Hualde Bilbao, Javier
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Hualde Bilbao
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Javier
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Economía
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INARBE. Institute for Advanced Research in Business and Economics
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Publication Open Access A novel test of economic convergence in time series(Springer, 2025-01-03) Hualde Bilbao, Javier; Olmo, José; Economía; Ekonomia; Institute for Advanced Research in Business and Economics - INARBEThis paper proposes a novel test for the hypothesis of economic convergence. We extend the standard definition of convergence based on the parity condition and say that two economies converge if the time series of economic output are positively cointegrated and cotrended. With this definition in place, our main contribution is to propose a test of positive cointegration that does not require estimation of the cointegrating relationship, but is able to differentiate between positive and negative cointegration. Once the possibility of positive cointegration is established in a first stage, we test for cotrending in a second stage. Our sequential proposal enjoys an excellent performance in small samples due to the fast convergence of our novel test statistic under positive cointegration. This is illustrated in a simulation exercise where we report clear evidence showing the outperformance of our proposed method compared to existing methods in the related literature that test for economic convergence using cointegration methods. The results are particularly strong for sample sizes between 25 and 50 observations. The empirical application testing for economic convergence between the G7 group of countries over the period 1990–2022 confirms these findings.Publication Open Access Truncated sum-of-squares estimation of fractional time series models with generalized power law trend(Institute of Mathematical Statistics, 2022) Hualde Bilbao, Javier; Nielsen, Morten Ørregaard; Economía; EkonomiaWe consider truncated (or conditional) sum-of-squares estimation of a parametric fractional time series model with an additive deterministic structure. The latter consists of both a drift term and a generalized power law trend. The memory parameter of the stochastic component and the power parameter of the deterministic trend component are both considered unknown real numbers to be estimated and belonging to arbitrarily large compact sets. Thus, our model captures different forms of nonstationarity and noninvertibility as well as a very flexible deterministic specification. As in related settings, the proof of consistency (which is a prerequisite for proving asymptotic normality) is challenging due to non-uniform convergence of the objective function over a large admissible parameter space and due to the competition between stochastic and deterministic components. As expected, parameter estimates related to the deterministic component are shown to be consistent and asymptotically normal only for parts of the parameter space depending on the relative strength of the stochastic and deterministic components. In contrast, we establish consistency and asymptotic normality of parameter estimates related to the stochastic component for the entire parameter space. Furthermore, the asymptotic distribution of the latter estimates is unaffected by the presence of the deterministic component, even when this is not consistently estimable. We also include Monte Carlo simulations to illustrate our results.