Mixed Hidden Markov Models for Longitudinal Data: An Overview

In this paper we review statistical methods which combine hidden Markov models (HMMs) and random effects models in a longitudinal setting, leading to the class of so‐called mixed HMMs. This class of models has several interesting features. It deals with the dependence of a response variable on covariates, serial dependence, and unobserved heterogeneity in an HMM framework. It exploits the properties of HMMs, such as the relatively simple dependence structure and the efficient computational procedure, and allows one to handle a variety of real‐world time‐dependent data. We give details of the Expectation‐Maximization algorithm for computing the maximum likelihood estimates of model parameters and we illustrate the method with two real applications describing the relationship between patent counts and research and development expenditures, and between stock and market returns via the Capital Asset Pricing Model.     

Stock Market’s responses to intraday investor sentiment

We investigate the effect of intraday sentiment on subsequent stock returns. Mispricing caused by intraday sentiment is not corrected immediately; rather, it lasts for about 30 min. After 30 min, however, investor sentiment negatively affects stock returns, suggesting that mispriced stocks are at least partially but not entirely adjusted back to their fundamental values. We also show that the effect of intraday sentiment depends on the degree of arbitrage. Intraday sentiment has little effect on firms that are easy to arbitrage. For these firms, the difference in the one-minute returns of firms with high and low sentiment is nearly zero, implying that any mispricing caused by intraday sentiment is immediately corrected for this group of firms. In contrast, among firms that are hard to arbitrage, the difference in the returns of firms with high and low sentiment lasts for about half an hour. This difference in the effect of intraday sentiment is not caused by the firms’ liquidities.     

Forecasting abnormal stock returns and trading volume using investor sentiment: Evidence from online search

We examine the ability of online ticker searches (e.g. XOM for Exxon Mobil) to forecast abnormal stock returns and trading volumes. Specifically, we argue that online ticker searches serve as a valid proxy for investor sentiment — a set of beliefs about cash flows and investment risks that are not necessarily justified by the facts at hand — which is generally associated with less sophisticated, retail investors. Based on prior research on investor sentiment, we expect online search intensity to forecast stock returns and trading volume, and also expect that highly volatile stocks, which are more difficult to arbitrage, will be more sensitive to search intensity than less volatile stocks. In a sample of S&P 500 firms over the period 2005-2008, we find that, over a weekly horizon, online search intensity reliably predicts abnormal stock returns and trading volumes, and that the sensitivity of returns to search intensity is positively related to the difficulty of a stock being arbitraged. More broadly, our study highlights the potential of employing online search data for other forecasting applications.     

Does investor sentiment impact the returns and volatility of Islamic equities?

In this paper, we estimate generalized autoregressive conditional heteroskedasticity (GARCH) and vector autoregressive (VAR) models to examine whether investor sentiment impacts the returns and volatility of various U.S. Dow Jones Islamic equity indices. The results from GARCH estimations show that changes in investor sentiment are positively correlated with the returns of the Shari’ah-compliant market portfolio. In addition, we find similar results for the three Shari’ah-compliant firm-size portfolios (i.e., large-, medium-, and small-cap). However, this relationship is stronger for harder to arbitrage Shari’ah-compliant stocks; that is, investor sentiment has a greater influence on small-cap equities. Additionally, estimations from the vector autoregressive model confirm the aforementioned results. In terms of volatility, GARCH estimations suggest that bullish shifts in investor sentiment in the current period are accompanied by lower conditional volatility in the ensuing period. In general, our findings suggest that as noise traders create more risk the market seems to reward them with higher expected returns.     

Hard to arbitrage,hard for analysts to forecast

This paper examines whether limits to arbitrage (LA) affect analysts' earnings forecast accuracy. Using the LA index, which is constructed from unique trading constraints in the Chinese stock market and other commonly used measures, we find that forecast accuracy is much lower for stocks with high LA. Moreover, our results are more suited to explanations of cognitive bias that turn to investor sentiment or limited attention and cannot be fully explained by more objective factors, including analyst ability, broker size, broker experience, and commission pressure. We also find that LA amplifies analyst forecast dispersion. Such results indicate that LA distorts analysts’ earnings expectations and provides new insight into how LA affects anomaly returns.     

固定交互效应面板截取模型的ECM算法

交互效应面板数据模型在社会经济问题的实证分析中具有很强的适用性,但现有研究主要集中于线性面板模型。本文将交互效应引入非线性的面板截取模型,并基于ECM算法,建立了有效估计量和识别程序。基于不同因子类型的仿真实验结果显示,ECM算法可以很好地识别面板截取样本中的非观测因子。ECM估计量具有良好的有限样本性质,与其他估计量相比具有更小的偏误和更快的收敛速度。尤其是当共同因子为低频平滑因子时,其表现最为理想。     

Are Austrian returns to education falling over time?

In this paper, we make a systematic presentation of returns to education in Austria for the period 1981–1997. We use consistent cross-sections from the Mikrozensus and find falling returns over time. These falling returns are neither caused by changes in the sample design and reduced willingness to reveal personal incomes in the survey, nor by a declining quality of education. Moreover, it is shown that especially returns to tertiary and secondary education have fallen. Estimating quantile regressions provides further interesting insights: returns fall for all quantiles alike, but the spread of returns is much lower for females. The overall picture of falling returns is consistent with a rise in the supply of highly educated workers in the last two decades.     

Portfolio Selection under Maximum Minimum Criterion

In this paper, we studied the problem of risky portfolio selection under uncertainty. Different from risk-return analytical methodology, we formulated a model under maximum minimal criterion of uncertain decision-making theory. If the investor had no any distribution information of the returns and (s)he knew the variation scopes of the returns by his/her knowledge of the market information or experts’ evaluations of the alternative risky assets, then we showed that the optimal portfolio strategy of the model under maximal minimal criterion could be obtained by solving linear programming. If the returns were known to be normal distributed, the investor’s optimal portfolio strategy could be obtained by solving a nonlinear programming. The paper also provided an algorithm to solve this programming. At last, the paper compared this model with Markowitz’s mean-varience (M-V) model and Young’s minmax model, and pointed out the distinctions and similarities between our model and the other two. Supported in part by Program for NCET, in part by the Key Project of Chinese Ministry of Education 104053.     

INFORMATION THEORETIC APPROACHES IN ECONOMICS

Economics has seen a recent rise in interest in information theory as an alternative framework to the conventional notion of equilibrium as a fixed state, such as Walrasian market‐clearing general equilibrium. The information theoretic approach is predicated on the notion of statistical equilibrium (SE) that takes a distribution over all possible states as an equilibrium, and therefore predicts the endogenous fluctuations of the system along with its central tendency simultaneously. For this reason, SE approaches can explain the observed data without relying on arbitrary assumptions about random noise and provide useful insights for many interesting economic problems that conventional methods have not been able to satisfactorily deal with. In this paper, we review the key elements of information theory focusing on the notions and applications of entropy and SE in economics, particularly paying attention to how entropy concepts open up a new frontline of economic research.     

Pair trading based on quantile forecasting of smooth transition GARCH models

Pair trading is a statistical arbitrage strategy used on similar assets with dissimilar valuations. We utilize smooth transition heteroskedastic models with a second-order logistic function to generate trading entry and exit signals and suggest two pair trading strategies: the first uses the upper and lower threshold values in the proposed model as trading entry and exit signals, while the second strategy instead takes one-step-ahead quantile forecasts obtained from the same model. We employ Bayesian Markov chain Monte Carlo sampling methods for updating the estimates and quantile forecasts. As an illustration, we conduct a simulation study and empirical analysis of the daily stock returns of 36 stocks from U.S. stock markets. We use the minimum square distance method to select ten stock pairs, choose additional five pairs consisting of two companies in the same industrial sector, and then finally consider pair trading profits for two out-of-sample periods in 2014 within a six-month time frame as well as for the entire year. The proposed strategies yield average annualized returns of at least 35.5% without a transaction cost and at least 18.4% with a transaction cost.     

Hypothesis testing in nonparametric models of production using multiple sample splits

Several tests of model structure developed by Kneip et al. (J Bus Econ Stat 34:435–456, 2016) and Daraio et al. (Econ J 21:170–191, 2018) rely on comparing sample means of two different efficiency estimators, one appropriate under the conditions of the null hypothesis and the other appropriate under the conditions of the alternative hypothesis. These tests rely on central limit theorems developed by Kneip et al. (Econ Theory 31:394–422, 2015) and Daraio et al. (Econ J 21:170–191, 2018), but require that the original sample be split randomly into two independent subsamples. This introduces some ambiguity surrounding the sample-split, which may be determined by choice of a seed for a random number generator. We develop a method that eliminates much of this ambiguity by repeating the random splits a large number of times. We use a bootstrap algorithm to exploit the information from the multiple sample-splits. Our simulation results show that in many cases, eliminating this ambiguity results in tests with better size and power than tests that employ a single sample-split.

     

Random Effects Misspecification Can Have Severe Consequences for Random Effects Inference in Linear Mixed Models

There has been considerable and controversial research over the past two decades into how successfully random effects misspecification in mixed models (i.e. assuming normality for the random effects when the true distribution is non‐normal) can be diagnosed and what its impacts are on estimation and inference. However, much of this research has focused on fixed effects inference in generalised linear mixed models. In this article, motivated by the increasing number of applications of mixed models where interest is on the variance components, we study the effects of random effects misspecification on random effects inference in linear mixed models, for which there is considerably less literature. Our findings are surprising and contrary to general belief: for point estimation, maximum likelihood estimation of the variance components under misspecification is consistent, although in finite samples, both the bias and mean squared error can be substantial. For inference, we show through theory and simulation that under misspecification, standard likelihood ratio tests of truly non‐zero variance components can suffer from severely inflated type I errors, and confidence intervals for the variance components can exhibit considerable under coverage. Furthermore, neither of these problems vanish asymptotically with increasing the number of clusters or cluster size. These results have major implications for random effects inference, especially if the true random effects distribution is heavier tailed than the normal. Fortunately, simple graphical and goodness‐of‐fit measures of the random effects predictions appear to have reasonable power at detecting misspecification. We apply linear mixed models to a survey of more than 4 000 high school students within 100 schools and analyse how mathematics achievement scores vary with student attributes and across different schools. The application demonstrates the sensitivity of mixed model inference to the true but unknown random effects distribution.     

Joint Bayesian Analysis of Parameters and States in Nonlinear non‐Gaussian State Space Models

We propose a new methodology for designing flexible proposal densities for the joint posterior density of parameters and states in a nonlinear, non‐Gaussian state space model. We show that a highly efficient Bayesian procedure emerges when these proposal densities are used in an independent Metropolis–Hastings algorithm or in importance sampling. Our method provides a computationally more efficient alternative to several recently proposed algorithms. We present extensive simulation evidence for stochastic intensity and stochastic volatility models based on Ornstein–Uhlenbeck processes. For our empirical study, we analyse the performance of our methods for corporate default panel data and stock index returns. Copyright © 2016 John Wiley & Sons, Ltd.     

Monitoring structural change in dynamic econometric models

The classical approach to testing for structural change employs retrospective tests using a historical data set of a given length. Here we consider a wide array of fluctuation‐type tests in a monitoring situation—given a history period for which a regression relationship is known to be stable, we test whether incoming data are consistent with the previously established relationship. Procedures based on estimates of the regression coefficients are extended in three directions: we introduce (a) procedures based on OLS residuals, (b) rescaled statistics and (c) alternative asymptotic boundaries. Compared to the existing tests our extensions offer ease of computation, improved size in finite samples for dynamic models and better power against certain alternatives, respectively. We apply our methods to three data sets, German M1 money demand, US labour productivity and S&P 500 stock returns. Copyright © 2005 John Wiley & Sons, Ltd.     

A No‐Arbitrage Structural Vector Autoregressive Model of the UK Yield Curve*

This article combines a Structural Vector Autoregression with a no‐arbitrage approach to build a multifactor Affine Term Structure Model (ATSM). The resulting No‐Arbitrage Structural Vector Autoregressive (NASVAR) model implies that expected excess returns are driven by structural macroeconomic shocks. This is in contrast with a standard ATSM, in which agents are concerned with non‐structural risks. As a simple application, we study the effects of supply, demand and monetary policy shocks on the UK yield curve. We show that all structural shocks affect the slope of the yield curve, with demand and supply shocks accounting for a large part of the time variation in bond yields.     

Non‐linear Predictability of UK Stock Market Returns*

Linear predictability of stock market returns has been widely reported. However, recently developed theoretical research has suggested that due to the interaction of noise and arbitrage traders, stock returns are inherently non‐linear, whereby market dynamics differ between small and large returns. This paper examines whether an exponential smooth transition threshold model, which is capable of capturing this non‐linear behaviour, can provide a better characterization of UK stock market returns than either a linear model or an alternate non‐linear model. The results of both in‐sample and out‐of‐sample specification tests support the exponential smooth transition threshold model and hence the belief that investor behaviour does differ between large and small returns.     

随机仓库布局问题模型与算法研究

通过讨论随机条件下仓库布局问题．建立了随机仓库布局问题机会约束规划模型，并设计出基于随机模拟的禁忌搜索算法求解模型，最后利用算例来验证算法的有效性。     

Alternative Indicators for the Risk of Non‐response Bias: A Simulation Study

The growth of non‐response rates for social science surveys has led to increased concern about the risk of non‐response bias. Unfortunately, the non‐response rate is a poor indicator of when non‐response bias is likely to occur. We consider in this paper a set of alternative indicators. A large‐scale simulation study is used to explore how each of these indicators performs in a variety of circumstances. Although, as expected, none of the indicators fully depict the impact of non‐response in survey estimates, we discuss how they can be used when creating a plausible account of the risks for non‐response bias for a survey. We also describe an interesting characteristic of the fraction of missing information that may be helpful in diagnosing not‐missing‐at‐random mechanisms in certain situations.     

The Relationship Between Stock Market Returns and Technical Efficiency Innovations: Evidence from the US Airline Industry

This paper analyzes the association between two firm performance measures: stock market returns and relative technical efficiency. Using linear programming techniques (Data Envelopment Analysis and Free Disposal Hull), technical efficiencies are calculated for a panel of eleven US airlines observed quarterly from 1970–1990. A relationship, between efficiency news in a quarter and stock market performance in the following two months, is found. A risky arbitrage portfolio strategy, of buying firms with the most positive efficiency news and short-selling those with the worst news during this time frame, results in zero beta risk yet yields annual returns of 17% and 18% for the two methodologies.     

A Simple Estimator of Two-Dimensional Copulas,with Applications1

Copulas are distributions with uniform marginals. Non-parametric copula estimates may violate the uniformity condition in finite samples. We look at whether it is possible to obtain valid piecewise linear copula densities by triangulation. The copula property imposes strict constraints on design points, making an equi-spaced grid a natural starting point. However, the mixed-integer nature of the problem makes a pure triangulation approach impractical on fine grids. As an alternative, we study the ways of approximating copula densities with triangular functions which guarantees that the estimator is a valid copula density. The family of resulting estimators can be viewed as a non-parametric MLE of B-spline coefficients on possibly non-equally spaced grids under simple linear constraints. As such, it can be easily solved using standard convex optimization tools and allows for a degree of localization. A simulation study shows an attractive performance of the estimator in small samples and compares it with some of the leading alternatives. We demonstrate empirical relevance of our approach using three applications. In the first application, we investigate how the body mass index of children depends on that of parents. In the second application, we construct a bivariate copula underlying the Gibson paradox from macroeconomics. In the third application, we show the benefit of using our approach in testing the null of independence against the alternative of an arbitrary dependence pattern.