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Estimating quadratic variation consistently in the presence of endogenous and diurnal measurement error

内生及日内测量误差下二次变差的一致估计

We propose an econometric model that captures the effects of market microstructure on a latent price process. In particular, we allow for correlation between the measurement error and the return process and we allow the measurement error process to have a diurnal heteroskedasticity. We propose a modification of the TSRVÂ estimator of quadratic variation. We show that this estimator is consistent, with a rate of convergence that depends on the size of the measurement error,…

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Out of sample forecasts of quadratic variation

二次变差的样本外预测

We compare the forecasts of Quadratic Variation given by the Realized Volatility (RV) and the Two Scales Realized Volatility (TSRV)Â computed from high frequency data in the presence of market microstructure noise, under several different dynamics for the volatility process and assumptions on the noise. We show that TSRV largely outperforms RV, whether looking at bias, variance, RMSE or out-of-sample forecasting ability. An empirical application to all DJIA stocks confirms…

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Nonparametric estimation of conditional VaR and expected shortfall

条件风险价值与预期损失的非参数估计

This paper considers a new nonparametric estimation of conditional value-at-risk and expected shortfall functions. Conditional value-at-risk is estimated by inverting the weighted double kernel local linear estimate of the conditional distribution function. The nonparametric estimator of conditional expected shortfall is constructed by a plugging-in method. Both the asymptotic normality and consistency of the proposed nonparametric estimators are established at both boundary…

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Testing for a change in persistence in the presence of non-stationary volatility

非平稳波动下的持续性变化检验

In this paper we consider tests for the null of (trend-) stationarity against the alternative of a change in persistence at some (known or unknown) point in the observed sample, either from I(0) to I(1) behaviour or vice versa, of, inter alia, [Kim, J., 2000. Detection of change in persistence of a linear time series. Journal of Econometrics 95, 97-116]. We show that in circumstances where the innovation process displays non-stationary unconditional volatility of a very…

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Testing for multivariate volatility functions using minimum volume sets and inverse regression

基于最小体积集合与逆回归的多变量波动函数检验

We propose two new types of nonparametric tests for investigating multivariate regression functions. The tests are based on cumulative sums coupled with either minimum volume sets or inverse regression ideas; involving no multivariate nonparametric regression estimation. The methods proposed facilitate the investigation for different features such as if a multivariate regression function is (i) constant, (ii)Â of a bathtub shape, and (iii) in a given parametric form. The…

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Specification testing in discretized diffusion models: Theory and practice

离散化扩散模型的设定检验:理论与实践

We propose two new tests for the specification of both the drift and the diffusion functions in a discretized version of a semiparametric continuous-time financial econometric model. Theoretically, we establish some asymptotic consistency results for the proposed tests. Practically, a simple selection procedure for the bandwidth parameter involved in each of the proposed tests is established based on the assessment of the power function of the test under study. To the best…

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Realized volatility forecasting and option pricing

已实现波动率预测与期权定价

A growing literature advocates the use of microstructure noise-contaminated high-frequency data for the purpose of volatility estimation. This paper evaluates and compares the quality of several recently-proposed estimators in the context of a relevant economic metric, i.e., profits from option pricing and trading. Using forecasts obtained by virtue of alternative volatility estimates, agents price short-term options on the S&P 500 index before trading with each other at…

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Correlation testing in time series, spatial and cross-sectional data

时间序列、空间与截面数据的相关性检验

We provide a general class of tests for correlation in time series, spatial, spatio-temporal and cross-sectional data. We motivate our focus by reviewing how computational and theoretical difficulties of point estimation mount, as one moves from regularly-spaced time series data, through forms of irregular spacing, and to spatial data of various kinds. A broad class of computationally simple tests is justified. These specialize to Lagrange multiplier tests against parametric…

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Seasonal unit root tests and the role of initial conditions

季节单位根检验与初始条件的作用

In the context of regression-based (quarterly) seasonal unit root tests, we examine the impact of initial conditions (one for each quarter) of the process on test power. We investigate the behaviour of the well-known OLS detrended HEGY seasonal unit root tests together with their quasi-differenced (QD) detrended analogues, when the initial conditions are not asymptotically negligible. We show that the asymptotic local power of a test at a given frequency depends on the value…

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Critical values for linearity tests in time-varying smooth transition autoregressive models when data are highly persistent

高持久性数据下时变平滑转换自回归模型线性检验的临界值

In this paper, we derive asymptotic distributions for linearity tests in time-varying smooth transition autoregressive models in the presence of a unit root. The limiting distributions are non-standard because of the unit root assumption, and it is shown that the linearity hypothesis is rejected far too often (up to 30.9% of the times at a 5% significance level) when using critical values from a chi-square distribution. Copyright The Author(s). Journal compilation Royal…

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Asymptotic properties of estimators for the linear panel regression model with random individual effects and serially correlated errors: the case of stationary and non-stationary regressors and residuals

含随机个体效应与序列相关误差的线性面板估计:平稳与非平稳情形

This paper studies the asymptotic properties of standard panel data estimators in a simple panel regression model with random error component disturbances. Both the regressor and the remainder disturbance term are assumed to be autoregressive and possibly non-stationary. Asymptotic distributions are derived for the standard panel data estimators including ordinary least squares (OLS), fixed effects (FE), first-difference (FD) and generalized least squares (GLS) estimators…

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Multiple local whittle estimation in stationary systems

平稳系统中的多参数局部 Whittle 估计

Moving from univariate to bivariate jointly dependent long-memory time series introduces a phase parameter (γ), at the frequency of principal interest, zero; for short-memory series γ=0 automatically. The latter case has also been stressed under long memory, along with the “fractional differencing” case γ=(δ2−δ1)π/2, where δ1, δ2 are the memory parameters of the two series. We develop time domain conditions under which these are and are not relevant, and relate the…

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Residual empirical processes for long and short memory time series

长记忆与短记忆时间序列的残差经验过程

This paper studies the residual empirical process of long- and short-memory time series regression models and establishes its uniform expansion under a general framework. The results are applied to the stochastic regression models and unstable autoregressive models. For the long-memory noise, it is shown that the limit distribution of the Kolmogorov–Smirnov test statistic studied in Ho and Hsing [Ann. Statist. 24 (1996) 992–1024] does not hold when the stochastic regression…

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Limit theorems for weighted samples with applications to sequential Monte Carlo methods

加权样本的极限定理及其在序贯蒙特卡洛方法中的应用

In the last decade, sequential Monte Carlo methods (SMC) emerged as a key tool in computational statistics [see, e.g., Sequential Monte Carlo Methods in Practice (2001) Springer, New York, Monte Carlo Strategies in Scientific Computing (2001) Springer, New York, Complex Stochastic Systems (2001) 109–173]. These algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to a weighted population of particles, which are generated…

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Efficient forecast tests for conditional policy forecasts

条件政策预测的有效性检验

Central Banks regularly make forecasts, such as the Fed's Greenbook forecast, that are conditioned on hypothetical paths for the policy interest rate. While there are good public policy reasons to evaluate the quality of such forecasts, up until now, the most common approach has been to ignore their conditional nature and apply standard forecast efficiency tests. In this paper we derive tests for the efficiency of conditional forecasts. Intuitively, these tests involve…

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Least-squares forecast averaging

最小二乘预测平均

This paper proposes forecast combination based on the method of Mallows Model Averaging (MMA). The method selects forecast weights by minimizing a Mallows criterion. This criterion is an asymptotically unbiased estimate of both the in-sample mean-squared error (MSE) and the out-of-sample one-step-ahead mean-squared forecast error (MSFE). Furthermore, the MMA weights are asymptotically mean-square optimal in the absence of time-series dependence. We show how to compute MMA…

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The relationship between the Beveridge–Nelson decomposition and other permanent–transitory decompositions that are popular in economics

贝弗里奇—纳尔逊分解与其他永久—暂时分解的关系

The Beveridge-Nelson (BN) decomposition is a model-based method for decomposing time series into permanent and transitory components. When constructed from an ARIMA model, it is closely related to decompositions based on unobserved components (UC) models with random walk trends and covariance stationary cycles. The decomposition when extended to I(2) models can also be related to non-model-based signal extraction filters such as the HP filter. We show that the BN…

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Time series properties of ARCH processes with persistent covariates

含持久协变量的ARCH过程的时间序列性质

We investigate the time series properties of a volatility model, whose conditional variance is specified as in ARCH with an additional persistent covariate. The included covariate is assumed to be an integrated or nearly integrated process, with its effect on volatility given by a wide class of nonlinear volatility functions. In the paper, such a model is shown to generate many important characteristics that are commonly observed in financial time series. In particular, the…

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Global yield curve dynamics and interactions: A dynamic Nelson–Siegel approach

全球收益率曲线动态与互动:动态 Nelson–Siegel 方法

The popular Nelson-Siegel [Nelson, C.R., Siegel, A.F., 1987. Parsimonious modeling of yield curves. Journal of Business 60, 473-489] yield curve is routinely fit to cross sections of intra-country bond yields, and Diebold-Li [Diebold, F.X., Li, C., 2006. Forecasting the term structure of government bond yields. Journal of Econometrics 130, 337-364] have recently proposed a dynamized version. In this paper we extend Diebold-Li to a global context, modeling a potentially large…

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Forecasting using a large number of predictors: Is Bayesian shrinkage a valid alternative to principal components?

大量预测变量下的预测:贝叶斯收缩能否替代主成分?

This paper considers Bayesian regression with normal and double-exponential priors as forecasting methods based on large panels of time series. We show that, empirically, these forecasts are highly correlated with principal component forecasts and that they perform equally well for a wide range of prior choices. Moreover, we study conditions for consistency of the forecast based on Bayesian regression as the cross-section and the sample size become large. This analysis…

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Trend/cycle decomposition of regime-switching processes

状态切换过程的趋势—周期分解

We present a new approach to trend/cycle decomposition of time series that follow regime-switching processes. The proposed approach, which we label the "regime-dependent steady-state" (RDSS) decomposition, is motivated as the appropriate generalization of the Beveridge and Nelson decomposition [Beveridge, S., Nelson, C.R., 1981. A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the…

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Markov-switching and the Beveridge–Nelson decomposition: Has US output persistence changed since 1984?

马尔可夫切换与贝弗里奇—纳尔逊分解:美国产出持续性是否改变?

We show that, for a class of univariate and multivariate Markov-switching models, exact calculation of the Beveridge-Nelson (BN) trend/cycle components is possible. The key to exact BN trend/cycle decomposition is to recognize that the latent first-order Markov-switching process in the model has an AR(1) representation, and that the model can be cast into a state-space form. Given the state-space representation, we show that impulse-response function analysis can be…

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Bayesian Model Averaging and exchange rate forecasts

贝叶斯模型平均与汇率预测

Exchange rate forecasting is hard and the seminal result of Meese and Rogoff [Meese, R., Rogoff, K., 1983. Empirical exchange rate models of the seventies: Do they fit out of sample? Journal of International Economics 14, 3-24] that the exchange rate is well approximated by a driftless random walk, at least for prediction purposes, still stands despite much effort at constructing other forecasting models. However, in several other macro and financial forecasting…

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Forecasting economic time series using targeted predictors

使用定向预测变量预测经济时间序列

This paper studies two refinements to the method of factor forecasting. First, we consider the method of quadratic principal components that allows the link function between the predictors and the factors to be non-linear. Second, the factors used in the forecasting equation are estimated in a way to take into account that the goal is to forecast a specific series. This is accomplished by applying the method of principal components to 'targeted predictors' selected using…

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