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β 混合厚尾时间序列中 Lasso 的理论保证AI 解读

Many theoretical results for lasso require the samples to be i.i.d. Recent work has provided guarantees for lasso assuming that the time series is generated by a sparse Vector Autoregressive (VAR) model with Gaussian innovations. Proofs of these results rely critically on the fact that the true data generating mechanism (DGM) is a finite-order Gaussian VAR. This assumption is quite brittle: linear transformations, including selecting a subset of variables, can lead to the…

Hurst 函数估计AI 解读

This paper considers a wide range of issues concerning the estimation of the Hurst function of a multifractional Brownian motion when the process is observed on a regular grid. A theoretical lower bound for the minimax risk of this inference problem is established for a wide class of smooth Hurst functions. We also propose a new nonparametric estimator and show that it is rate optimal. Implementation issues of the estimator including how to overcome the presence of a…

时变系数协整回归的核方法推断AI 解读

This paper studies nonlinear cointegrating models with time-varying coefficients and multiple nonstationary regressors using classic kernel smoothing methods to estimate the coefficient functions. Extending earlier work on nonstationary kernel regression to take account of practical features of the data, we allow the regressors to be cointegrated and to embody a mixture of stochastic and deterministic trends, complications which result in asymptotic degeneracy of the…

分数阶单整过程错设模型的估计问题AI 解读

This short paper provides a comprehensive set of new theoretical results on the impact of mis-specifying the short run dynamics in fractionally integrated processes. We show that four alternative parametric estimators – frequency domain maximum likelihood, Whittle, time domain maximum likelihood and conditional sum of squares – converge to the same pseudo-true value under common mis-specification, and that they possess a common asymptotic distribution. The results are…

高频采样下的平稳性检验AI 解读

The high frequency behavior of the KPSS test, which is most commonly used to test for stationarity, is analyzed in a continuous time framework. Our asymptotics show that the test has no discriminatory power at high frequency: It either always rejects stationarity or has no nontrivial power at high frequency. The test becomes valid at high frequency only when the bandwidth of its long-run variance estimate is chosen suitably in our framework. We also analyze the…

利用机器学习估计永久价格冲击AI 解读

In this paper, we show that vector auto-regression (VAR) models, which are commonly used to estimate permanent price impact, are misspecified and can produce conflicting and incorrect inferences when the price impact function is nonlinear. We propose an alternative method to estimate permanent price impact by modifying a reinforcement learning (RL) framework. Our approach assumes the data is stationary and Markov, but is otherwise unrestrictive. We obtain empirical estimates…

自回归模型中脉冲响应推断的一致有效性AI 解读

Existing proofs of the asymptotic validity of conventional methods of impulse response inference based on higher-order autoregressions are pointwise only. In this paper, we establish the uniform asymptotic validity of conventional asymptotic and bootstrap inference about individual impulse responses and vectors of impulse responses when the horizon is fixed with respect to the sample size. For inference about vectors of impulse responses based on Wald test statistics to be…

含全局幂律趋势与局部非参数趋势的半参数模型推断AI 解读

We consider a model with both a parametric global trend and a nonparametric local trend. This model may be of interest in a number of applications in economics, finance, ecology, and geology. We first propose two hypothesis tests to detect whether two nested special cases are appropriate. For the case where both null hypotheses are rejected, we propose an estimation method to capture certain aspects of the time trend. We establish consistency and some distribution theory in…

含外生回归变量的混合因果—非因果自回归模型AI 解读

Summary Mixed causal–noncausal autoregressive (MAR) models have been proposed to model time series exhibiting nonlinear dynamics. Possible exogenous regressors are typically substituted into the error term to maintain the MAR structure of the dependent variable. We introduce a representation including these covariates called MARX to study their direct impact. The asymptotic distribution of the MARX parameters is derived for a class of non‐Gaussian densities. For a Student…

发达与新兴经济体实际活动的共同波动：全球与群组特有国际因子的检验AI 解读

Summary Although globalization has shaped the world economy in recent decades, emerging economies have experienced impressive growth compared to developed economies, suggesting specific comovements within developed and emerging business cycles. Using observed developed and emerging real economy activity variables, we investigate whether the latter assertion can be supported by observed data. Based on a two‐level factor model, we assume these activity variables can be…

混合随机局部单位根模型AI 解读

Two approaches have dominated formulations designed to capture small departures from unit root autoregressions. The first involves deterministic departures that include local-to-unity (LUR) and mildly (or moderately) integrated (MI) specifications where departures shrink to zero as the sample size n→∞. The second approach allows for stochastic departures from unity, leading to stochastic unit root (STUR) specifications. This paper introduces a hybrid local stochastic unit…

从平稳到轻度非平稳变化的序贯监测AI 解读

We develop and study sequential testing procedures á la Chu et al. (1996) for on-line detection of changes in a time series from stationarity to mild forms of non-stationarity. The proposed tests are based on sequential CUSUM and KPSS-type detector processes, and are shown to provide consistent detection under a wide range of change point models, including changes in the parameters of ARMA and GARCH series from values within the model’s stationarity parameter region to…

含零波动系数的增广双重自回归模型的非标准推断AI 解读

This paper considers an augmented double autoregressive (DAR) model, which allows null volatility coefficients to circumvent the over-parameterization problem in the DAR model. Since the volatility coefficients might be on the boundary, the statistical inference methods based on the Gaussian quasi-maximum likelihood estimation (GQMLE) become non-standard, and their asymptotics require the data to have a finite sixth moment, which narrows the applicable scope in studying…

基于鞅变换的Copula拟合优度检验AI 解读

This paper proposes an asymptotically distribution-free test for copulas with dynamic marginal distributions, such as GARCH and ARMA processes. The test is based on the empirical copula process with parametrically estimated marginal distributions. By applying the Khmaladze (1982, 1988, 1993) martingale transformation method, the transformed empirical process converges to a standard Gaussian process, so the resulting test statistics are asymptotically distribution-free. Monte…

面板数据模型中个体效应与时间效应的判定AI 解读

In this paper we propose a jackknife method to determine individual and time effects in linear panel data models. We first show that when both the serial and cross-sectional correlations among the idiosyncratic error terms are weak, our jackknife method can pick up the correct model with probability approaching one (w.p.a.1). In the presence of moderate or strong degree of serial correlation, we modify our jackknife criterion function and show that the modified jackknife…

建模结构突变能否提高预测准确性？AI 解读

Mean square forecast error loss implies a bias–variance trade-off that suggests that structural breaks of small magnitude should be ignored. In this paper, we provide a test to determine whether modeling a structural break improves forecast accuracy. The test is near optimal even when the date of a local-to-zero break is not consistently estimable. The results extend to forecast combinations that weight the post-break sample and the full sample forecasts by our test…

多期限预测误差的时变不确定性建模AI 解读

We estimate uncertainty measures for point forecasts obtained from survey data, pooling information embedded in observed forecast errors for different forecast horizons. To track time-varying uncertainty in the associated forecast errors, we derive a multiple-horizon specification of stochastic volatility. We apply our method to forecasts for various macroeconomic variables from the Survey of Professional Forecasters. Compared to simple variance approaches, our stochastic…

英国区域产出增长：始于1970年、更及时且频率更高的估计AI 解读

Summary Output growth estimates for regions of the UK are currently published at an annual frequency only, released with a long delay, and offer limited historical coverage. To improve the regional database this paper develops a mixed‐frequency multivariate model and uses it to produce consistent estimates of quarterly regional output growth dating back to 1970. We describe how these estimates are updated and evaluated on an ongoing, quarterly basis to publish online (at…

页岩革命与原油价格动态的转变AI 解读

Summary Oil price fluctuates in response to both demand and supply shocks. This paper proposes a new methodology that allows for timely identification of the shifting contribution from the two types of shock through a joint analysis of crude futures options and stock index options. Historical analysis shows that crude oil price movements are dominated by supply shocks from 2004 to 2008, but demand shocks have become much more dominant since then. The large demand shock…

石油供给冲击对美国经济活动的影响：我们学到了什么？AI 解读

Summary Estimated responses of real oil prices and US gross domestic product (GDP) to oil supply disruptions vary widely. We show that most variation is attributable to differences in identification assumptions and in the model specification. Models that allow for a large short‐run price elasticity of oil supply imply a larger response of oil prices and a larger, longer lived contraction in US real GDP. We find that, if we condition on a range of supply elasticity values…

基于随机扰动的因子个数秩估计AI 解读

Summary We introduce a random-perturbation-based rank estimator of the number of factors of a large-dimensional approximate factor model. An expansion of the rank estimator demonstrates that the random perturbation reduces the biases due to the persistence of the factor series and the dependence between the factor and error series. A central limit theorem for the rank estimator with convergence rate higher than root $n$ gives a new hypothesis-testing procedure for both…

时间序列误差下非参数回归的多尺度推断与长期方差估计AI 解读

Summary We develop new multiscale methods to test qualitative hypotheses about the function m in the non-parametric regression model Yt, T = m(t/T) + ɛt with time series errors ɛt. In time series applications, m represents a non-parametric time trend. Practitioners are often interested in whether the trend m has certain shape properties. For example, they would like to know whether m is constant or whether it is increasing or decreasing in certain time intervals. Our…

通过样本分割一致选择变点数量AI 解读

In multiple change-point analysis, one of the major challenges is to estimate the number of change-points. Most existing approaches attempt to minimize a Schwarz information criterion which balances a term quantifying model fit with a penalization term accounting for model complexity that increases with the number of change-points and limits overfitting. However, different penalization terms are required to adapt to different contexts of multiple change-point problems and…

厚尾向量误差修正模型的推断AI 解读

This paper first studies the full rank least squares estimator (FLSE) of the heavy-tailed vector error correction (VEC) models. It is shown that the rate of convergence of the FLSE related to the long-run parameters is n (sample size) and its limiting distribution is a stochastic integral in terms of two stable random processes when the tail index α∈(0,2). Furthermore, we show that the rate of convergence of the FLSE related to the short-term parameters is n1∕αL̃(n) and its…