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A non-linear dynamic model of the variance risk premium

方差风险溢价的非线性动态模型

We propose a new class of non-linear diffusion processes for modeling financial markets data. Our non-linear diffusions are obtained as transformations of affine processes. We show that asset-pricing and estimation is possible and likelihood estimation is straightforward. We estimate a non-linear diffusion model for the VIX index under both the objective measure and the risk-neutral measure where the latter is obtained from futures prices. We find evidence of significant…

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Good and bad uncertainty: Macroeconomic and financial market implications

好与坏的不确定性:宏观经济和金融市场含义

Does macroeconomic uncertainty increase or decrease aggregate growth and asset prices? To address this question, we decompose aggregate uncertainty into ‘good’ and ‘bad’ volatility components, associated with positive and negative innovations to macroeconomic growth. We document that in line with our theoretical framework, these two uncertainties have opposite impact on aggregate growth and asset prices. Good uncertainty predicts an increase in future economic activity, such…

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LET’S GET LADE: ROBUST ESTIMATION OF SEMIPARAMETRIC MULTIPLICATIVE VOLATILITY MODELS

半参数乘法波动率模型的稳健最小绝对偏差估计

We investigate a model in which we connect slowly time varying unconditional long-run volatility with short-run conditional volatility whose representation is given as a semi-strong GARCH(1,1) process with heavy tailed errors. We focus on robust estimation of both long-run and short-run volatilities. Our estimation is semiparametric since the long-run volatility is totally unspecified whereas the short-run conditional volatility is a parametric semi-strong GARCH(1,1)…

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ASYMPTOTIC INFERENCE FOR AR MODELS WITH HEAVY-TAILED G-GARCH NOISES

含厚尾 G-GARCH 噪声的自回归模型渐近推断

It is well known that the least squares estimator (LSE) of an AR( p ) model with i.i.d. (independent and identically distributed) noises is n 1/ α L ( n )-consistent when the tail index α of the noise is within (0,2) and is n 1/2 -consistent when α ≥ 2, where L ( n ) is a slowly varying function. When the noises are not i.i.d., however, the case is far from clear. This paper studies the LSE of AR( p ) models with heavy-tailed G-GARCH(1,1) noises. When the tail index α of…

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MODELING NONSTATIONARY AND LEPTOKURTIC FINANCIAL TIME SERIES

非平稳与尖峰厚尾金融时间序列的建模

Financial time series is often assumed to be stationary and has a normal distribution in the literature. Both assumptions are however unrealistic. This paper proposes a new methodology with a focus on volatility estimation that is able to account for nonstationarity and heavy tails simultaneously. In particular, a local exponential smoothing (LES) approach is developed, in which weak estimates with different memory parameters are aggregated in a locally adaptive way. The…

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Forecasting Equity Premium: Global Historical Average Versus Local Historical Average and Constraints

股权风险溢价预测:全局历史平均、局部历史平均与约束

The equity premium, return on equity minus return on risk-free asset, is expected to be positive. We consider imposing such positivity constraint in local historical average (LHA) in nonparametric kernel regression framework. It is also extended to the semiparametric single index model when multiple predictors are used. We construct the constrained LHA estimator via an indicator function which operates as “model-selection” between the unconstrained LHA and the bound of the…

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A flexible semiparametric forecasting model for time series

一种灵活的半参数时间序列预测模型

In this paper, we propose a semiparametric procedure called the “Model Averaging MArginal Regression” (MAMAR) that is flexible for forecasting of time series. This procedure considers approximating a multivariate regression function by an affine combination of one-dimensional marginal regression functions. The weight parameters involved in the approximation are estimated by least squares on the basis of the first-stage nonparametric kernel estimates of the marginal…

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Nonparametric specification tests for stochastic volatility models based on volatility density

基于波动率密度的随机波动率模型非参数设定检验

This paper develops a specification test for stochastic volatility models by comparing the nonparametric kernel deconvolution density estimator of an integrated volatility density with its parametric counterpart. L2 distance is used to measure the discrepancy. The asymptotic null distributions of the test statistics are established and the asymptotic power functions are computed. Through Monte Carlo simulations, the size and power properties of the test statistics are…

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Instrumental variable and variable addition based inference in predictive regressions

预测回归中基于工具变量与变量增补的推断

Valid inference in predictive regressions depends in a crucial manner on the degree of persistence of the predictor variables. The paper studies test procedures that are robust in the sense that their asymptotic null distributions are invariant to the persistence of the predictor, that is, the limiting distribution is the same irrespective of whether the regressors are stationary or (nearly) integrated. Existing procedures are often conservative (e.g. tests based on…

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Does anything beat 5-minute RV? A comparison of realized measures across multiple asset classes

能否超越五分钟已实现方差?跨资产类别的已实现测度比较

We study the accuracy of a variety of estimators of asset price variation constructed from high-frequency data (“realized measures”), and compare them with a simple “realized variance” (RV) estimator. In total, we consider over 400 different estimators, using 11 years of data on 31 different financial assets spanning five asset classes. When 5-minute RV is taken as the benchmark, we find little evidence that it is outperformed by any other measures. When using inference…

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VAR for VaR: Measuring tail dependence using multivariate regression quantiles

用于 VaR 的 VAR:以多元回归分位数衡量尾部依赖

This paper proposes methods for estimation and inference in multivariate, multi-quantile models. The theory can simultaneously accommodate models with multiple random variables, multiple confidence levels, and multiple lags of the associated quantiles. The proposed framework can be conveniently thought of as a vector autoregressive (VAR) extension to quantile models. We estimate a simple version of the model using market equity returns data to analyze spillovers in the…

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Learning, confidence, and option prices

学习、信心与期权价格

The option-market evidence suggests that investors are concerned with large downward moves in equity prices, which occur once every one to two years in the data. This evidence is puzzling because there are no concurrent jumps in macroeconomic fundamentals. I estimate a confidence-risk model where agents use a constant gain specification to learn about the unobserved expected growth from the cross-section of signals. While consumption shocks are Gaussian, investors’…

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Nonparametric tests for constant tail dependence with an application to energy and finance

尾部依赖恒定性的非参数检验及能源与金融应用

New tests for detecting structural breaks in the tail dependence of multivariate time series using the concept of tail copulas are presented. To obtain asymptotic properties, we derive a new limit result for the sequential empirical tail copula process. Moreover, consistency of both the tests and a break-point estimator are proven. We analyze the finite sample behavior of the tests by Monte Carlo simulations. Finally, and crucial from a risk management perspective, we apply…

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Explicit form of approximate transition probability density functions of diffusion processes

扩散过程近似转移概率密度的显式形式

A continuous-time diffusion process is very popular in modeling and provides useful tools to analyze particularly, but not restricted to, a variety of economic and financial variables. The transition probability density function (TPDF) of a diffusion process plays an important role in understanding and explaining the dynamics of the process. A new way to find closed-form approximate TPDFs for multivariate diffusions is proposed in this paper. This method can be applied to…

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Inference on sets in finance

金融中的集合推断

We consider the problem of inference on a class of sets describing a collection of admissible models as solutions to a single smooth inequality. Classical and recent examples include the Hansen–Jagannathan sets of admissible stochastic discount factors, Markowitz–Fama mean–variance sets for asset portfolio returns, and the set of structural elasticities in Chetty's (2012) analysis of demand with optimization frictions. The econometric structure of the problem allows us to…

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Maximization by parts in extremum estimation

极值估计中的分部极大化

In this paper, we present various iterative algorithms for extremum estimation in cases where direct computation of the extremum estimator or via the Newton–Raphson algorithm is difficult, if not impossible. While the Newton–Raphson algorithm makes use of the full Hessian matrix, which may be difficult to evaluate, our algorithms use parts of the Hessian matrix only, the parts that are easier to compute. We establish consistency and asymptotic efficiency of our iterative…

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The three-pass regression filter: A new approach to forecasting using many predictors

三遍回归滤波:利用大量预测变量进行预测的新方法

We forecast a single time series using many predictor variables with a new estimator called the three-pass regression filter (3PRF). It is calculated in closed form and conveniently represented as a set of ordinary least squares regressions. 3PRF forecasts are consistent for the infeasible best forecast when both the time dimension and cross section dimension become large. This requires specifying only the number of relevant factors driving the forecast target, regardless of…

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Risks of large portfolios

大型投资组合的风险

The risk of a large portfolio is often estimated by substituting a good estimator of the volatility matrix. However, the accuracy of such a risk estimator is largely unknown. We study factor-based risk estimators under a large amount of assets, and introduce a high-confidence level upper bound (H-CLUB) to assess the estimation. The H-CLUB is constructed using the confidence interval of risk estimators with either known or unknown factors. We derive the limiting distribution…

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Generalized risk premia

广义风险溢价

This paper develops an optimal trading strategy explicitly linked to an agent׳s preferences and assessment of the distribution of asset returns. The price of this strategy is a portfolio of implied moments, and its expected excess returns naturally accommodate compensation for higher-order moment risk. Variance risk and the equity premium approximate it to first order and it nests cross-sectional asset pricing models such as the linear Capital Asset Pricing Model (CAPM). An…

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Information-theoretic optimality of observation-driven time series models for continuous responses

连续响应观测驱动时间序列模型的信息论最优性

We investigate information-theoretic optimality properties of the score function of the predictive likelihood as a device for updating a real-valued time-varying parameter in a univariate observation-driven model with continuous responses. We restrict our attention to models with updates of one lag order. The results provide theoretical justification for a class of score-driven models which includes the generalized autoregressive conditional heteroskedasticity model as a…

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Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator

使用无偏似然估计时的 MCMC 高效实现

When an unbiased estimator of the likelihood is used within a Metropolis–Hastings chain, it is necessary to trade off the number of Monte Carlo samples used to construct this estimator against the asymptotic variances of the averages computed under this chain. Using many Monte Carlo samples will typically result in Metropolis–Hastings averages with lower asymptotic variances than the corresponding averages that use fewer samples; however, the computing time required to…

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PRICING KERNEL ESTIMATION: A LOCAL ESTIMATING EQUATION APPROACH

定价核估计:局部估计方程方法

This paper investigates a general semiparametric stochastic discount factor formulation that avoids functional form misspecification. A new semiparametric estimation procedure is proposed which combines orthogonality conditions and local linear fitting to give a semiparametric generalized estimating equation approach. Asymptotic properties of the estimators are established and we explore the empirical usefulness of the proposed approach to value-weighted stock returns.

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Local Adaptive Multiplicative Error Models for High-Frequency Forecasts

We propose a local adaptive multiplicative error model (MEM) accommodating time-varying parameters. MEM parameters are adaptively estimated based on a sequential testing procedure. A data-driven optimal length of local windows is selected, yielding adaptive forecasts at each point in time. Analysing 1-minute cumulative trading volumes of five large NASDAQ stocks in 2008, we show that local windows of approximately 3 to 4 hours are reasonable to capture parameter variations…

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What is the chance that the equity premium varies over time? Evidence from regressions on the dividend-price ratio

股票风险溢价随时间变化的可能性:股息价格比回归的证据

We examine the evidence on excess stock return predictability in a Bayesian setting in which the investor faces uncertainty about both the existence and strength of predictability. When we apply our methods to the dividend-price ratio, we find that even investors who are quite skeptical about the existence of predictability sharply modify their views in favor of predictability when confronted by the historical time series of returns and predictor variables. Correctly taking…

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