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持续期驱动长程依赖过程的渐近理论AI 解读

We consider processes with second order long range dependence resulting from heavy tailed durations. We refer to this phenomenon as duration-driven long range dependence (DDLRD), as opposed to the more widely studied linear long range dependence based on fractional differencing of an iid process. We consider in detail two specific processes having DDLRD, originally presented in Taqqu and Levy (1986), and Parke (1999). For these processes, we obtain the limiting distribution…

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同期门限自回归模型：估计、检验与预测AI 解读

This paper proposes a contemporaneous smooth transition threshold autoregressive model (C-STAR) as a modification of the smooth transition threshold autoregressive model surveyed in Teräsvirta (1998), in which the regime weights depend on the ex ante probability that a latent regime-specific variable will exceed a threshold value. We argue that the contemporaneous model is well-suited to rational expectations applications (and pricing exercises), in that it allows the…

季节性单位根假设的有效检验AI 解读

In this paper we derive, under the assumption of Gaussian errors with known error covariance matrix, asymptotic local power bounds for seasonal unit root tests for both known and unknown deterministic scenarios and for an arbitrary seasonal aspect. We demonstrate that the optimal test of a unit root at a given spectral frequency behaves asymptotically independently of whether unit roots exist at other frequencies or not. We also develop modified versions of the optimal tests…

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基于已实现极差的积分方差估计AI 解读

We provide a set of probabilistic laws for estimating the quadratic variation of continuous semimartingales with realized range-based variance -- a statistic that replaces every squared return of realized variance with a normalized squared range. If the entire sample path of the process is available, and under a set of weak conditions, our statistic is consistent and has a mixed Gaussian limit, whose precision is five times greater than that of realized variance. In…

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条件异方差下的广义秩估计量AI 解读

In this paper, we extend the classical idea of Rank-estimation of parameters from homoscedastic problems to heteroscedastic problems. In particular, we define a class of rank estimators of the parameters associated with the conditional mean function of an autoregressive model through a three-steps procedure and then derive their asymp- totic distributions. The class of models considered includes Engel’s ARCH model and the threshold heteroscedastic model. The class of…

加权重复中位数平滑与滤波AI 解读

We propose weighted repeated median filters and smoothers for robust nonparametric regression in general and for robust online signal extraction from time series in particular. The new methods allow us to remove outlying sequences and to preserve discontinuities (shifts) in the underlying regression function (the signal) in the presence of local linear trends. Suitable weighting of the observations according to their distances in the design space reduces the bias arising…

Brock–Dechert–Scheinkman检验的秩扩展AI 解读

This article proposes new tests of randomness for innovations in a large class of time series models. These tests are based on functionals of empirical processes constructed from either the model residuals or their associated ranks. The asymptotic behavior of these processes is determined under the null hypothesis of randomness. The limiting distributions are seen to be independent of estimation errors under appropriate regularity conditions. Several test statistics are…

非参数函数估计的非平衡Haar技术AI 解读

The discrete unbalanced Haar (UH) transform is a decomposition of one-dimensional data with respect to an orthonormal Haar-like basis where jumps in the basis vectors do not necessarily occur in the middle of their support. We introduce a multiscale procedure for estimation in Gaussian noise that consists of three steps: a UH transform, thresholding of the decomposition coefficients, and the inverse UH transform. We show that our estimator is mean squared consistent with…

非齐次泊松过程的贝叶斯预测及呼叫中心应用AI 解读

A call center is a centralized hub where customer and other telephone calls are handled by an organization. In today's economy, call centers have become the primary points of contact between customers and businesses. Thus accurate predictions of call arrival rates are indispensable to help call center practitioners staff their call centers efficiently and cost-effectively. This article proposes a multiplicative model for modeling and forecasting within-day arrival rates to a…

未知损失函数下的预测最优性检验AI 解读

Empirical tests of forecast optimality have traditionally been conducted under the assumption of mean squared error loss or some other known loss function. In this article we establish new testable properties that hold when the forecaster's loss function is unknown but testable restrictions can be imposed on the data-generating process, trading off conditions on the data-generating process against conditions on the loss function. We propose flexible estimation of the…

函数型观测独立性的 Portmanteau 综合检验AI 解读

In various fields, observations are curves over some natural time interval. These curves often arise from finely spaced measurements (e.g., in physical sciences and finance) or from smoothing unequally spaced sparse measurements. Recent years have seen the development of tools for analyzing such data in the growing field of functional data analysis. To validate the assumptions underlying these tools, it is important to verify that the functional observations form a simple…

高频金融数据的多尺度跳跃与波动率分析AI 解读

The wide availability of high-frequency data for many financial instruments stimulates an upsurge interest in statistical research on the estimation of volatility. Jump-diffusion processes observed with market microstructure noise are frequently used to model high-frequency financial data. Yet existing methods are developed for either noisy data from a continuous-diffusion price model or data from a jump-diffusion price model without noise. We propose methods to cope with…

差分AR(1)过程协方差矩阵的行列式AI 解读

In this note, determinants are explicitly calculated for the covariance matrices of differenced and double-differenced AR(1) variables.The author thanks Peter C.B. Phillips for introducing the author to Grenander and Szegö's book on Toeplitz matrices and giving useful comments. The author also thanks two anonymous referees for helpful comments on earlier drafts of the note.

分数单整过程的长期协方差矩阵AI 解读

An asymptotic expansion is given for the autocovariance matrix of a vector of stationary long-memory processes with memory parameters d ∈ [0,½). The theory is then applied to deliver formulas for the long-run covariance matrices of multivariate time series with long memory.Phillips acknowledges partial support from a Kelly Fellowship and from the NSF under grant SES 04-142254. This may be proved directly using a Fourier integral asymptotic expansion when the spectrum of the…

存在多次水平突变的自回归单位根检验AI 解读

The asymptotic distributions of augmented Dickey–Fuller (ADF) unit root tests for autoregressive processes with a unit or near-unit root are discussed in the presence of multiple stochastic level shifts of large size occurring independently in time. The distributions depend on a Brownian motion and a Poisson-type jump process. Due to the latter, tests based on standard critical values experience power losses increasing rapidly with the number and the magnitude of the shifts.…

参数位于边界时的高阶渐近理论及其GARCH应用AI 解读

Andrews (1999, Econometrica 67, 1341–1383) derived the first-order asymptotic theory for a very general class of estimators when a parameter is on a boundary. We derive the second-order asymptotic theory in this setting in some special cases. We focus on the behavior of the quasi maximum likelihood estimator (QMLE) in stationary and nonstationary generalized autoregressive conditionally heteroskedastic (GARCH) models when constraints are imposed in the maximization…

检测单位根与平稳性的序贯监测程序AI 解读

When analyzing time series an important issue is to decide whether the time series is stationary or a random walk. Relaxing these notions, we consider the problem to decide in favor of the I(0) or I(1) property. Fixed-sample statistical tests for that problem are well studied in the literature. In this paper we provide first results for the problem of monitoring sequentially a time series. Our stopping times are based on a sequential version of a kernel-weighted…

现值关系、格兰杰非因果性与VAR稳定性AI 解读

When in the class of “exact” present value (PV) relations the decision variables do not Granger cause the explanatory variables, and a vector autoregressive (VAR) process is used to derive the cross-equation restrictions, the system embodies explosive roots, which hardly can be reconciled with the typical features observed in most macroeconomic time series. This paper investigates the issue.I thank Paolo Paruolo and two anonymous referees for helpful comments and suggestions…