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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 28 Nov 2010 20:33:38 +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/Nov/28/t12909763246hkie8sg5rq38nj.htm/, Retrieved Mon, 29 Apr 2024 08:05:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=102732, Retrieved Mon, 29 Apr 2024 08:05:41 +0000

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User-defined keywords

Estimated Impact

189

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

F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [Central Tendency] [Workshop 8, Robus...] [2010-11-28 19:41:12] [d946de7cca328fbcf207448a112523ab]
-         [Central Tendency] [WS 8 Robustness o...] [2010-11-28 20:01:42] [8081b8996d5947580de3eb171e82db4f]
- RMPD        [(Partial) Autocorrelation Function] [WS 8 Autocorrelat...] [2010-11-28 20:33:38] [4d0f7ea43b071af5c75b527ee1ef14c2] [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	'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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102732&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102732&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102732&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.557211	4.28	3.5e-05
2	0.300491	2.3081	0.012258
3	0.011975	0.092	0.463513
4	-0.313546	-2.4084	0.009583
5	-0.437905	-3.3636	0.000678
6	-0.494812	-3.8007	0.000172
7	-0.3998	-3.0709	0.001612
8	-0.316102	-2.428	0.009125
9	0.030066	0.2309	0.409079
10	0.228072	1.7519	0.042497
11	0.30152	2.316	0.012025
12	0.56194	4.3163	3.1e-05
13	0.387924	2.9797	0.002092
14	0.303042	2.3277	0.011688
15	0.110983	0.8525	0.198698
16	-0.12354	-0.9489	0.173263
17	-0.280017	-2.1509	0.017797

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.557211 & 4.28 & 3.5e-05 \tabularnewline
2 & 0.300491 & 2.3081 & 0.012258 \tabularnewline
3 & 0.011975 & 0.092 & 0.463513 \tabularnewline
4 & -0.313546 & -2.4084 & 0.009583 \tabularnewline
5 & -0.437905 & -3.3636 & 0.000678 \tabularnewline
6 & -0.494812 & -3.8007 & 0.000172 \tabularnewline
7 & -0.3998 & -3.0709 & 0.001612 \tabularnewline
8 & -0.316102 & -2.428 & 0.009125 \tabularnewline
9 & 0.030066 & 0.2309 & 0.409079 \tabularnewline
10 & 0.228072 & 1.7519 & 0.042497 \tabularnewline
11 & 0.30152 & 2.316 & 0.012025 \tabularnewline
12 & 0.56194 & 4.3163 & 3.1e-05 \tabularnewline
13 & 0.387924 & 2.9797 & 0.002092 \tabularnewline
14 & 0.303042 & 2.3277 & 0.011688 \tabularnewline
15 & 0.110983 & 0.8525 & 0.198698 \tabularnewline
16 & -0.12354 & -0.9489 & 0.173263 \tabularnewline
17 & -0.280017 & -2.1509 & 0.017797 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102732&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]0.557211[/C][C]4.28[/C][C]3.5e-05[/C][/ROW]
[ROW][C]2[/C][C]0.300491[/C][C]2.3081[/C][C]0.012258[/C][/ROW]
[ROW][C]3[/C][C]0.011975[/C][C]0.092[/C][C]0.463513[/C][/ROW]
[ROW][C]4[/C][C]-0.313546[/C][C]-2.4084[/C][C]0.009583[/C][/ROW]
[ROW][C]5[/C][C]-0.437905[/C][C]-3.3636[/C][C]0.000678[/C][/ROW]
[ROW][C]6[/C][C]-0.494812[/C][C]-3.8007[/C][C]0.000172[/C][/ROW]
[ROW][C]7[/C][C]-0.3998[/C][C]-3.0709[/C][C]0.001612[/C][/ROW]
[ROW][C]8[/C][C]-0.316102[/C][C]-2.428[/C][C]0.009125[/C][/ROW]
[ROW][C]9[/C][C]0.030066[/C][C]0.2309[/C][C]0.409079[/C][/ROW]
[ROW][C]10[/C][C]0.228072[/C][C]1.7519[/C][C]0.042497[/C][/ROW]
[ROW][C]11[/C][C]0.30152[/C][C]2.316[/C][C]0.012025[/C][/ROW]
[ROW][C]12[/C][C]0.56194[/C][C]4.3163[/C][C]3.1e-05[/C][/ROW]
[ROW][C]13[/C][C]0.387924[/C][C]2.9797[/C][C]0.002092[/C][/ROW]
[ROW][C]14[/C][C]0.303042[/C][C]2.3277[/C][C]0.011688[/C][/ROW]
[ROW][C]15[/C][C]0.110983[/C][C]0.8525[/C][C]0.198698[/C][/ROW]
[ROW][C]16[/C][C]-0.12354[/C][C]-0.9489[/C][C]0.173263[/C][/ROW]
[ROW][C]17[/C][C]-0.280017[/C][C]-2.1509[/C][C]0.017797[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102732&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102732&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	0.557211	4.28	3.5e-05
2	0.300491	2.3081	0.012258
3	0.011975	0.092	0.463513
4	-0.313546	-2.4084	0.009583
5	-0.437905	-3.3636	0.000678
6	-0.494812	-3.8007	0.000172
7	-0.3998	-3.0709	0.001612
8	-0.316102	-2.428	0.009125
9	0.030066	0.2309	0.409079
10	0.228072	1.7519	0.042497
11	0.30152	2.316	0.012025
12	0.56194	4.3163	3.1e-05
13	0.387924	2.9797	0.002092
14	0.303042	2.3277	0.011688
15	0.110983	0.8525	0.198698
16	-0.12354	-0.9489	0.173263
17	-0.280017	-2.1509	0.017797

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.557211	4.28	3.5e-05
2	-0.014493	-0.1113	0.45587
3	-0.217318	-1.6693	0.050183
4	-0.352832	-2.7102	0.004396
5	-0.14806	-1.1373	0.130012
6	-0.165583	-1.2719	0.104206
7	-0.065274	-0.5014	0.308986
8	-0.218362	-1.6773	0.049391
9	0.228349	1.754	0.042314
10	0.029483	0.2265	0.410812
11	-0.074828	-0.5748	0.283817
12	0.378785	2.9095	0.002549
13	-0.103588	-0.7957	0.214706
14	0.154812	1.1891	0.119575
15	0.02248	0.1727	0.431751
16	0.014289	0.1098	0.456486
17	0.04763	0.3658	0.357893

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.557211 & 4.28 & 3.5e-05 \tabularnewline
2 & -0.014493 & -0.1113 & 0.45587 \tabularnewline
3 & -0.217318 & -1.6693 & 0.050183 \tabularnewline
4 & -0.352832 & -2.7102 & 0.004396 \tabularnewline
5 & -0.14806 & -1.1373 & 0.130012 \tabularnewline
6 & -0.165583 & -1.2719 & 0.104206 \tabularnewline
7 & -0.065274 & -0.5014 & 0.308986 \tabularnewline
8 & -0.218362 & -1.6773 & 0.049391 \tabularnewline
9 & 0.228349 & 1.754 & 0.042314 \tabularnewline
10 & 0.029483 & 0.2265 & 0.410812 \tabularnewline
11 & -0.074828 & -0.5748 & 0.283817 \tabularnewline
12 & 0.378785 & 2.9095 & 0.002549 \tabularnewline
13 & -0.103588 & -0.7957 & 0.214706 \tabularnewline
14 & 0.154812 & 1.1891 & 0.119575 \tabularnewline
15 & 0.02248 & 0.1727 & 0.431751 \tabularnewline
16 & 0.014289 & 0.1098 & 0.456486 \tabularnewline
17 & 0.04763 & 0.3658 & 0.357893 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102732&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]0.557211[/C][C]4.28[/C][C]3.5e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.014493[/C][C]-0.1113[/C][C]0.45587[/C][/ROW]
[ROW][C]3[/C][C]-0.217318[/C][C]-1.6693[/C][C]0.050183[/C][/ROW]
[ROW][C]4[/C][C]-0.352832[/C][C]-2.7102[/C][C]0.004396[/C][/ROW]
[ROW][C]5[/C][C]-0.14806[/C][C]-1.1373[/C][C]0.130012[/C][/ROW]
[ROW][C]6[/C][C]-0.165583[/C][C]-1.2719[/C][C]0.104206[/C][/ROW]
[ROW][C]7[/C][C]-0.065274[/C][C]-0.5014[/C][C]0.308986[/C][/ROW]
[ROW][C]8[/C][C]-0.218362[/C][C]-1.6773[/C][C]0.049391[/C][/ROW]
[ROW][C]9[/C][C]0.228349[/C][C]1.754[/C][C]0.042314[/C][/ROW]
[ROW][C]10[/C][C]0.029483[/C][C]0.2265[/C][C]0.410812[/C][/ROW]
[ROW][C]11[/C][C]-0.074828[/C][C]-0.5748[/C][C]0.283817[/C][/ROW]
[ROW][C]12[/C][C]0.378785[/C][C]2.9095[/C][C]0.002549[/C][/ROW]
[ROW][C]13[/C][C]-0.103588[/C][C]-0.7957[/C][C]0.214706[/C][/ROW]
[ROW][C]14[/C][C]0.154812[/C][C]1.1891[/C][C]0.119575[/C][/ROW]
[ROW][C]15[/C][C]0.02248[/C][C]0.1727[/C][C]0.431751[/C][/ROW]
[ROW][C]16[/C][C]0.014289[/C][C]0.1098[/C][C]0.456486[/C][/ROW]
[ROW][C]17[/C][C]0.04763[/C][C]0.3658[/C][C]0.357893[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102732&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102732&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	0.557211	4.28	3.5e-05
2	-0.014493	-0.1113	0.45587
3	-0.217318	-1.6693	0.050183
4	-0.352832	-2.7102	0.004396
5	-0.14806	-1.1373	0.130012
6	-0.165583	-1.2719	0.104206
7	-0.065274	-0.5014	0.308986
8	-0.218362	-1.6773	0.049391
9	0.228349	1.754	0.042314
10	0.029483	0.2265	0.410812
11	-0.074828	-0.5748	0.283817
12	0.378785	2.9095	0.002549
13	-0.103588	-0.7957	0.214706
14	0.154812	1.1891	0.119575
15	0.02248	0.1727	0.431751
16	0.014289	0.1098	0.456486
17	0.04763	0.3658	0.357893

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 ;

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code