Joint and marginal specification tests for conditional mean and variance models

This article proposes a class of joint and marginal spectral diagnostic tests for parametric conditional means and variances of linear and nonlinear time series models. The use of joint and marginal tests is motivated from the fact that marginal tests for the conditional variance may lead to misleading conclusions when the conditional mean is misspecified. The new tests are based on a generalized spectral approach and do not need to choose a lag order depending on the sample size or to smooth the data. Moreover, the proposed tests are robust to higher order dependence of unknown form, in particular to conditional skewness and kurtosis. It turns out that the asymptotic null distributions of the new tests depend on the data generating process. Hence, we implement the tests with the assistance of a wild bootstrap procedure. A simulation study compares the finite sample performance of the proposed and competing tests, and shows that our tests can play a valuable role in time series modeling. Finally, an application to the S&P 500 highlights the merits of our approach.     

Modelling dependence using skew t copulas: Bayesian inference and applications

We construct a copula from the skew t distribution of Sahu et al. ( 2003 ). This copula can capture asymmetric and extreme dependence between variables, and is one of the few copulas that can do so and still be used in high dimensions effectively. However, it is difficult to estimate the copula model by maximum likelihood when the multivariate dimension is high, or when some or all of the marginal distributions are discrete‐valued, or when the parameters in the marginal distributions and copula are estimated jointly. We therefore propose a Bayesian approach that overcomes all these problems. The computations are undertaken using a Markov chain Monte Carlo simulation method which exploits the conditionally Gaussian representation of the skew t distribution. We employ the approach in two contemporary econometric studies. The first is the modelling of regional spot prices in the Australian electricity market. Here, we observe complex non‐Gaussian margins and nonlinear inter‐regional dependence. Accurate characterization of this dependence is important for the study of market integration and risk management purposes. The second is the modelling of ordinal exposure measures for 15 major websites. Dependence between websites is important when measuring the impact of multi‐site advertising campaigns. In both cases the skew t copula substantially outperforms symmetric elliptical copula alternatives, demonstrating that the skew t copula is a powerful modelling tool when coupled with Bayesian inference. Copyright © 2010 John Wiley & Sons, Ltd.     

Modeling and forecasting of stock index volatility with APARCH models under ordered restriction

This article examines volatility models for modeling and forecasting the Standard & Poor 500 (S&P 500) daily stock index returns, including the autoregressive moving average, the Taylor and Schwert generalized autoregressive conditional heteroscedasticity (GARCH), the Glosten, Jagannathan and Runkle GARCH and asymmetric power ARCH (APARCH) with the following conditional distributions: normal, Student's t and skewed Student's t‐distributions. In addition, we undertake unit root (augmented Dickey–Fuller and Phillip–Perron) tests, co‐integration test and error correction model. We study the stationary APARCH (p) model with parameters, and the uniform convergence, strong consistency and asymptotic normality are prove under simple ordered restriction. In fitting these models to S&P 500 daily stock index return data over the period 1 January 2002 to 31 December 2012, we found that the APARCH model using a skewed Student's t‐distribution is the most effective and successful for modeling and forecasting the daily stock index returns series. The results of this study would be of great value to policy makers and investors in managing risk in stock markets trading.     

Forecasting daily return densities from intraday data: A multifractal approach

This paper proposes a new approach for estimating and forecasting the moments and probability density function of daily financial returns from intraday data. This is achieved through a new application of the distributional scaling laws for the class of multifractal processes. Density forecasts from the new multifractal approach are typically found to provide substantial improvements in predictive ability over existing forecasting methods for the EUR/USD exchange rate, and are also competitive with existing methods when forecasting the daily return density of the S&P500 and NASDAQ-100 equity index.     

Asymmetry in the jump-size distribution of the S&P 500: Evidence from equity and option markets

This paper studies alternative distributions for the size of price jumps in the S&P 500 index. We introduce a range of new jump-diffusion models and extend popular double-jump specifications that have become ubiquitous in the finance literature. The dynamic properties of these models are tested on both a long time series of S&P 500 returns and a large sample of European vanilla option prices. We discuss the in- and out-of-sample option pricing performance and provide detailed evidence of jump risk premia. Models with double-gamma jump size distributions are found to outperform benchmark models with normally distributed jump sizes.     

A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation

This paper presents a Bayesian approach to bandwidth selection for multivariate kernel regression. A Monte Carlo study shows that under the average squared error criterion, the Bayesian bandwidth selector is comparable to the cross-validation method and clearly outperforms the bootstrapping and rule-of-thumb bandwidth selectors. The Bayesian bandwidth selector is applied to a multivariate kernel regression model that is often used to estimate the state-price density of Arrow–Debreu securities with the S&P 500 index options data and the DAX index options data. The proposed Bayesian bandwidth selector represents a data-driven solution to the problem of choosing bandwidths for the multivariate kernel regression involved in the nonparametric estimation of the state-price density pioneered by Aït-Sahalia and Lo [Aït-Sahalia, Y., Lo, A.W., 1998. Nonparametric estimation of state-price densities implicit in financial asset prices. The Journal of Finance, 53, 499, 547.]     

Estimation and model selection of semiparametric multivariate survival functions under general censorship

We study estimation and model selection of semiparametric models of multivariate survival functions for censored data, which are characterized by possibly misspecified parametric copulas and nonparametric marginal survivals. We obtain the consistency and root-n$n$ asymptotic normality of a two-step copula estimator to the pseudo-true copula parameter value according to KLIC, and provide a simple consistent estimator of its asymptotic variance, allowing for a first-step nonparametric estimation of the marginal survivals. We establish the asymptotic distribution of the penalized pseudo-likelihood ratio statistic for comparing multiple semiparametric multivariate survival functions subject to copula misspecification and general censorship. An empirical application is provided.     

Modeling non-normal corporate bond yield spreads by copula

This research focuses on modeling for how corporate bond yield spreads are affected by explanatory variables such as equity volatility, interest rate volatility, r, slope, rating, liquidity, coupon rate, and maturity. The existing literature assumes normality and linearity in the analysis, which is not the case in our sample. Thus, through a powerful and flexible copula approach, we study the dependence at the mean of the joint distribution by using the Gaussian copula marginal regression method and the dependence structure at the tails by using various copula functions. To our knowledge, this is the first application of the copula marginal regression model to bond market data. In addition, we employ several copula functions to test for the tail dependence between yield spreads and other explanatory variables. We find stronger tail dependence in the joint upper tail for the relation between equity volatility and yield spreads, among others. This result indicates the positive effect of equity volatility on yield spreads in the upper tail is greater than that in the low tail. This finding should be useful to practitioners, such as investors. By relying on better-fitting, more meaningful statistical models, this paper contributes to the extant literature on how corporate bond yield spreads are determined.     

Markov switching quantile autoregression

This paper considers the location‐scale quantile autoregression in which the location and scale parameters are subject to regime shifts. The regime changes in lower and upper tails are determined by the outcome of a latent, discrete‐state Markov process. The new method provides direct inference and estimate for different parts of a non‐stationary time series distribution. Bayesian inference for switching regimes within a quantile, via a three‐parameter asymmetric Laplace distribution, is adapted and designed for parameter estimation. Using the Bayesian output, the marginal likelihood is readily available for testing the presence and the number of regimes. The simulation study shows that the predictability of regimes and conditional quantiles by using asymmetric Laplace distribution as the likelihood is fairly comparable with the true model distributions. However, ignoring that autoregressive coefficients might be quantile dependent leads to substantial bias in both regime inference and quantile prediction. The potential of this new approach is illustrated in the empirical applications to the US inflation and real exchange rates for asymmetric dynamics and the S&P 500 index returns of different frequencies for financial market risk assessment.     

Bayesian median autoregression for robust time series forecasting

We develop a Bayesian median autoregressive (BayesMAR) model for time series forecasting. The proposed method utilizes time-varying quantile regression at the median, favorably inheriting the robustness of median regression in contrast to the widely used mean-based methods. Motivated by a working Laplace likelihood approach in Bayesian quantile regression, BayesMAR adopts a parametric model bearing the same structure as autoregressive models by altering the Gaussian error to Laplace, leading to a simple, robust, and interpretable modeling strategy for time series forecasting. We estimate model parameters by Markov chain Monte Carlo. Bayesian model averaging is used to account for model uncertainty, including the uncertainty in the autoregressive order, in addition to a Bayesian model selection approach. The proposed methods are illustrated using simulations and real data applications. An application to U.S. macroeconomic data forecasting shows that BayesMAR leads to favorable and often superior predictive performance compared to the selected mean-based alternatives under various loss functions that encompass both point and probabilistic forecasts. The proposed methods are generic and can be used to complement a rich class of methods that build on autoregressive models.     

Smoothly mixing regressions

This paper extends the conventional Bayesian mixture of normals model by permitting state probabilities to depend on observed covariates. The dependence is captured by a simple multinomial probit model. A conventional and rapidly mixing MCMC algorithm provides access to the posterior distribution at modest computational cost. This model is competitive with existing econometric models, as documented in the paper's illustrations. The first illustration studies quantiles of the distribution of earnings of men conditional on age and education, and shows that smoothly mixing regressions are an attractive alternative to nonBayesian quantile regression. The second illustration models serial dependence in the S&P 500 return, and shows that the model compares favorably with ARCH models using out of sample likelihood criteria.     

A fuzzy bi-level method for modeling age-specific migration

Modeling and forecasting international migration are significant research areas since migration forecasts are vital in decision making and policy design regarding economy, security, society, and resource allocation. The methods for modeling and forecasting migration rely on strict subjective or statistical assumptions which may not always be met. In addition, lack of a universally accepted definition of the term “migrant” and the ambiguities in data due to recording and collection systems result in inconsistencies and vagueness in migration modeling. Considering these, in this paper, a fuzzy bi-level age-specific migration modeling method is proposed. The bi-level structure embedded in the model makes use of the well-known Lee-Carter method as well as fuzzy regression, singular value decomposition technique, and hierarchical clustering to reflect the general characteristics of the country of concern together with the distinct emigration and immigration behaviors of the age groups. Bayesian time series models are fitted to the time-variant fuzzy parameters obtained through the proposed method to forecast future migration values. The proposed method is applied on female and male age-specific emigration and immigration counts of Finland for 1990–2010 period and Germany for 1995–2012 period, and the future values are forecasted for 2011–2025 and 2013–2025 respectively. The method is compared with an existing Bayesian approach and the numerical findings display that the proposed fuzzy method is superior to the existing one in modeling and forecasting age-specific migration values within significantly narrower prediction intervals.     

A reexamination of the equity-premium puzzle: A robust non-parametric approach

Recent tests of stochastic dominance of several orders, proposed by Linton, Maasoumi and Whang [Linton, O., Maasoumi, E., & Whang, Y. (2005). Consistent testing for stochastic dominance under general sampling schemes. Review of Economic Studies, 72(3), 735–765], are applied to reexamine the equity-premium puzzle. An advantage of this non-parametric approach is that it provides a framework to assess whether the existence of a premium is due to particular cardinal choices of either the utility function or the underlying returns distribution, or both. The approach is applied to the original Mehra–Prescott data and more recent data that include daily yields on Treasury bonds and daily returns on the S&P500 and the NASDAQ indexes. The empirical results show little evidence of stochastic dominance among the assets investigated. This suggests that the observed equity premium represents compensation for bearing higher risk, taking into account higher-order moments such as skewness and kurtosis. There is some evidence of a reverse puzzle, whereby Treasury bonds stochastically dominate equities at the third order, a result which potentially reflects insufficient compensation to investors for bearing the negative skewness associated with the S&P500 index.     

Statistics of extreme events in risk management: The impact of the subprime and global financial crisis on the German stock market

Given the growing need for managing financial risk and the recent global crisis, risk prediction is a crucial issue in banking and finance. In this paper, we show how recent advances in the statistical analysis of extreme events can provide solid methodological fundamentals for modeling extreme events. Our approach uses self-exciting marked point processes for estimating the tail of loss distributions. The main result is that the time between extreme events plays an important role in the statistical analysis of these events and could therefore be useful to forecast the size and intensity of future extreme events in financial markets. We illustrate this point by measuring the impact of the subprime and global financial crisis on the German stock market in extenso, and briefly as a benchmark in the US stock market. With the help of our fitted models, we backtest the Value at Risk at various quantiles to assess the likeliness of different extreme movements on the DAX, S&P 500 and Nasdaq stock market indices during the crisis. The results show that the proposed models provide accurate risk measures according to the Basel Committee and make better use of the available information.     

Optimal model averaging forecasting in high-dimensional survival analysis

This article considers ultrahigh-dimensional forecasting problems with survival response variables. We propose a two-step model averaging procedure for improving the forecasting accuracy of the true conditional mean of a survival response variable. The first step is to construct a class of candidate models, each with low-dimensional covariates. For this, a feature screening procedure is developed to separate the active and inactive predictors through a marginal Buckley–James index, and to group covariates with a similar index size together to form regression models with survival response variables. The proposed screening method can select active predictors under covariate-dependent censoring, and enjoys sure screening consistency under mild regularity conditions. The second step is to find the optimal model weights for averaging by adapting a delete-one cross-validation criterion, without the standard constraint that the weights sum to one. The theoretical results show that the delete-one cross-validation criterion achieves the lowest possible forecasting loss asymptotically. Numerical studies demonstrate the superior performance of the proposed variable screening and model averaging procedures over existing methods.     

Forecasting the volatility of asset returns: The informational gains from option prices

A new class of forecasting models is proposed that extends the realized GARCH class of models through the inclusion of option prices to forecast the variance of asset returns. The VIX is used to approximate option prices, resulting in a set of cross-equation restrictions on the model’s parameters. The full model is characterized by a nonlinear system of three equations containing asset returns, the realized variance, and the VIX, with estimation of the parameters based on maximum likelihood methods. The forecasting properties of the new class of forecasting models, as well as a number of special cases, are investigated and applied to forecasting the daily S&P500 index realized variance using intra-day and daily data from September 2001 to November 2017. The forecasting results provide strong support for including the realized variance and the VIX to improve variance forecasts, with linear conditional variance models performing well for short-term one-day-ahead forecasts, whereas log-linear conditional variance models tend to perform better for intermediate five-day-ahead forecasts.     

Robust linear static panel data models using ε-contamination

The paper develops a general Bayesian framework for robust linear static panel data models using$\epsilon$-contamination. A two-step approach is employed to derive the conditional type-II maximum likelihood (ML-II) posterior distribution of the coefficients and individual effects. The ML-II posterior means are weighted averages of the Bayes estimator under a base prior and the data-dependent empirical Bayes estimator. Two-stage and three stage hierarchy estimators are developed and their finite sample performance is investigated through a series of Monte Carlo experiments. These include standard random effects as well as Mundlak-type, Chamberlain-type and Hausman–Taylor-type models. The simulation results underscore the relatively good performance of the three-stage hierarchy estimator. Within a single theoretical framework, our Bayesian approach encompasses a variety of specifications while conventional methods require separate estimators for each case.     

Twitter’s daily happiness sentiment,economic policy uncertainty,and stock index fluctuations

This research applies quantile Granger causality and impulse-response analyses to evaluate the causal linkages among Twitter’s daily happiness sentiment, economic policy uncertainty (EPU), and S&P 500 indices across the U.S. stock market cycles. We present notable evidence of bi-directional causality among cyclical components of Twitter’s daily happiness sentiment, economic policy uncertainty, and S&P 500 indices for most quantiles. The causal linkage of Twitter’s daily happiness sentiment and S&P 500 indices identified in this study reconciles the so-called Easterlin Paradox and Easterlin Illusion arguments from previous studies on income-happiness relationship. Moreover, given a high (low) EPU level, the positive (negative) impulse-response effects between the Twitter’s daily happiness sentiment and the S&P 500 indices are justified during a stock market bust cycle, but the signs of these correlations change to negative (positive) during a stock market boom cycle. These findings imply that investors’ hedging strategies can be linked to the surveillance of the Twitter’s daily happiness sentiment index.     

Functional data analysis for volatility

We introduce a functional volatility process for modeling volatility trajectories for high frequency observations in financial markets and describe functional representations and data-based recovery of the process from repeated observations. A study of its asymptotic properties, as the frequency of observed trades increases, is complemented by simulations and an application to the analysis of intra-day volatility patterns of the S&P 500 index. The proposed volatility model is found to be useful to identify recurring patterns of volatility and for successful prediction of future volatility, through the application of functional regression and prediction techniques.