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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 02 Dec 2008 11:11:32 -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/t12282415210024xirfrg8qlp1.htm/, Retrieved Tue, 28 May 2024 09:13:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28184, Retrieved Tue, 28 May 2024 09:13:23 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

173

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

F     [(Partial) Autocorrelation Function] [] [2008-12-02 14:36:59] [b53e8d20687f12ca59f39c9b7c3a629a]
F         [(Partial) Autocorrelation Function] [Q6] [2008-12-02 18:11:32] [d41d8cd98f00b204e9800998ecf8427e] [Current]

Feedback Forum

2008-12-03 19:32:26 [407693b66d7f2e0b350979005057872d] [reply] 
We zien hier als we differentiëren door de kleine d op 1 te zetten is het langzaam dalens patroon weg.  Een langzaam dalend patroon in de ACF. 
Als we voor  grote d ook nog eens een 1 invullen dan is de trend helemaal weggewerkt.  We hebben de reeks stationair gemaakt.   
Bij de VRM gaan we op zoek naar de kleinste varantie door kleine en grote d te differentiëren.  152.689254257193 is de kleinste waarde voor de variantie.   
Die is de spectraalanalyse zonder dat we de parameter veranderd hebben.  We zien regelmatige golfbewegingen op de grafiek, sterke pieken met lage frequenties.  De lnge termijn trend heeft een belangrijk effect. Bij het cumulatief periodogram zien we een steile grafiek met lange termijn trend met nog eens een trapfunctie in de grafiek.   
Als we de kleine d op 1 zetten hebben we geen dalende grafiek meer.  De stijging in het cumulatief periodogram is zeer groot we spreken hier van significante stijgingen.   
Als we de grote d op 1 zetten zien we gen duidelijke trapbeweging meer dse seizonale trend is helemaal  verdwenen.   
2008-12-04 18:48:07 [c97d2ae59c98cf77a04815c1edffab5a] [reply] 
we hebben hier gedifferentieerd met d=1 
je ziet duidelijk dat de lange termijn trend verdwenen is, maar de seizoenaliteit is nog altijd aanwezig(dalend patroon). 
dit was ook duidelijker geweest als je time lags= 60 had ingesteld. 
we moeten dus nog seizoenaal differentiëren D=1

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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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28184&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28184&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28184&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	'George Udny Yule' @ 72.249.76.132

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=28184&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=28184&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28184&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=28184&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=28184&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28184&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 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

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