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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 05:14:43 -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/2008/Dec/02/t1228220246fj6kkn23l3hc0pz.htm/, Retrieved Sun, 19 May 2024 10:50:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27651, Retrieved Sun, 19 May 2024 10:50:52 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

207

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] [f9c5a49917ff87aeb076072f2749ef70]
F   P       [(Partial) Autocorrelation Function] [tinneke_debock.wo...] [2008-12-02 12:14:43] [20137734a2343a7bbbd59daaec7ad301] [Current]

Feedback Forum

2008-12-08 13:51:36 [Dave Bellekens] [reply] 
Hier wordt de juiste conclusie getrokken. We moeten inderdaad kijken naar de laagst mogelijk variantie, omdat deze het model weergeeft dat het meeste zal verklaren. We kijken bij deze laagste waarde naar de overéénstemmende differentiatis om te weten welke d en D we moeten gebruiken om de tijdreeks stationair te maken. 
 
We hadden hier ook zeker moeten kijken naar de getrimde variantie. Deze is een betere parameter dan de gewone variantie, omdat er bij de getrimde geen rekening wordt gehouden met mogelijke outliers.
2008-12-08 15:47:02 [Jonas Scheltjens] [reply] 
De student is hier juist, we moeten inderdaad het risico of volaliteit in de gegevensreeks verkleinen en zodanig voor de kleinste variantie opteren (aangezien de kleinste variantie gepaard gaat met het minste risico). Indien we de kleinste waarde hebben gevonden zien we inderdaad dat de graad van de seizoenale en niet-seizoenale differentiatie 1 zou moeten zijn (goed om de markering te gebruiken in de tabel). We moeten ook rekening houden met het gegeven dat de variantie gevoelig is voor outliers. Het is dus niet fout te stellen dat de autocorrelation function betrouwbaarder is. Indien er zich toch outliers voordoen dient er gekeken te worden naar de getrimde waarden. Hier uit zijn de 5% hoogste en laagste waarden uit de reeks weggelaten. Dit geeft dan een meer  betrouwbaar beeld.

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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=27651&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=27651&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27651&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	-0.309815	-3.546	0.000272
2	0.095351	1.0913	0.138562
3	-0.096891	-1.109	0.134738
4	-0.098995	-1.133	0.129631
5	0.061001	0.6982	0.24315
6	-0.000288	-0.0033	0.498688
7	-0.056108	-0.6422	0.260936
8	-0.060966	-0.6978	0.243274
9	0.175917	2.0135	0.023057
10	-0.140279	-1.6056	0.055389
11	0.069735	0.7982	0.213112
12	-0.133673	-1.53	0.064219
13	0.087177	0.9978	0.160111
14	0.002494	0.0286	0.488633
15	0.065332	0.7478	0.227972
16	-0.109162	-1.2494	0.106871
17	-0.000338	-0.0039	0.498462
18	0.044028	0.5039	0.307582
19	-0.113945	-1.3042	0.097232
20	-0.091271	-1.0446	0.149054
21	0.041943	0.4801	0.315994

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.309815 & -3.546 & 0.000272 \tabularnewline
2 & 0.095351 & 1.0913 & 0.138562 \tabularnewline
3 & -0.096891 & -1.109 & 0.134738 \tabularnewline
4 & -0.098995 & -1.133 & 0.129631 \tabularnewline
5 & 0.061001 & 0.6982 & 0.24315 \tabularnewline
6 & -0.000288 & -0.0033 & 0.498688 \tabularnewline
7 & -0.056108 & -0.6422 & 0.260936 \tabularnewline
8 & -0.060966 & -0.6978 & 0.243274 \tabularnewline
9 & 0.175917 & 2.0135 & 0.023057 \tabularnewline
10 & -0.140279 & -1.6056 & 0.055389 \tabularnewline
11 & 0.069735 & 0.7982 & 0.213112 \tabularnewline
12 & -0.133673 & -1.53 & 0.064219 \tabularnewline
13 & 0.087177 & 0.9978 & 0.160111 \tabularnewline
14 & 0.002494 & 0.0286 & 0.488633 \tabularnewline
15 & 0.065332 & 0.7478 & 0.227972 \tabularnewline
16 & -0.109162 & -1.2494 & 0.106871 \tabularnewline
17 & -0.000338 & -0.0039 & 0.498462 \tabularnewline
18 & 0.044028 & 0.5039 & 0.307582 \tabularnewline
19 & -0.113945 & -1.3042 & 0.097232 \tabularnewline
20 & -0.091271 & -1.0446 & 0.149054 \tabularnewline
21 & 0.041943 & 0.4801 & 0.315994 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27651&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]-0.309815[/C][C]-3.546[/C][C]0.000272[/C][/ROW]
[ROW][C]2[/C][C]0.095351[/C][C]1.0913[/C][C]0.138562[/C][/ROW]
[ROW][C]3[/C][C]-0.096891[/C][C]-1.109[/C][C]0.134738[/C][/ROW]
[ROW][C]4[/C][C]-0.098995[/C][C]-1.133[/C][C]0.129631[/C][/ROW]
[ROW][C]5[/C][C]0.061001[/C][C]0.6982[/C][C]0.24315[/C][/ROW]
[ROW][C]6[/C][C]-0.000288[/C][C]-0.0033[/C][C]0.498688[/C][/ROW]
[ROW][C]7[/C][C]-0.056108[/C][C]-0.6422[/C][C]0.260936[/C][/ROW]
[ROW][C]8[/C][C]-0.060966[/C][C]-0.6978[/C][C]0.243274[/C][/ROW]
[ROW][C]9[/C][C]0.175917[/C][C]2.0135[/C][C]0.023057[/C][/ROW]
[ROW][C]10[/C][C]-0.140279[/C][C]-1.6056[/C][C]0.055389[/C][/ROW]
[ROW][C]11[/C][C]0.069735[/C][C]0.7982[/C][C]0.213112[/C][/ROW]
[ROW][C]12[/C][C]-0.133673[/C][C]-1.53[/C][C]0.064219[/C][/ROW]
[ROW][C]13[/C][C]0.087177[/C][C]0.9978[/C][C]0.160111[/C][/ROW]
[ROW][C]14[/C][C]0.002494[/C][C]0.0286[/C][C]0.488633[/C][/ROW]
[ROW][C]15[/C][C]0.065332[/C][C]0.7478[/C][C]0.227972[/C][/ROW]
[ROW][C]16[/C][C]-0.109162[/C][C]-1.2494[/C][C]0.106871[/C][/ROW]
[ROW][C]17[/C][C]-0.000338[/C][C]-0.0039[/C][C]0.498462[/C][/ROW]
[ROW][C]18[/C][C]0.044028[/C][C]0.5039[/C][C]0.307582[/C][/ROW]
[ROW][C]19[/C][C]-0.113945[/C][C]-1.3042[/C][C]0.097232[/C][/ROW]
[ROW][C]20[/C][C]-0.091271[/C][C]-1.0446[/C][C]0.149054[/C][/ROW]
[ROW][C]21[/C][C]0.041943[/C][C]0.4801[/C][C]0.315994[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27651&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27651&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	-0.309815	-3.546	0.000272
2	0.095351	1.0913	0.138562
3	-0.096891	-1.109	0.134738
4	-0.098995	-1.133	0.129631
5	0.061001	0.6982	0.24315
6	-0.000288	-0.0033	0.498688
7	-0.056108	-0.6422	0.260936
8	-0.060966	-0.6978	0.243274
9	0.175917	2.0135	0.023057
10	-0.140279	-1.6056	0.055389
11	0.069735	0.7982	0.213112
12	-0.133673	-1.53	0.064219
13	0.087177	0.9978	0.160111
14	0.002494	0.0286	0.488633
15	0.065332	0.7478	0.227972
16	-0.109162	-1.2494	0.106871
17	-0.000338	-0.0039	0.498462
18	0.044028	0.5039	0.307582
19	-0.113945	-1.3042	0.097232
20	-0.091271	-1.0446	0.149054
21	0.041943	0.4801	0.315994

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.309815	-3.546	0.000272
2	-0.000701	-0.008	0.496806
3	-0.074718	-0.8552	0.197005
4	-0.166761	-1.9087	0.029247
5	-0.015146	-0.1734	0.431319
6	0.018288	0.2093	0.417265
7	-0.088086	-1.0082	0.157611
8	-0.133888	-1.5324	0.063916
9	0.156405	1.7901	0.03787
10	-0.05875	-0.6724	0.251251
11	-0.052428	-0.6001	0.274749
12	-0.115013	-1.3164	0.095172
13	0.059956	0.6862	0.246893
14	0.004318	0.0494	0.48033
15	0.036587	0.4188	0.338041
16	-0.086599	-0.9912	0.161715
17	-0.027835	-0.3186	0.375275
18	0.019117	0.2188	0.41357
19	-0.113792	-1.3024	0.097531
20	-0.256883	-2.9402	0.00194
21	0.006843	0.0783	0.468846

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.309815 & -3.546 & 0.000272 \tabularnewline
2 & -0.000701 & -0.008 & 0.496806 \tabularnewline
3 & -0.074718 & -0.8552 & 0.197005 \tabularnewline
4 & -0.166761 & -1.9087 & 0.029247 \tabularnewline
5 & -0.015146 & -0.1734 & 0.431319 \tabularnewline
6 & 0.018288 & 0.2093 & 0.417265 \tabularnewline
7 & -0.088086 & -1.0082 & 0.157611 \tabularnewline
8 & -0.133888 & -1.5324 & 0.063916 \tabularnewline
9 & 0.156405 & 1.7901 & 0.03787 \tabularnewline
10 & -0.05875 & -0.6724 & 0.251251 \tabularnewline
11 & -0.052428 & -0.6001 & 0.274749 \tabularnewline
12 & -0.115013 & -1.3164 & 0.095172 \tabularnewline
13 & 0.059956 & 0.6862 & 0.246893 \tabularnewline
14 & 0.004318 & 0.0494 & 0.48033 \tabularnewline
15 & 0.036587 & 0.4188 & 0.338041 \tabularnewline
16 & -0.086599 & -0.9912 & 0.161715 \tabularnewline
17 & -0.027835 & -0.3186 & 0.375275 \tabularnewline
18 & 0.019117 & 0.2188 & 0.41357 \tabularnewline
19 & -0.113792 & -1.3024 & 0.097531 \tabularnewline
20 & -0.256883 & -2.9402 & 0.00194 \tabularnewline
21 & 0.006843 & 0.0783 & 0.468846 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27651&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]-0.309815[/C][C]-3.546[/C][C]0.000272[/C][/ROW]
[ROW][C]2[/C][C]-0.000701[/C][C]-0.008[/C][C]0.496806[/C][/ROW]
[ROW][C]3[/C][C]-0.074718[/C][C]-0.8552[/C][C]0.197005[/C][/ROW]
[ROW][C]4[/C][C]-0.166761[/C][C]-1.9087[/C][C]0.029247[/C][/ROW]
[ROW][C]5[/C][C]-0.015146[/C][C]-0.1734[/C][C]0.431319[/C][/ROW]
[ROW][C]6[/C][C]0.018288[/C][C]0.2093[/C][C]0.417265[/C][/ROW]
[ROW][C]7[/C][C]-0.088086[/C][C]-1.0082[/C][C]0.157611[/C][/ROW]
[ROW][C]8[/C][C]-0.133888[/C][C]-1.5324[/C][C]0.063916[/C][/ROW]
[ROW][C]9[/C][C]0.156405[/C][C]1.7901[/C][C]0.03787[/C][/ROW]
[ROW][C]10[/C][C]-0.05875[/C][C]-0.6724[/C][C]0.251251[/C][/ROW]
[ROW][C]11[/C][C]-0.052428[/C][C]-0.6001[/C][C]0.274749[/C][/ROW]
[ROW][C]12[/C][C]-0.115013[/C][C]-1.3164[/C][C]0.095172[/C][/ROW]
[ROW][C]13[/C][C]0.059956[/C][C]0.6862[/C][C]0.246893[/C][/ROW]
[ROW][C]14[/C][C]0.004318[/C][C]0.0494[/C][C]0.48033[/C][/ROW]
[ROW][C]15[/C][C]0.036587[/C][C]0.4188[/C][C]0.338041[/C][/ROW]
[ROW][C]16[/C][C]-0.086599[/C][C]-0.9912[/C][C]0.161715[/C][/ROW]
[ROW][C]17[/C][C]-0.027835[/C][C]-0.3186[/C][C]0.375275[/C][/ROW]
[ROW][C]18[/C][C]0.019117[/C][C]0.2188[/C][C]0.41357[/C][/ROW]
[ROW][C]19[/C][C]-0.113792[/C][C]-1.3024[/C][C]0.097531[/C][/ROW]
[ROW][C]20[/C][C]-0.256883[/C][C]-2.9402[/C][C]0.00194[/C][/ROW]
[ROW][C]21[/C][C]0.006843[/C][C]0.0783[/C][C]0.468846[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27651&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27651&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	-0.309815	-3.546	0.000272
2	-0.000701	-0.008	0.496806
3	-0.074718	-0.8552	0.197005
4	-0.166761	-1.9087	0.029247
5	-0.015146	-0.1734	0.431319
6	0.018288	0.2093	0.417265
7	-0.088086	-1.0082	0.157611
8	-0.133888	-1.5324	0.063916
9	0.156405	1.7901	0.03787
10	-0.05875	-0.6724	0.251251
11	-0.052428	-0.6001	0.274749
12	-0.115013	-1.3164	0.095172
13	0.059956	0.6862	0.246893
14	0.004318	0.0494	0.48033
15	0.036587	0.4188	0.338041
16	-0.086599	-0.9912	0.161715
17	-0.027835	-0.3186	0.375275
18	0.019117	0.2188	0.41357
19	-0.113792	-1.3024	0.097531
20	-0.256883	-2.9402	0.00194
21	0.006843	0.0783	0.468846

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

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