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Author's title

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, 02 Dec 2008 05:06:20 -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/02/t12282196386s2r5c5ho4y3m69.htm/, Retrieved Sun, 19 May 2024 11:15:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27634, Retrieved Sun, 19 May 2024 11:15:59 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

202

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]
F RMPD    [(Partial) Autocorrelation Function] [tinneke_debock.wo...] [2008-12-02 12:06:20] [20137734a2343a7bbbd59daaec7ad301] [Current]
F   P       [(Partial) Autocorrelation Function] [tinneke_debock.wo...] [2008-12-02 12:09:32] [f9c5a49917ff87aeb076072f2749ef70] 
-   P       [(Partial) Autocorrelation Function] [tinneke_debock.wo...] [2008-12-02 12:14:43] [f9c5a49917ff87aeb076072f2749ef70] 
F   P       [(Partial) Autocorrelation Function] [tinneke_debock.wo...] [2008-12-02 12:14:43] [f9c5a49917ff87aeb076072f2749ef70] 
F RMP       [Spectral Analysis] [tinneke_debock.wo...] [2008-12-02 12:20:07] [f9c5a49917ff87aeb076072f2749ef70] 
F             [Spectral Analysis] [tinneke_debock.wo...] [2008-12-02 12:23:14] [f9c5a49917ff87aeb076072f2749ef70] 
F               [Spectral Analysis] [tinneke_debock.wo...] [2008-12-02 12:27:13] [f9c5a49917ff87aeb076072f2749ef70] 

Feedback Forum

2008-12-08 13:48:38 [Dave Bellekens] [reply] 
Bij éénmaal differentiëren merken we inderdaad dat de trend is verdwenen uit de reeks. We zien echter nog steeds pieken optreden bij lags 12,24 en 36. Dit wijst er op dat er nog steeds seizoenaliteit in de reeks zit en we dus D moeten aanpassen.
2008-12-08 15:45:27 [Jonas Scheltjens] [reply] 
Na de differentiatie is inderdaad de lange termijn trend verdwenen door de parameter d op 1 te zetten. Het is ook correct dat er nog een seizoenaliteit op te merken valt. Dit kunnen we overduidelijk zien aan de pieken op lag 12,24,36.. Verder kunnen we nog toevoegen dat we hier een langzame daling merken van de seizoenale autocorrelatiecoëfficiënten. De seizoenaliteit moeten we wegwerken door de parameter D op 1 te zetten.

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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=27634&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=27634&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27634&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	0.302855	3.6216	0.000203
2	-0.102148	-1.2215	0.111952
3	-0.241273	-2.8852	0.002259
4	-0.300402	-3.5923	0.000225
5	-0.094073	-1.1249	0.131248
6	-0.078443	-0.938	0.174904
7	-0.092362	-1.1045	0.135618
8	-0.294802	-3.5253	0.000284
9	-0.191778	-2.2933	0.011643
10	-0.104917	-1.2546	0.105831
11	0.282931	3.3834	0.000462
12	0.829178	9.9155	0
13	0.284501	3.4021	0.000434
14	-0.105752	-1.2646	0.104035
15	-0.222131	-2.6563	0.004399
16	-0.231076	-2.7633	0.003238
17	-0.062279	-0.7447	0.228823
18	-0.066185	-0.7915	0.214994
19	-0.0904	-1.081	0.140753
20	-0.29711	-3.5529	0.000258
21	-0.162732	-1.946	0.026808

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.302855 & 3.6216 & 0.000203 \tabularnewline
2 & -0.102148 & -1.2215 & 0.111952 \tabularnewline
3 & -0.241273 & -2.8852 & 0.002259 \tabularnewline
4 & -0.300402 & -3.5923 & 0.000225 \tabularnewline
5 & -0.094073 & -1.1249 & 0.131248 \tabularnewline
6 & -0.078443 & -0.938 & 0.174904 \tabularnewline
7 & -0.092362 & -1.1045 & 0.135618 \tabularnewline
8 & -0.294802 & -3.5253 & 0.000284 \tabularnewline
9 & -0.191778 & -2.2933 & 0.011643 \tabularnewline
10 & -0.104917 & -1.2546 & 0.105831 \tabularnewline
11 & 0.282931 & 3.3834 & 0.000462 \tabularnewline
12 & 0.829178 & 9.9155 & 0 \tabularnewline
13 & 0.284501 & 3.4021 & 0.000434 \tabularnewline
14 & -0.105752 & -1.2646 & 0.104035 \tabularnewline
15 & -0.222131 & -2.6563 & 0.004399 \tabularnewline
16 & -0.231076 & -2.7633 & 0.003238 \tabularnewline
17 & -0.062279 & -0.7447 & 0.228823 \tabularnewline
18 & -0.066185 & -0.7915 & 0.214994 \tabularnewline
19 & -0.0904 & -1.081 & 0.140753 \tabularnewline
20 & -0.29711 & -3.5529 & 0.000258 \tabularnewline
21 & -0.162732 & -1.946 & 0.026808 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27634&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]0.302855[/C][C]3.6216[/C][C]0.000203[/C][/ROW]
[ROW][C]2[/C][C]-0.102148[/C][C]-1.2215[/C][C]0.111952[/C][/ROW]
[ROW][C]3[/C][C]-0.241273[/C][C]-2.8852[/C][C]0.002259[/C][/ROW]
[ROW][C]4[/C][C]-0.300402[/C][C]-3.5923[/C][C]0.000225[/C][/ROW]
[ROW][C]5[/C][C]-0.094073[/C][C]-1.1249[/C][C]0.131248[/C][/ROW]
[ROW][C]6[/C][C]-0.078443[/C][C]-0.938[/C][C]0.174904[/C][/ROW]
[ROW][C]7[/C][C]-0.092362[/C][C]-1.1045[/C][C]0.135618[/C][/ROW]
[ROW][C]8[/C][C]-0.294802[/C][C]-3.5253[/C][C]0.000284[/C][/ROW]
[ROW][C]9[/C][C]-0.191778[/C][C]-2.2933[/C][C]0.011643[/C][/ROW]
[ROW][C]10[/C][C]-0.104917[/C][C]-1.2546[/C][C]0.105831[/C][/ROW]
[ROW][C]11[/C][C]0.282931[/C][C]3.3834[/C][C]0.000462[/C][/ROW]
[ROW][C]12[/C][C]0.829178[/C][C]9.9155[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.284501[/C][C]3.4021[/C][C]0.000434[/C][/ROW]
[ROW][C]14[/C][C]-0.105752[/C][C]-1.2646[/C][C]0.104035[/C][/ROW]
[ROW][C]15[/C][C]-0.222131[/C][C]-2.6563[/C][C]0.004399[/C][/ROW]
[ROW][C]16[/C][C]-0.231076[/C][C]-2.7633[/C][C]0.003238[/C][/ROW]
[ROW][C]17[/C][C]-0.062279[/C][C]-0.7447[/C][C]0.228823[/C][/ROW]
[ROW][C]18[/C][C]-0.066185[/C][C]-0.7915[/C][C]0.214994[/C][/ROW]
[ROW][C]19[/C][C]-0.0904[/C][C]-1.081[/C][C]0.140753[/C][/ROW]
[ROW][C]20[/C][C]-0.29711[/C][C]-3.5529[/C][C]0.000258[/C][/ROW]
[ROW][C]21[/C][C]-0.162732[/C][C]-1.946[/C][C]0.026808[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27634&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27634&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	0.302855	3.6216	0.000203
2	-0.102148	-1.2215	0.111952
3	-0.241273	-2.8852	0.002259
4	-0.300402	-3.5923	0.000225
5	-0.094073	-1.1249	0.131248
6	-0.078443	-0.938	0.174904
7	-0.092362	-1.1045	0.135618
8	-0.294802	-3.5253	0.000284
9	-0.191778	-2.2933	0.011643
10	-0.104917	-1.2546	0.105831
11	0.282931	3.3834	0.000462
12	0.829178	9.9155	0
13	0.284501	3.4021	0.000434
14	-0.105752	-1.2646	0.104035
15	-0.222131	-2.6563	0.004399
16	-0.231076	-2.7633	0.003238
17	-0.062279	-0.7447	0.228823
18	-0.066185	-0.7915	0.214994
19	-0.0904	-1.081	0.140753
20	-0.29711	-3.5529	0.000258
21	-0.162732	-1.946	0.026808

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.302855	3.6216	0.000203
2	-0.213446	-2.5524	0.005873
3	-0.160447	-1.9187	0.02851
4	-0.22163	-2.6503	0.004474
5	0.010084	0.1206	0.452095
6	-0.190643	-2.2798	0.012051
7	-0.153657	-1.8375	0.034108
8	-0.454732	-5.4378	0
9	-0.233751	-2.7953	0.002949
10	-0.547297	-6.5447	0
11	-0.130043	-1.5551	0.061067
12	0.571287	6.8316	0
13	-0.149281	-1.7851	0.038179
14	-0.171815	-2.0546	0.020869
15	0.067207	0.8037	0.211457
16	0.062464	0.747	0.228158
17	0.007638	0.0913	0.463678
18	-0.079945	-0.956	0.170343
19	0.037143	0.4442	0.328795
20	-0.094677	-1.1322	0.129729
21	-0.004683	-0.056	0.477707

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.302855 & 3.6216 & 0.000203 \tabularnewline
2 & -0.213446 & -2.5524 & 0.005873 \tabularnewline
3 & -0.160447 & -1.9187 & 0.02851 \tabularnewline
4 & -0.22163 & -2.6503 & 0.004474 \tabularnewline
5 & 0.010084 & 0.1206 & 0.452095 \tabularnewline
6 & -0.190643 & -2.2798 & 0.012051 \tabularnewline
7 & -0.153657 & -1.8375 & 0.034108 \tabularnewline
8 & -0.454732 & -5.4378 & 0 \tabularnewline
9 & -0.233751 & -2.7953 & 0.002949 \tabularnewline
10 & -0.547297 & -6.5447 & 0 \tabularnewline
11 & -0.130043 & -1.5551 & 0.061067 \tabularnewline
12 & 0.571287 & 6.8316 & 0 \tabularnewline
13 & -0.149281 & -1.7851 & 0.038179 \tabularnewline
14 & -0.171815 & -2.0546 & 0.020869 \tabularnewline
15 & 0.067207 & 0.8037 & 0.211457 \tabularnewline
16 & 0.062464 & 0.747 & 0.228158 \tabularnewline
17 & 0.007638 & 0.0913 & 0.463678 \tabularnewline
18 & -0.079945 & -0.956 & 0.170343 \tabularnewline
19 & 0.037143 & 0.4442 & 0.328795 \tabularnewline
20 & -0.094677 & -1.1322 & 0.129729 \tabularnewline
21 & -0.004683 & -0.056 & 0.477707 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27634&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]0.302855[/C][C]3.6216[/C][C]0.000203[/C][/ROW]
[ROW][C]2[/C][C]-0.213446[/C][C]-2.5524[/C][C]0.005873[/C][/ROW]
[ROW][C]3[/C][C]-0.160447[/C][C]-1.9187[/C][C]0.02851[/C][/ROW]
[ROW][C]4[/C][C]-0.22163[/C][C]-2.6503[/C][C]0.004474[/C][/ROW]
[ROW][C]5[/C][C]0.010084[/C][C]0.1206[/C][C]0.452095[/C][/ROW]
[ROW][C]6[/C][C]-0.190643[/C][C]-2.2798[/C][C]0.012051[/C][/ROW]
[ROW][C]7[/C][C]-0.153657[/C][C]-1.8375[/C][C]0.034108[/C][/ROW]
[ROW][C]8[/C][C]-0.454732[/C][C]-5.4378[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]-0.233751[/C][C]-2.7953[/C][C]0.002949[/C][/ROW]
[ROW][C]10[/C][C]-0.547297[/C][C]-6.5447[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]-0.130043[/C][C]-1.5551[/C][C]0.061067[/C][/ROW]
[ROW][C]12[/C][C]0.571287[/C][C]6.8316[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.149281[/C][C]-1.7851[/C][C]0.038179[/C][/ROW]
[ROW][C]14[/C][C]-0.171815[/C][C]-2.0546[/C][C]0.020869[/C][/ROW]
[ROW][C]15[/C][C]0.067207[/C][C]0.8037[/C][C]0.211457[/C][/ROW]
[ROW][C]16[/C][C]0.062464[/C][C]0.747[/C][C]0.228158[/C][/ROW]
[ROW][C]17[/C][C]0.007638[/C][C]0.0913[/C][C]0.463678[/C][/ROW]
[ROW][C]18[/C][C]-0.079945[/C][C]-0.956[/C][C]0.170343[/C][/ROW]
[ROW][C]19[/C][C]0.037143[/C][C]0.4442[/C][C]0.328795[/C][/ROW]
[ROW][C]20[/C][C]-0.094677[/C][C]-1.1322[/C][C]0.129729[/C][/ROW]
[ROW][C]21[/C][C]-0.004683[/C][C]-0.056[/C][C]0.477707[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27634&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27634&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	0.302855	3.6216	0.000203
2	-0.213446	-2.5524	0.005873
3	-0.160447	-1.9187	0.02851
4	-0.22163	-2.6503	0.004474
5	0.010084	0.1206	0.452095
6	-0.190643	-2.2798	0.012051
7	-0.153657	-1.8375	0.034108
8	-0.454732	-5.4378	0
9	-0.233751	-2.7953	0.002949
10	-0.547297	-6.5447	0
11	-0.130043	-1.5551	0.061067
12	0.571287	6.8316	0
13	-0.149281	-1.7851	0.038179
14	-0.171815	-2.0546	0.020869
15	0.067207	0.8037	0.211457
16	0.062464	0.747	0.228158
17	0.007638	0.0913	0.463678
18	-0.079945	-0.956	0.170343
19	0.037143	0.4442	0.328795
20	-0.094677	-1.1322	0.129729
21	-0.004683	-0.056	0.477707

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 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; 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