Both stochastic dominance and Omegaratio can be used to examine whether the market is efficient, whether there is any arbitrage opportunity in the market and whether there is any anomaly in the market. In this paper, we first study the relationship between stochastic dominance and the Omega ratio. We find that second-order stochastic dominance (SD) and/or second-order risk-seeking SD (RSD) alone for any two prospects is not sufficient to imply Omega ratio dominance insofar that the Omega ratio of one asset is always greater than that of the other one. We extend the theory of risk measures by proving that the preference of second-order SD implies the preference of the corresponding Omega ratios only when the return threshold is less than the mean of the higher return asset. On the other hand, the preference of the second-order RSD implies the preference of the corresponding Omega ratios only when the return threshold is larger than the mean of the smaller return asset. Nonetheless, first-order SD does imply Omega ratio dominance. Thereafter, we apply the theory developed in this paper to examine the relationship between property size and property investment in the Hong Kong real estate market. We conclude that the Hong Kong real estate market is not efficient and there are expected arbitrage opportunities and anomalies in the Hong Kong real estate market. Our findings are useful for investors and policy makers in real estate.
Summary
In modelling volatility in financial time series, the double‐threshold autoregressive conditional heteroscedastic (DTARCH) model has been demonstrated as a useful variant of the autoregressive conditional heteroscedastic (ARCH) models. In this paper, we propose a weighted composite quantile regression method for simultaneously estimating the autoregressive parameters and the ARCH parameters in the DTARCH model. This method involves a sequence of weights and takes a data‐driven weighting scheme to maximize the asymptotic efficiency of the estimators. Under regularity conditions, we establish asymptotic distributions of the proposed estimators for a variety of heavy‐ or light‐tailed error distributions. Simulations are conducted to compare the performance of different estimators, and the proposed approach is used to analyse the daily S&P 500 Composite index, both of which endorse our theoretical results.
Both stochastic dominance and Omegaratio can be used to examine whether the market is efficient, whether there is any arbitrage opportunity in the market and whether there is any anomaly in the market. In this paper, we first study the relationship between stochastic dominance and the Omega ratio. We find that second-order stochastic dominance (SD) and/or second-order risk-seeking SD (RSD) alone for any two prospects is not sufficient to imply Omega ratio dominance insofar that the Omega ratio of one asset is always greater than that of the other one. We extend the theory of risk measures by proving that the preference of second-order SD implies the preference of the corresponding Omega ratios only when the return threshold is less than the mean of the higher return asset. On the other hand, the preference of the second-order RSD implies the preference of the corresponding Omega ratios only when the return threshold is larger than the mean of the smaller return asset. Nonetheless, first-order SD does imply Omega ratio dominance. Thereafter, we apply the theory developed in this paper to examine the relationship between property size and property investment in the Hong Kong real estate market. We conclude that the Hong Kong real estate market is not efficient and there are expected arbitrage opportunities and anomalies in the Hong Kong real estate market. Our findings are useful for investors and policy makers in real estate.
Key wo& and phrases: Backfitting algorithm; generalized likelihood ratio; local polynomial regression; Wilks phenomenon.MSC 2ooO: Primary 62607; secondary 62G 10,621 12.Abstracr: Semiparametric additive models (SAMs) are very useful in multivariate nonparametric regression. In this paper, the authors study nonparametric testing problems for the nonparametric components of SAMs. Using the backfitting algorithm and the local polynomial smoothing technique. they extend to SAMs the generalized likelihood ratio tests of Fan & Jiang (2005). The authors show that the proposed tests possess the Wilks-type property and that they can detect alternatives nearing the null hypothesis with a rate arbitrarily close to root-n while error distributions are unspecified. They report simulations which demonstrate the Wilks phenomenon and the powers of their tests. They illustrate the performance of their approach by simulation and using the Boston housing data set.etude de tests du rapport des vraisernblances generalises perrnettant d'eprouver la structure des rnodeles additifs sernipararnetriques tecter des conue-hypothbses s'approchant de I'hypothbse nulle A un taux arbitrairement proche de radical n, peu importe la loi des erreurs. Us font &at de simulations illustrant le phCnombne de Wilks et la puissance de leurs tests. 11s tvaluent la performance de leur approche 1 I'aide de simulations et d'un jeu de donn6es sur la valeur des propriCt6s Boston.
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