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Articles • Trends Comput. Appl. Math. 23 (2) • May-Aug 2022 • https://doi.org/10.5540/tcam.2022.023.02.00283 copy

Análise do Valor-p Determinado pela Estatística τ na Aplicação do Teste de Dickey-Fuller Aumentado

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

In this paper we evaluate how much influence the number of selected lags has in the p-value obtained from the statistic considered in an augmented Dickey-Fuller test (ADF). Three experiments with different series sizes were carried out considering the presence (or not) of a constant and/or trend, and also different number of lags. Autoregressive models (AR1) are used in the data generating process through the Monte Carlo method, considering different values for the coefficient associated with the first lag. After the application of the ADF test, we calculate the proportion of times when the null hypothesis was rejected in each scenario, and perform an analysis of variance (considering chi-square statistic) to verify the influence of the number of selected lags in the p-value. Results show that if a unit root is verified, then the test presents a good performance, regardless of the number of lags. However, the same was not observed in cases where the time series does not present a unit root.

Keywords:
stationarity; unit root; time series; ADF test

T	Constante	Constante e tendência	Sem constante e sem tendência
30	0,04011	0,04091	0,05555
	(0,00411)	(0,00630)	(0,00446)
50	0,3085	0,00862	0,04723
	(0,00428)	(0,00409)	(0,00588)
100	0,01506	0,00435	0,05918
	(0,00282)	(0,00154)	(0,00484)

T	Fonte de variação	gl	SQ	$χ_{c a l c}^{2}$	valor-p
30	Defasagens	10	0,00146	5,84	0,0817
	Componentes	2	0,00927	37,08	<0,0001
50	Defasagens	12	0,00235	9,40	0,0869
	Componentes	2	0,11075	443,00	<0,0001
100	Defasagens	14	0,00192	7,68	0,0478
	Componentes	2	0,25189	1.007,56	<0,0001

T	ϕ	Constante	Constante e tendência	Sem constante e sem tendência	Total
	0,95	0,05736	0,04554	0,28318	0,12870
		(0,00642)	(0,00706)	(0,10915)	(0,12681)
	0,75	0,27339	0,07782	0,53309	0,29509
30		(0,27055)	(0,04468)	(0,33477)	(0,30720)
	0,55	0,33618	0,21045	0,54191	0,36285
		(0,35251)	(0,25953)	(0,35732)	(0,35401)
	Total	0,22248	0,11127	0,45273	0,26216
		(0,27648)	(0,16413)	(0,30574)	(0,29104)
	0,95	0,06431	0,08477	0,35623	0,16844
		(0,01212)	(0,02396)	(0,12262)	(0,15214)
	0,75	0,37669	0,26400	0,67008	0,4369
50		(0,32106)	(0,23523)	(0,28933)	(0,32639)
	0,55	0,43977	0,41300	0,70185	0,51821
		(0,36722)	(0,35827)	(0,29068)	(0,35669)
	Total	0,29359	0,25392	0,57605	0,37452
		(0,32068)	(0,27689)	(0,28781)	(0,32663)
	0,95	0,10607	0,21727	0,54647	0,28993
		(0,02086)	(0,06903)	(0,11764)	(0,20813)
	0,75	0,63773	0,56573	0,89433	0,69927
100		(0,28566)	(0,27417)	(0,13363)	(0,28273)
	0,55	0,71113	0,69440	0,92780	0,77778
		(0,28211)	(0,28655)	(0,10584)	(0,25899)
	Total	0,58753	0,56950	0,88103	0,59694
		(0,31349)	(0,28203)	(0,12968)	(0,32952)

T	Fonte de variação	gl	SQ	$χ_{c a l c}^{2}$	valor-p
	Defasagens	10	5,068	20.272	<0,0001
	Componente	2	3,549	14.196	<0,0001
30	Coeficiente	2	1,640	6.560	<0,0001
	Componente × Coeficiente	4	0,212	848	<0,0001
	Defasagens × Componente	20	0,860	3.440	<0,0001
	Defasagens × Coeficiente	20	1,912	7.648	<0,0001
	Defasagens	12	8,585	34.340	<0,0001
50	Componente	2	3,874	15.496	<0,0001
	Coeficiente	2	4,328	17.312	<0,0001
	Componente × Coeficiente	4	0,157	628	<0,0001
	Defasagens × Componente	20	0,258	1.032	<0,0001
	Defasagens × Coeficiente	20	2,767	11.068	<0,0001
	Defasagens	14	7,546	30.184	<0,0001
	Componente	2	4,172	16.688	<0,0001
100	Coeficiente	2	10,179	40.716	<0,0001
	Componente × Coeficiente	4	0,328	1.312	<0,0001
	Defasagens × Componente	20	0,298	1.192	<0,0001
	Defasagens × Coeficiente	20	1,649	6.596	<0,0001

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