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Motivated by empirical features that characterize cryptocurrency volatility data, the authors develop a forecasting strategy that can account for both model uncertainty and heteroskedasticity of unknown form. The theoretical investigation establishes the asymptotic optimality of the proposed heteroskedastic model averaging heterogeneous autoregressive (H-MAHAR) estimator under mild conditions. The authors additionally examine the convergence rate of the estimated weights of the proposed H-MAHAR estimator. This analysis sheds new light on the asymptotic properties of the least squares model averaging estimator under alternative complicated data generating processes (DGPs). To examine the performance of the H-MAHAR estimator, the authors conduct an out-of-sample forecasting application involving 22 different cryptocurrency assets. The results emphasize the importance of accounting for both model uncertainty and heteroskedasticity in practice.

Bagging (bootstrap aggregating) is a smoothing method to improve predictive ability under the presence of parameter estimation uncertainty and model uncertainty. In Lee and Yang (2006), we examined how (equal-weighted and BMA-weighted) bagging works for one-step-ahead binary prediction with an asymmetric cost function for time series, where we considered simple cases with particular choices of a linlin tick loss function and an algorithm to estimate a linear quantile regression model. In the present chapter, we examine how bagging predictors work with different aggregating (averaging) schemes, for multi-step forecast horizons, with a general class of tick loss functions, with different estimation algorithms, for nonlinear quantile regression models, and for different data frequencies. Bagging quantile predictors are constructed via (weighted) averaging over predictors trained on bootstrapped training samples, and bagging binary predictors are conducted via (majority) voting on predictors trained on the bootstrapped training samples. We find that median bagging and trimmed-mean bagging can alleviate the problem of extreme predictors from bootstrap samples and have better performance than equally weighted bagging predictors; that bagging works better at longer forecast horizons; that bagging works well with highly nonlinear quantile regression models (e.g., artificial neural network), and with general tick loss functions. We also find that the performance of bagging may be affected by using different quantile estimation algorithms (in small samples, even if the estimation is consistent) and by using different frequencies of time series data.

I review the burgeoning literature on applications of Markov regime switching models in empirical finance. In particular, distinct attention is devoted to the ability of Markov Switching models to fit the data, filter unknown regimes and states on the basis of the data, to allow a powerful tool to test hypotheses formulated in light of financial theories, and to their forecasting performance with reference to both point and density predictions. The review covers papers concerning a multiplicity of sub-fields in financial economics, ranging from empirical analyses of stock returns, the term structure of default-free interest rates, the dynamics of exchange rates, as well as the joint process of stock and bond returns.

Good market timing skills can be an important factor contributing to hedge funds’ outperformance. In this chapter, we use a unique semiparametric panel data model capable of providing consistent short period estimates of the return correlations with three market factors for a sample of Long/Short equity hedge funds. We find evidence of significant market timing ability by fund managers around market crisis periods. Studying the behavior of individual fund managers, we show that at the 10% significance level, 17.12% of funds exhibit good linear timing skills and 21.32% of funds possess some level of good nonlinear market timing skills. Further, we find that market timing strategies of hedge funds are different in good and bad markets, and that a significant number of managers behave more conservatively when the market return is expected to be far above average and more aggressively when the market return is expected to be far below average. We find that good market timers are also likely to possess good stock selection skills.

This survey focuses on two families of nonlinear vector time series models, the family of vector threshold regression (VTR) models and that of vector smooth transition regression (VSTR) models. These two model classes contain incomplete models in the sense that strongly exogeneous variables are allowed in the equations. The emphasis is on stationary models, but the considerations also include nonstationary VTR and VSTR models with cointegrated variables. Model specification, estimation and evaluation is considered, and the use of the models illustrated by macroeconomic examples from the literature.

Firms with linear pricing offer their customers the same price for each unit of a good or service. Anything else is nonlinear pricing. Nonlinear pricing in imperfect markets indicates a fundamental asymmetry in information between firms and consumers. Consumers are commonly expected to exhibit quality- or quantity-preference differences and have different reservation values for different product attributes. The firms, however, cannot observe consumers' preferences. When complete information regarding preferences is not observable, nonlinear pricing strategies with firms offering a menu or schedule of prices allow consumers to sort themselves according to their own preferences, resulting in market segmentation.

I survey applications of Markov switching models to the asset pricing and portfolio choice literatures. In particular, I discuss the potential that Markov switching models have to fit financial time series and at the same time provide powerful tools to test hypotheses formulated in the light of financial theories, and to generate positive economic value, as measured by risk-adjusted performances, in dynamic asset allocation applications. The chapter also reviews the role of Markov switching dynamics in modern asset pricing models in which the no-arbitrage principle is used to characterize the properties of the fundamental pricing measure in the presence of regimes.