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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 09 Dec 2008 00:25:43 -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/09/t1228807613k59zvjosugmrduh.htm/, Retrieved Fri, 17 May 2024 03:04:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31188, Retrieved Fri, 17 May 2024 03:04:46 +0000

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Estimated Impact

156

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

F     [(Partial) Autocorrelation Function] [step 2 ACF] [2008-12-08 19:48:28] [4300be8b33fd3dcdacd2aa9800ceba23]
F         [(Partial) Autocorrelation Function] [part 2 ACF] [2008-12-09 07:25:43] [541f63fa3157af9df10fc4d202b2a90b] [Current]
-   P       [(Partial) Autocorrelation Function] [Verbeterde versie...] [2008-12-13 13:59:43] [9e54d1454d464f1bf9ee4a54d5d56945] 

Feedback Forum

2008-12-13 13:57:33 [An De Koninck] [reply] 
Hier is inderdaad duidelijk sprake van een lange termijntrend. Af en toe is er wel precies een observatie die de trend wil doorbreken (zie bv lag 12), maar over het geheel gezien is dit een rustig dalende autocorrelatie. 
Het is wel opmerkelijk dat deze trend net wil doorbroken worden op lag 12 en 24. Dit kan seizonaliteit betekenen.  
De student zegt dat de lange termijntrend weggewerkt dan worden door d=1 en D=1 te maken, maar deze parameters zijn al zo ingesteld. Op die manier kan je het dus niet oplossen.  
2008-12-13 14:03:11 [An De Koninck] [reply] 
Ik zie net dat je met de parameters die je bij de VRM had gevonden, niet verdergewerkt hebt. Deze waren reeds d=1 en D=1 dus als je deze parameters had gebruikt had je ineens de lange termijntrend kunnen wegwerken. 
 
Ik heb een nieuwe link aangemaakt, rekening houdend met de parameters gevonden bij de VRM (dus d=1 en D=1): http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/13/t12291769396vl2vztw911oo9s.htm 
 
Hier zie je dat de lange termijntrend verdwenen is.  
Seizonaliteit is echter nog aanwezig. Dit kan je zien in de tweede grafiek (partial autocorrelation). Lag 12 en 24 zijn duidelijk significant.
2008-12-16 07:20:01 [Bonifer Spillemaeckers] [reply] 
De student lost dit goed op. Opnieuw had dit wat uitvoeriger mogen bespreken.  
 
De student had hier de lags op 60 moeten zetten. Zo kun je meer informatie uit de grafiek halen.  
 
We gaan hier dus kijken naar de autocorrelation function. Bij deze functie zet je eerst de parameters d en D gelijk aan 0. Er is hier duidelijk een lange termijn trend waarneembaar. Dit merkt de student goed op. Bij lag 12,24,36,48,60 zien we telkens opnieuw een kleine stijging. Dit kan wel eens te maken hebben met seizoenaliteit.  
 
http://www.freestatistics.org/blog/date/2008/Dec/15/t1229381091t0xvl0ao9wi88qs.htm  
 
Om de lange termijn trend uit de reeks te halen, stellen we d=1. Hier werk je dus met de parameters d=1 en D=0. Doordat we d hebben gelijkgesteld aan 1, zien we duidelijk dat de LT-trend verdwenen is. Hier kunnen we nu ook met zekerheid vaststellen dat er seizoenaliteit aanwezig is (te zien bij lag 12,24,36,48,60).  
 
http://www.freestatistics.org/blog/date/2008/Dec/15/t1229381212nu1u9w88mdsriy0.htm  
 
Om de seizoenaliteit uit de reeks te halen, stellen we D=1. Hier werk je dus met de parameters d=1 en D=1. Er valt nu duidelijk te bemerken dat er geen LT-trend en seizoenaliteit meer zichtbaar is.  
 
http://www.freestatistics.org/blog/date/2008/Dec/15/t1229381305fz3rpjl29mw45q3.htm

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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=31188&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=31188&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31188&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	0.958297	18.483	0
2	0.915218	17.6521	0
3	0.883412	17.0386	0
4	0.870088	16.7816	0
5	0.861735	16.6205	0
6	0.832367	16.0541	0
7	0.812153	15.6642	0
8	0.775095	14.9495	0
9	0.745592	14.3805	0
10	0.734652	14.1695	0
11	0.739154	14.2563	0
12	0.743705	14.3441	0
13	0.693188	13.3697	0
14	0.64416	12.4241	0
15	0.611393	11.7921	0
16	0.599793	11.5684	0
17	0.597409	11.5224	0
18	0.577954	11.1472	0
19	0.568953	10.9736	0
20	0.543776	10.488	0
21	0.526232	10.1496	0
22	0.525701	10.1394	0
23	0.537712	10.371	0
24	0.551354	10.6341	0
25	0.512849	9.8915	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.958297 & 18.483 & 0 \tabularnewline
2 & 0.915218 & 17.6521 & 0 \tabularnewline
3 & 0.883412 & 17.0386 & 0 \tabularnewline
4 & 0.870088 & 16.7816 & 0 \tabularnewline
5 & 0.861735 & 16.6205 & 0 \tabularnewline
6 & 0.832367 & 16.0541 & 0 \tabularnewline
7 & 0.812153 & 15.6642 & 0 \tabularnewline
8 & 0.775095 & 14.9495 & 0 \tabularnewline
9 & 0.745592 & 14.3805 & 0 \tabularnewline
10 & 0.734652 & 14.1695 & 0 \tabularnewline
11 & 0.739154 & 14.2563 & 0 \tabularnewline
12 & 0.743705 & 14.3441 & 0 \tabularnewline
13 & 0.693188 & 13.3697 & 0 \tabularnewline
14 & 0.64416 & 12.4241 & 0 \tabularnewline
15 & 0.611393 & 11.7921 & 0 \tabularnewline
16 & 0.599793 & 11.5684 & 0 \tabularnewline
17 & 0.597409 & 11.5224 & 0 \tabularnewline
18 & 0.577954 & 11.1472 & 0 \tabularnewline
19 & 0.568953 & 10.9736 & 0 \tabularnewline
20 & 0.543776 & 10.488 & 0 \tabularnewline
21 & 0.526232 & 10.1496 & 0 \tabularnewline
22 & 0.525701 & 10.1394 & 0 \tabularnewline
23 & 0.537712 & 10.371 & 0 \tabularnewline
24 & 0.551354 & 10.6341 & 0 \tabularnewline
25 & 0.512849 & 9.8915 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31188&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]0.958297[/C][C]18.483[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.915218[/C][C]17.6521[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.883412[/C][C]17.0386[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.870088[/C][C]16.7816[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.861735[/C][C]16.6205[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.832367[/C][C]16.0541[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.812153[/C][C]15.6642[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.775095[/C][C]14.9495[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.745592[/C][C]14.3805[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.734652[/C][C]14.1695[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.739154[/C][C]14.2563[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.743705[/C][C]14.3441[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.693188[/C][C]13.3697[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.64416[/C][C]12.4241[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.611393[/C][C]11.7921[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.599793[/C][C]11.5684[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.597409[/C][C]11.5224[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.577954[/C][C]11.1472[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.568953[/C][C]10.9736[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.543776[/C][C]10.488[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.526232[/C][C]10.1496[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.525701[/C][C]10.1394[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.537712[/C][C]10.371[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]0.551354[/C][C]10.6341[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]0.512849[/C][C]9.8915[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31188&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31188&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	0.958297	18.483	0
2	0.915218	17.6521	0
3	0.883412	17.0386	0
4	0.870088	16.7816	0
5	0.861735	16.6205	0
6	0.832367	16.0541	0
7	0.812153	15.6642	0
8	0.775095	14.9495	0
9	0.745592	14.3805	0
10	0.734652	14.1695	0
11	0.739154	14.2563	0
12	0.743705	14.3441	0
13	0.693188	13.3697	0
14	0.64416	12.4241	0
15	0.611393	11.7921	0
16	0.599793	11.5684	0
17	0.597409	11.5224	0
18	0.577954	11.1472	0
19	0.568953	10.9736	0
20	0.543776	10.488	0
21	0.526232	10.1496	0
22	0.525701	10.1394	0
23	0.537712	10.371	0
24	0.551354	10.6341	0
25	0.512849	9.8915	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.958297	18.483	0
2	-0.038138	-0.7356	0.231227
3	0.116008	2.2375	0.012923
4	0.207345	3.9991	3.8e-05
5	0.071295	1.3751	0.084967
6	-0.216629	-4.1782	1.8e-05
7	0.177843	3.4301	0.000336
8	-0.280159	-5.4035	0
9	0.051585	0.9949	0.160206
10	0.221443	4.271	1.2e-05
11	0.189049	3.6462	0.000152
12	-0.045031	-0.8685	0.192833
13	-0.550158	-10.6111	0
14	0.048685	0.939	0.17417
15	0.139152	2.6839	0.003802
16	0.058966	1.1373	0.128074
17	0.145015	2.797	0.002713
18	0.056415	1.0881	0.13863
19	0.089168	1.7198	0.04315
20	-0.085304	-1.6453	0.050378
21	0.010706	0.2065	0.418258
22	0.020453	0.3945	0.346725
23	-0.016396	-0.3162	0.376
24	0.056489	1.0895	0.138315
25	-0.235006	-4.5326	4e-06

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.958297 & 18.483 & 0 \tabularnewline
2 & -0.038138 & -0.7356 & 0.231227 \tabularnewline
3 & 0.116008 & 2.2375 & 0.012923 \tabularnewline
4 & 0.207345 & 3.9991 & 3.8e-05 \tabularnewline
5 & 0.071295 & 1.3751 & 0.084967 \tabularnewline
6 & -0.216629 & -4.1782 & 1.8e-05 \tabularnewline
7 & 0.177843 & 3.4301 & 0.000336 \tabularnewline
8 & -0.280159 & -5.4035 & 0 \tabularnewline
9 & 0.051585 & 0.9949 & 0.160206 \tabularnewline
10 & 0.221443 & 4.271 & 1.2e-05 \tabularnewline
11 & 0.189049 & 3.6462 & 0.000152 \tabularnewline
12 & -0.045031 & -0.8685 & 0.192833 \tabularnewline
13 & -0.550158 & -10.6111 & 0 \tabularnewline
14 & 0.048685 & 0.939 & 0.17417 \tabularnewline
15 & 0.139152 & 2.6839 & 0.003802 \tabularnewline
16 & 0.058966 & 1.1373 & 0.128074 \tabularnewline
17 & 0.145015 & 2.797 & 0.002713 \tabularnewline
18 & 0.056415 & 1.0881 & 0.13863 \tabularnewline
19 & 0.089168 & 1.7198 & 0.04315 \tabularnewline
20 & -0.085304 & -1.6453 & 0.050378 \tabularnewline
21 & 0.010706 & 0.2065 & 0.418258 \tabularnewline
22 & 0.020453 & 0.3945 & 0.346725 \tabularnewline
23 & -0.016396 & -0.3162 & 0.376 \tabularnewline
24 & 0.056489 & 1.0895 & 0.138315 \tabularnewline
25 & -0.235006 & -4.5326 & 4e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31188&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]0.958297[/C][C]18.483[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.038138[/C][C]-0.7356[/C][C]0.231227[/C][/ROW]
[ROW][C]3[/C][C]0.116008[/C][C]2.2375[/C][C]0.012923[/C][/ROW]
[ROW][C]4[/C][C]0.207345[/C][C]3.9991[/C][C]3.8e-05[/C][/ROW]
[ROW][C]5[/C][C]0.071295[/C][C]1.3751[/C][C]0.084967[/C][/ROW]
[ROW][C]6[/C][C]-0.216629[/C][C]-4.1782[/C][C]1.8e-05[/C][/ROW]
[ROW][C]7[/C][C]0.177843[/C][C]3.4301[/C][C]0.000336[/C][/ROW]
[ROW][C]8[/C][C]-0.280159[/C][C]-5.4035[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.051585[/C][C]0.9949[/C][C]0.160206[/C][/ROW]
[ROW][C]10[/C][C]0.221443[/C][C]4.271[/C][C]1.2e-05[/C][/ROW]
[ROW][C]11[/C][C]0.189049[/C][C]3.6462[/C][C]0.000152[/C][/ROW]
[ROW][C]12[/C][C]-0.045031[/C][C]-0.8685[/C][C]0.192833[/C][/ROW]
[ROW][C]13[/C][C]-0.550158[/C][C]-10.6111[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.048685[/C][C]0.939[/C][C]0.17417[/C][/ROW]
[ROW][C]15[/C][C]0.139152[/C][C]2.6839[/C][C]0.003802[/C][/ROW]
[ROW][C]16[/C][C]0.058966[/C][C]1.1373[/C][C]0.128074[/C][/ROW]
[ROW][C]17[/C][C]0.145015[/C][C]2.797[/C][C]0.002713[/C][/ROW]
[ROW][C]18[/C][C]0.056415[/C][C]1.0881[/C][C]0.13863[/C][/ROW]
[ROW][C]19[/C][C]0.089168[/C][C]1.7198[/C][C]0.04315[/C][/ROW]
[ROW][C]20[/C][C]-0.085304[/C][C]-1.6453[/C][C]0.050378[/C][/ROW]
[ROW][C]21[/C][C]0.010706[/C][C]0.2065[/C][C]0.418258[/C][/ROW]
[ROW][C]22[/C][C]0.020453[/C][C]0.3945[/C][C]0.346725[/C][/ROW]
[ROW][C]23[/C][C]-0.016396[/C][C]-0.3162[/C][C]0.376[/C][/ROW]
[ROW][C]24[/C][C]0.056489[/C][C]1.0895[/C][C]0.138315[/C][/ROW]
[ROW][C]25[/C][C]-0.235006[/C][C]-4.5326[/C][C]4e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31188&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31188&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	0.958297	18.483	0
2	-0.038138	-0.7356	0.231227
3	0.116008	2.2375	0.012923
4	0.207345	3.9991	3.8e-05
5	0.071295	1.3751	0.084967
6	-0.216629	-4.1782	1.8e-05
7	0.177843	3.4301	0.000336
8	-0.280159	-5.4035	0
9	0.051585	0.9949	0.160206
10	0.221443	4.271	1.2e-05
11	0.189049	3.6462	0.000152
12	-0.045031	-0.8685	0.192833
13	-0.550158	-10.6111	0
14	0.048685	0.939	0.17417
15	0.139152	2.6839	0.003802
16	0.058966	1.1373	0.128074
17	0.145015	2.797	0.002713
18	0.056415	1.0881	0.13863
19	0.089168	1.7198	0.04315
20	-0.085304	-1.6453	0.050378
21	0.010706	0.2065	0.418258
22	0.020453	0.3945	0.346725
23	-0.016396	-0.3162	0.376
24	0.056489	1.0895	0.138315
25	-0.235006	-4.5326	4e-06

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 ;

Parameters (R input):

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