2.3084 & 0.011718 \tabularnewline
13 & -0.023008 & -0.2109 & 0.416751 \tabularnewline
14 & 0.050764 & 0.4653 & 0.321475 \tabularnewline
15 & -0.077946 & -0.7144 & 0.238485 \tabularnewline
16 & -0.245162 & -2.247 & 0.013633 \tabularnewline
17 & -0.129931 & -1.1908 & 0.118537 \tabularnewline
18 & -0.222404 & -2.0384 & 0.02233 \tabularnewline
19 & -0.261056 & -2.3926 & 0.00948 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112414&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]0.471632[/C][C]4.3226[/C][C]2.1e-05[/C][/ROW]
[ROW][C]2[/C][C]0.435323[/C][C]3.9898[/C][C]7e-05[/C][/ROW]
[ROW][C]3[/C][C]0.425968[/C][C]3.9041[/C][C]9.5e-05[/C][/ROW]
[ROW][C]4[/C][C]0.06033[/C][C]0.5529[/C][C]0.290888[/C][/ROW]
[ROW][C]5[/C][C]0.139573[/C][C]1.2792[/C][C]0.102174[/C][/ROW]
[ROW][C]6[/C][C]0.096826[/C][C]0.8874[/C][C]0.188693[/C][/ROW]
[ROW][C]7[/C][C]-0.042997[/C][C]-0.3941[/C][C]0.347263[/C][/ROW]
[ROW][C]8[/C][C]-0.009589[/C][C]-0.0879[/C][C]0.465089[/C][/ROW]
[ROW][C]9[/C][C]0.037341[/C][C]0.3422[/C][C]0.366515[/C][/ROW]
[ROW][C]10[/C][C]-0.052043[/C][C]-0.477[/C][C]0.317306[/C][/ROW]
[ROW][C]11[/C][C]0.087265[/C][C]0.7998[/C][C]0.213043[/C][/ROW]
[ROW][C]12[/C][C]0.251864[/C][C]2.3084[/C][C]0.011718[/C][/ROW]
[ROW][C]13[/C][C]-0.023008[/C][C]-0.2109[/C][C]0.416751[/C][/ROW]
[ROW][C]14[/C][C]0.050764[/C][C]0.4653[/C][C]0.321475[/C][/ROW]
[ROW][C]15[/C][C]-0.077946[/C][C]-0.7144[/C][C]0.238485[/C][/ROW]
[ROW][C]16[/C][C]-0.245162[/C][C]-2.247[/C][C]0.013633[/C][/ROW]
[ROW][C]17[/C][C]-0.129931[/C][C]-1.1908[/C][C]0.118537[/C][/ROW]
[ROW][C]18[/C][C]-0.222404[/C][C]-2.0384[/C][C]0.02233[/C][/ROW]
[ROW][C]19[/C][C]-0.261056[/C][C]-2.3926[/C][C]0.00948[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112414&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112414&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	0.471632	4.3226	2.1e-05
2	0.435323	3.9898	7e-05
3	0.425968	3.9041	9.5e-05
4	0.06033	0.5529	0.290888
5	0.139573	1.2792	0.102174
6	0.096826	0.8874	0.188693
7	-0.042997	-0.3941	0.347263
8	-0.009589	-0.0879	0.465089
9	0.037341	0.3422	0.366515
10	-0.052043	-0.477	0.317306
11	0.087265	0.7998	0.213043
12	0.251864	2.3084	0.011718
13	-0.023008	-0.2109	0.416751
14	0.050764	0.4653	0.321475
15	-0.077946	-0.7144	0.238485
16	-0.245162	-2.247	0.013633
17	-0.129931	-1.1908	0.118537
18	-0.222404	-2.0384	0.02233
19	-0.261056	-2.3926	0.00948

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.471632	4.3226	2.1e-05
2	0.273786	2.5093	0.007009
3	0.205402	1.8825	0.031613
4	-0.358592	-3.2865	0.000741
5	0.058545	0.5366	0.296491
6	0.069213	0.6343	0.26379
7	-0.021689	-0.1988	0.421456
8	-0.124054	-1.137	0.129391
9	0.143913	1.319	0.095379
10	-0.02745	-0.2516	0.400989
11	0.134398	1.2318	0.110734
12	0.257842	2.3632	0.010215
13	-0.33072	-3.0311	0.00162
14	-0.200341	-1.8362	0.034936
15	-0.177637	-1.6281	0.053628
16	0.098456	0.9024	0.184722
17	-0.013335	-0.1222	0.451509
18	-0.029734	-0.2725	0.392946
19	-0.116703	-1.0696	0.143932

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.471632 & 4.3226 & 2.1e-05 \tabularnewline
2 & 0.273786 & 2.5093 & 0.007009 \tabularnewline
3 & 0.205402 & 1.8825 & 0.031613 \tabularnewline
4 & -0.358592 & -3.2865 & 0.000741 \tabularnewline
5 & 0.058545 & 0.5366 & 0.296491 \tabularnewline
6 & 0.069213 & 0.6343 & 0.26379 \tabularnewline
7 & -0.021689 & -0.1988 & 0.421456 \tabularnewline
8 & -0.124054 & -1.137 & 0.129391 \tabularnewline
9 & 0.143913 & 1.319 & 0.095379 \tabularnewline
10 & -0.02745 & -0.2516 & 0.400989 \tabularnewline
11 & 0.134398 & 1.2318 & 0.110734 \tabularnewline
12 & 0.257842 & 2.3632 & 0.010215 \tabularnewline
13 & -0.33072 & -3.0311 & 0.00162 \tabularnewline
14 & -0.200341 & -1.8362 & 0.034936 \tabularnewline
15 & -0.177637 & -1.6281 & 0.053628 \tabularnewline
16 & 0.098456 & 0.9024 & 0.184722 \tabularnewline
17 & -0.013335 & -0.1222 & 0.451509 \tabularnewline
18 & -0.029734 & -0.2725 & 0.392946 \tabularnewline
19 & -0.116703 & -1.0696 & 0.143932 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112414&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]0.471632[/C][C]4.3226[/C][C]2.1e-05[/C][/ROW]
[ROW][C]2[/C][C]0.273786[/C][C]2.5093[/C][C]0.007009[/C][/ROW]
[ROW][C]3[/C][C]0.205402[/C][C]1.8825[/C][C]0.031613[/C][/ROW]
[ROW][C]4[/C][C]-0.358592[/C][C]-3.2865[/C][C]0.000741[/C][/ROW]
[ROW][C]5[/C][C]0.058545[/C][C]0.5366[/C][C]0.296491[/C][/ROW]
[ROW][C]6[/C][C]0.069213[/C][C]0.6343[/C][C]0.26379[/C][/ROW]
[ROW][C]7[/C][C]-0.021689[/C][C]-0.1988[/C][C]0.421456[/C][/ROW]
[ROW][C]8[/C][C]-0.124054[/C][C]-1.137[/C][C]0.129391[/C][/ROW]
[ROW][C]9[/C][C]0.143913[/C][C]1.319[/C][C]0.095379[/C][/ROW]
[ROW][C]10[/C][C]-0.02745[/C][C]-0.2516[/C][C]0.400989[/C][/ROW]
[ROW][C]11[/C][C]0.134398[/C][C]1.2318[/C][C]0.110734[/C][/ROW]
[ROW][C]12[/C][C]0.257842[/C][C]2.3632[/C][C]0.010215[/C][/ROW]
[ROW][C]13[/C][C]-0.33072[/C][C]-3.0311[/C][C]0.00162[/C][/ROW]
[ROW][C]14[/C][C]-0.200341[/C][C]-1.8362[/C][C]0.034936[/C][/ROW]
[ROW][C]15[/C][C]-0.177637[/C][C]-1.6281[/C][C]0.053628[/C][/ROW]
[ROW][C]16[/C][C]0.098456[/C][C]0.9024[/C][C]0.184722[/C][/ROW]
[ROW][C]17[/C][C]-0.013335[/C][C]-0.1222[/C][C]0.451509[/C][/ROW]
[ROW][C]18[/C][C]-0.029734[/C][C]-0.2725[/C][C]0.392946[/C][/ROW]
[ROW][C]19[/C][C]-0.116703[/C][C]-1.0696[/C][C]0.143932[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112414&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112414&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	0.471632	4.3226	2.1e-05
2	0.273786	2.5093	0.007009
3	0.205402	1.8825	0.031613
4	-0.358592	-3.2865	0.000741
5	0.058545	0.5366	0.296491
6	0.069213	0.6343	0.26379
7	-0.021689	-0.1988	0.421456
8	-0.124054	-1.137	0.129391
9	0.143913	1.319	0.095379
10	-0.02745	-0.2516	0.400989
11	0.134398	1.2318	0.110734
12	0.257842	2.3632	0.010215
13	-0.33072	-3.0311	0.00162
14	-0.200341	-1.8362	0.034936
15	-0.177637	-1.6281	0.053628
16	0.098456	0.9024	0.184722
17	-0.013335	-0.1222	0.451509
18	-0.029734	-0.2725	0.392946
19	-0.116703	-1.0696	0.143932

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 ; par8 = ;

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