Finite Sample Experiments Research Articles

Model-free bootstrap for a general class of stationary time series

A model-free bootstrap procedure for a general class of stationary time series is introduced. The theoretical framework is established, showing asymptotic validity of bootstrap confidence intervals for many statistics of interest. In addition, asymptotic validity of one-step ahead bootstrap prediction intervals is also demonstrated. Finite-sample experiments are conducted to empirically confirm the performance of the new method, and to compare with popular methods such as the block bootstrap and the autoregressive (AR)-sieve bootstrap.

Estimation of Sparsity-Induced Weak Factor Models

This article investigates estimation of sparsity-induced weak factor (sWF) models, with large cross-sectional and time-series dimensions (N and T, respectively). It assumes that the kth largest eigenvalue of a data covariance matrix grows proportionally to with unknown exponents for . Employing the same rotation of the principal components (PC) estimator, the growth rate αk is linked to the degree of sparsity of kth factor loadings. This is much weaker than the typical assumption on the recent factor models, in which all the r largest eigenvalues diverge proportionally to N. We apply the method of sparse orthogonal factor regression (SOFAR) by Uematsu et al. (2019) to estimate the sWF models and derive the estimation error bound. Importantly, our method also yields consistent estimation of αk . A finite sample experiment shows that the performance of the new estimator uniformly dominates that of the PC estimator. We apply our method to forecasting bond yields and the results demonstrate that our method outperforms that based on the PC. We also analyze S&P500 firm security returns and find that the first factor is consistently near strong while the others are weak.

Fast and efficient algorithms for sparse semiparametric bifunctional regression

SummaryA new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a single‐index structure, while the other is included linearly through the high‐dimensional vector formed by its discretised observations. For this model, two new algorithms are presented for selecting relevant variables in the linear part and estimating the model. Both procedures utilise the functional origin of linear covariates. Finite sample experiments demonstrated the scope of application of both algorithms: the first method is a fast algorithm that provides a solution (without loss in predictive ability) for the significant computational time required by standard variable selection methods for estimating this model, and the second algorithm completes the set of relevant linear covariates provided by the first, thus improving its predictive efficiency. Some asymptotic results theoretically support both procedures. A real data application demonstrated the applicability of the presented methodology from a predictive perspective in terms of the interpretability of outputs and low computational cost.

Estimation of Weak Factor Models

This paper investigates estimation of sparsity-induced weak factor (sWF) models, with large cross-sectional and time-series dimensions (N and T, respectively). It assumes that the kth largest eigenvalue of a data covariance matrix grows proportionally to N^alpha_k with unknown exponents 0 < alpha_k <= 1 for k=1,...,r. Employing the same rotation of the principal components (PC) estimator, the growth rate alpha_k is linked to the degree of sparsity of kth factor loadings. This is much weaker than the typical assumption on the recent factor models, in which all the r largest eigenvalues diverge proportionally to N. We apply the method of sparse orthogonal factor regression (SOFAR) by Uematsu et al (2018) to estimate the sWF models and derive the estimation error bound. Importantly, our method also yields consistent estimation of alpha_k. A finite sample experiment shows that the performance of the new estimator uniformly dominates that of the PC estimator. We apply our method to forecasting bond yields and the results demonstrate that our method outperforms that based on the PC. We also analyze S&P500 firm security returns and find that the first factor is consistently near strong while the others are weak.

Stationary bootstrapping for panel cointegration tests under cross-sectional dependence

Stationary bootstrapping is applied to panel cointegration tests which are based on the ordinary least-squares estimator and the seemingly unrelated regression (SUR) estimator of the residual unit root. Large sample validity of stationary bootstrapping is established. A finite sample experiment reveals that size performances of the bootstrap tests are much less sensitive to cross-sectional correlation than those of existing tests and a test based on the SUR estimator has substantially better power than existing tests.

Non parametric derivative estimation with confidence bands

ABSTRACTWe propose a spline-based derivative estimation. Derivative estimation plays an important role in the exploration of structures in curves. Consistency property of the estimator is obtained under some mild assumptions. We construct simultaneous confidence bands for the derivatives, therefore statistical inference for the relative change of curves can be derived. Finite-sample experiments confirm the asymptotic results. We illustrate the methods with applications to a fossil dataset and a US climate dataset.

Two-step spline estimating equations for generalized additive partially linear models with large cluster sizes

We propose a two-step estimating procedure for generalized additive partially linear models with clustered data using estimating equations. Our proposed method applies to the case that the number of observations per cluster is allowed to increase with the number of independent subjects. We establish oracle properties for the two-step estimator of each function component such that it performs as well as the univariate function estimator by assuming that the parametric vector and all other function components are known. Asymptotic distributions and consistency properties of the estimators are obtained. Finite-sample experiments with both simulated continuous and binary response variables confirm the asymptotic results. We illustrate the methods with an application to a U.S. unemployment data set.

Joint analysis and estimation of stock prices and trading volume in Barndorff-Nielsen and Shephard stochastic volatility models

We introduce a variant of the Barndorff-Nielsen and Shephard stochastic volatility model where the non-Gaussian Ornstein–Uhlenbeck process describes some measure of trading intensity like trading volume or number of trades instead of unobservable instantaneous variance. We develop an explicit estimator based on martingale estimating functions in a bivariate model that is not a diffusion, but admits jumps. It is assumed that both the quantities are observed on a discrete grid of fixed width, and the observation horizon tends to infinity. We show that the estimator is consistent and asymptotically normal and give explicit expressions of the asymptotic covariance matrix. Our method is illustrated by a finite sample experiment and a statistical analysis of IBM™ stock from the New York Stock Exchange and Microsoft Corporation™ stock from Nasdaq during a history of five years.

The Effect of Estimating Parameters on Long‐Term Forecasts for Cointegrated Systems

ABSTRACTThis paper concerns Long‐term forecasts for cointegrated processes. First, it considers the case where the parameters of the model are known. The paper analytically shows that neither cointegration nor integration constraint matters in Long‐term forecasts. It is an alternative implication of Long‐term forecasts for cointegrated processes, extending the results of previous influential studies. The appropriate Mote Carlo experiment supports our analytical result. Secondly, and more importantly, it considers the case where the parameters of the model are estimated. The paper shows that accuracy of the estimation of the drift term is crucial in Long‐term forecasts. Namely, the relative accuracy of various Long‐term forecasts depends upon the relative magnitude of variances of estimators of the drift term. It further experimentally shows that in finite samples the univariate ARIMA forecast, whose drift term is estimated by the simple time average of differenced data, is better than the cointegrated system forecast, whose parameters are estimated by the well‐known Johansen's ML method. Based upon finite sample experiments, it recommends the univariate ARIMA forecast rather than the conventional cointegrated system forecast in finite samples for its practical usefulness and robustness against model misspecifications. Copyright © 2011 John Wiley &amp; Sons, Ltd.

On Asymptotic Theory and Finite Sample Experiments

theme of the volume is doggedly operational. In effect, one is encouraged to formulate each Econometric problem precisely as dictated by the requisite Economic Theory, and solve the resultant estimation problem directly, by numerically maximizing the relevant likelihood function, thus eschewing approximations of unknown magnitude and importance. finite sample behaviour of the adopted estimator can then be simulated to provide evidence on the reliability of the empirical results. In this rather novel methodology, the large body of established theory on the asymptotic of estimators is assigned a limited role and merits discussion in but one chapter. The small sample problem stems from the fact that asymptotic results provide no clear guide to finite sample distributions (p. 219), although . . one would like to know how large is 'large' (p. 76). Agreed, and specifically investigating this should surely be an important objective of experimental work on small-sample properties. However, comparisons with asymptotic results materialize only for situations in which the Maximum Likelihood Estimator is believed consistent and asymptotically efficient, even though Goldfeld and Quandt (G-Q below) consider a most commendable number of examples of mis-specified models or incorrect estimator choices. One of the main purposes of this review article is to indicate how valuable asymptotic theory can be in clarifying simulation work by applying it to their findings on the magnitudes and directions of the biases observed in Ordinary Least Squares estimates for their system