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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 04 Dec 2009 01:57:43 -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/04/t1259917096kpt8pfops3xaf1w.htm/, Retrieved Sat, 27 Apr 2024 14:01:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63185, Retrieved Sat, 27 Apr 2024 14:01:03 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

139

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

-     [Univariate Data Series] [Werkloosheid bij ...] [2009-11-03 09:24:35] [1ff3eeaee490dfcff07aa4917fec66b8]
- RMPD    [(Partial) Autocorrelation Function] [ACF] [2009-12-04 08:57:43] [cfc54cb9f3f8d85fe8957f0f7c48844d] [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	'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63185&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63185&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63185&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.017337	-0.1332	0.447257
2	0.149965	1.1519	0.127003
3	-0.058234	-0.4473	0.328147
4	-0.00463	-0.0356	0.485875
5	-0.186211	-1.4303	0.078951
6	0.040189	0.3087	0.379321
7	0.133218	1.0233	0.15518
8	-0.029695	-0.2281	0.410182
9	0.115044	0.8837	0.19023
10	-0.034218	-0.2628	0.396797
11	0.347393	2.6684	0.004913
12	-0.148666	-1.1419	0.12905
13	0.048587	0.3732	0.355167
14	-0.052057	-0.3999	0.345354
15	-0.061163	-0.4698	0.320113
16	-0.266151	-2.0443	0.022695
17	-0.021925	-0.1684	0.433417
18	-0.054559	-0.4191	0.338342

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.017337 & -0.1332 & 0.447257 \tabularnewline
2 & 0.149965 & 1.1519 & 0.127003 \tabularnewline
3 & -0.058234 & -0.4473 & 0.328147 \tabularnewline
4 & -0.00463 & -0.0356 & 0.485875 \tabularnewline
5 & -0.186211 & -1.4303 & 0.078951 \tabularnewline
6 & 0.040189 & 0.3087 & 0.379321 \tabularnewline
7 & 0.133218 & 1.0233 & 0.15518 \tabularnewline
8 & -0.029695 & -0.2281 & 0.410182 \tabularnewline
9 & 0.115044 & 0.8837 & 0.19023 \tabularnewline
10 & -0.034218 & -0.2628 & 0.396797 \tabularnewline
11 & 0.347393 & 2.6684 & 0.004913 \tabularnewline
12 & -0.148666 & -1.1419 & 0.12905 \tabularnewline
13 & 0.048587 & 0.3732 & 0.355167 \tabularnewline
14 & -0.052057 & -0.3999 & 0.345354 \tabularnewline
15 & -0.061163 & -0.4698 & 0.320113 \tabularnewline
16 & -0.266151 & -2.0443 & 0.022695 \tabularnewline
17 & -0.021925 & -0.1684 & 0.433417 \tabularnewline
18 & -0.054559 & -0.4191 & 0.338342 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63185&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]-0.017337[/C][C]-0.1332[/C][C]0.447257[/C][/ROW]
[ROW][C]2[/C][C]0.149965[/C][C]1.1519[/C][C]0.127003[/C][/ROW]
[ROW][C]3[/C][C]-0.058234[/C][C]-0.4473[/C][C]0.328147[/C][/ROW]
[ROW][C]4[/C][C]-0.00463[/C][C]-0.0356[/C][C]0.485875[/C][/ROW]
[ROW][C]5[/C][C]-0.186211[/C][C]-1.4303[/C][C]0.078951[/C][/ROW]
[ROW][C]6[/C][C]0.040189[/C][C]0.3087[/C][C]0.379321[/C][/ROW]
[ROW][C]7[/C][C]0.133218[/C][C]1.0233[/C][C]0.15518[/C][/ROW]
[ROW][C]8[/C][C]-0.029695[/C][C]-0.2281[/C][C]0.410182[/C][/ROW]
[ROW][C]9[/C][C]0.115044[/C][C]0.8837[/C][C]0.19023[/C][/ROW]
[ROW][C]10[/C][C]-0.034218[/C][C]-0.2628[/C][C]0.396797[/C][/ROW]
[ROW][C]11[/C][C]0.347393[/C][C]2.6684[/C][C]0.004913[/C][/ROW]
[ROW][C]12[/C][C]-0.148666[/C][C]-1.1419[/C][C]0.12905[/C][/ROW]
[ROW][C]13[/C][C]0.048587[/C][C]0.3732[/C][C]0.355167[/C][/ROW]
[ROW][C]14[/C][C]-0.052057[/C][C]-0.3999[/C][C]0.345354[/C][/ROW]
[ROW][C]15[/C][C]-0.061163[/C][C]-0.4698[/C][C]0.320113[/C][/ROW]
[ROW][C]16[/C][C]-0.266151[/C][C]-2.0443[/C][C]0.022695[/C][/ROW]
[ROW][C]17[/C][C]-0.021925[/C][C]-0.1684[/C][C]0.433417[/C][/ROW]
[ROW][C]18[/C][C]-0.054559[/C][C]-0.4191[/C][C]0.338342[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63185&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63185&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	-0.017337	-0.1332	0.447257
2	0.149965	1.1519	0.127003
3	-0.058234	-0.4473	0.328147
4	-0.00463	-0.0356	0.485875
5	-0.186211	-1.4303	0.078951
6	0.040189	0.3087	0.379321
7	0.133218	1.0233	0.15518
8	-0.029695	-0.2281	0.410182
9	0.115044	0.8837	0.19023
10	-0.034218	-0.2628	0.396797
11	0.347393	2.6684	0.004913
12	-0.148666	-1.1419	0.12905
13	0.048587	0.3732	0.355167
14	-0.052057	-0.3999	0.345354
15	-0.061163	-0.4698	0.320113
16	-0.266151	-2.0443	0.022695
17	-0.021925	-0.1684	0.433417
18	-0.054559	-0.4191	0.338342

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.017337	-0.1332	0.447257
2	0.14971	1.1499	0.127404
3	-0.054669	-0.4199	0.338034
4	-0.029034	-0.223	0.412147
5	-0.17421	-1.3381	0.092994
6	0.040574	0.3117	0.378202
7	0.196252	1.5074	0.068517
8	-0.059033	-0.4534	0.325948
9	0.063947	0.4912	0.312557
10	-0.044961	-0.3454	0.365528
11	0.374162	2.874	0.002814
12	-0.102154	-0.7847	0.217896
13	-0.107387	-0.8249	0.206388
14	0.019729	0.1515	0.440032
15	-0.057135	-0.4389	0.331182
16	-0.187125	-1.4373	0.077953
17	-0.11689	-0.8978	0.186458
18	-0.117625	-0.9035	0.184968

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.017337 & -0.1332 & 0.447257 \tabularnewline
2 & 0.14971 & 1.1499 & 0.127404 \tabularnewline
3 & -0.054669 & -0.4199 & 0.338034 \tabularnewline
4 & -0.029034 & -0.223 & 0.412147 \tabularnewline
5 & -0.17421 & -1.3381 & 0.092994 \tabularnewline
6 & 0.040574 & 0.3117 & 0.378202 \tabularnewline
7 & 0.196252 & 1.5074 & 0.068517 \tabularnewline
8 & -0.059033 & -0.4534 & 0.325948 \tabularnewline
9 & 0.063947 & 0.4912 & 0.312557 \tabularnewline
10 & -0.044961 & -0.3454 & 0.365528 \tabularnewline
11 & 0.374162 & 2.874 & 0.002814 \tabularnewline
12 & -0.102154 & -0.7847 & 0.217896 \tabularnewline
13 & -0.107387 & -0.8249 & 0.206388 \tabularnewline
14 & 0.019729 & 0.1515 & 0.440032 \tabularnewline
15 & -0.057135 & -0.4389 & 0.331182 \tabularnewline
16 & -0.187125 & -1.4373 & 0.077953 \tabularnewline
17 & -0.11689 & -0.8978 & 0.186458 \tabularnewline
18 & -0.117625 & -0.9035 & 0.184968 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63185&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]-0.017337[/C][C]-0.1332[/C][C]0.447257[/C][/ROW]
[ROW][C]2[/C][C]0.14971[/C][C]1.1499[/C][C]0.127404[/C][/ROW]
[ROW][C]3[/C][C]-0.054669[/C][C]-0.4199[/C][C]0.338034[/C][/ROW]
[ROW][C]4[/C][C]-0.029034[/C][C]-0.223[/C][C]0.412147[/C][/ROW]
[ROW][C]5[/C][C]-0.17421[/C][C]-1.3381[/C][C]0.092994[/C][/ROW]
[ROW][C]6[/C][C]0.040574[/C][C]0.3117[/C][C]0.378202[/C][/ROW]
[ROW][C]7[/C][C]0.196252[/C][C]1.5074[/C][C]0.068517[/C][/ROW]
[ROW][C]8[/C][C]-0.059033[/C][C]-0.4534[/C][C]0.325948[/C][/ROW]
[ROW][C]9[/C][C]0.063947[/C][C]0.4912[/C][C]0.312557[/C][/ROW]
[ROW][C]10[/C][C]-0.044961[/C][C]-0.3454[/C][C]0.365528[/C][/ROW]
[ROW][C]11[/C][C]0.374162[/C][C]2.874[/C][C]0.002814[/C][/ROW]
[ROW][C]12[/C][C]-0.102154[/C][C]-0.7847[/C][C]0.217896[/C][/ROW]
[ROW][C]13[/C][C]-0.107387[/C][C]-0.8249[/C][C]0.206388[/C][/ROW]
[ROW][C]14[/C][C]0.019729[/C][C]0.1515[/C][C]0.440032[/C][/ROW]
[ROW][C]15[/C][C]-0.057135[/C][C]-0.4389[/C][C]0.331182[/C][/ROW]
[ROW][C]16[/C][C]-0.187125[/C][C]-1.4373[/C][C]0.077953[/C][/ROW]
[ROW][C]17[/C][C]-0.11689[/C][C]-0.8978[/C][C]0.186458[/C][/ROW]
[ROW][C]18[/C][C]-0.117625[/C][C]-0.9035[/C][C]0.184968[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63185&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63185&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	-0.017337	-0.1332	0.447257
2	0.14971	1.1499	0.127404
3	-0.054669	-0.4199	0.338034
4	-0.029034	-0.223	0.412147
5	-0.17421	-1.3381	0.092994
6	0.040574	0.3117	0.378202
7	0.196252	1.5074	0.068517
8	-0.059033	-0.4534	0.325948
9	0.063947	0.4912	0.312557
10	-0.044961	-0.3454	0.365528
11	0.374162	2.874	0.002814
12	-0.102154	-0.7847	0.217896
13	-0.107387	-0.8249	0.206388
14	0.019729	0.1515	0.440032
15	-0.057135	-0.4389	0.331182
16	-0.187125	-1.4373	0.077953
17	-0.11689	-0.8978	0.186458
18	-0.117625	-0.9035	0.184968

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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Input Parameters & R Code