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未知阈值的回归折点模型AI 解读

This article explores estimation and inference in a regression kink model with an unknown threshold. A regression kink model (or continuous threshold model) is a threshold regression constrained to be everywhere continuous with a kink at an unknown threshold. We present methods for estimation, to test for the presence of the threshold, for inference on the regression parameters, and for inference on the regression function. A novel finding is that inference on the regression…

评论AI 解读

Factor-augmented regression is widely applied to forecasting in a data-rich environment. For most papers in the literature, a small number of factors are assumed to generate the comovement of a lar...

因子增广回归预测：频率学派模型平均方法AI 解读

This paper considers forecast combination with factor-augmented regression. In this framework, a large number of forecasting models are available, varying by the choice of factors and the number of lags. We investigate forecast combination across models using weights that minimize the Mallows and the leave-h-out cross validation criteria. The unobserved factor regressors are estimated by principle components of a large panel with N predictors over T periods. With these…

近单位根自回归模型的平均估计量AI 解读

This paper uses local-to-unity theory to evaluate the asymptotic mean-squared error (AMSE) and forecast expected squared error from least-squares estimation of an autoregressive model with a root close to unity. We investigate unconstrained estimation, estimation imposing the unit root constraint, pre-test estimation, model selection estimation, and model average estimation. We find that the asymptotic risk depends only on the local-to-unity parameter, facilitating simple…

可能存在结构断点的回归平均估计量AI 解读

This paper investigates selection and averaging of linear regressions with a possible structural break. Our main contribution is the construction of a Mallows criterion for the structural break model. We show that the correct penalty term is nonstandard and depends on unknown parameters, but it can be approximated by an average of limiting cases to yield a feasible penalty with good performance. Following Hansen (2007, Econometrica 75, 1175–1189) we recommend averaging the…

最小二乘预测平均AI 解读

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…

区间预测与参数不确定性AI 解读

Forecast intervals generalize point forecasts to represent and incorporate uncertainty. Forecast intervals calculated from dynamic models typically sidestep the issue of parameter estimation. This paper shows how to construct asymptotic forecast intervals which incorporate the uncertainty due to parameter estimation. Our proposed solution is a simple proportional adjustment to the interval endpoints, the adjustment factor depending on the asymptotic variance of the interval…

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含单位根的门槛自回归模型AI 解读

This paper develops an asymptotic theory of inference for an unrestricted two-regime threshold autoregressive (TAR) model with an autoregressive unit root. We find that the asymptotic null distribution of Wald tests for a threshold are nonstandard and different from the stationary case, and suggest basing inference on a bootstrap approximation. We also study the asymptotic null distributions of tests for an autoregressive unit root, and find that they are nonstandard and…

样本划分与门槛估计AI 解读

Threshold models have a wide variety of applications in economics. Direct applications include models of separating and multiple equilibria. Other applications include empirical sample splitting when the sample split is based on a continuously-distributed variable such as firm size. In addition, threshold models may be used as a parsimonious strategy for nonparametric function estimation. For example, the threshold autoregressive model (TAR) is popular in the nonlinear time…

网格Bootstrap与自回归模型AI 解读

A "grid" bootstrap method is proposed for confidence-interval construction, which has improved performance over conventional bootstrap methods when the sampling distribution depends upon the parameter of interest. The basic idea is to calculate the bootstrap distribution over a grid of values of the parameter of interest and form the confidence interval by the no-rejection principle. Our primary motivation is given by autoregressive models, where it is known that…

结构变化检验的近似渐近 p 值AI 解读

Numerical approximations to the asymptotic distributions of recently proposed tests for structural change are presented. This enables easy yet accurate calculation of asymptotic p-values. Keywords: parameter stability, changepoint models

结构变化检验的近似渐近p值AI 解读

Numerical approximations to the asymptotic distributions of recently proposed tests for structural change are presented. This enables easy yet accurate calculation of asymptotic p values. A GAUSS program is available to perform the computations.

原假设下干扰参数未被识别时的统计推断AI 解读

The authors study the asymptotic distribution of econometric tests involving nuisance parameters that are not identified under the null hypotheses. In general, the asymptotic distributions depend upon a large number of unknown parameters. The authors show that a transformation based upon a conditional probability measure yields an asymptotic distribution free of nuisance parameters and they show that this transformation can be easily approximated via simulation. The theory…

存在机制转换的协整模型中基于残差的检验AI 解读

In this paper we examine tests for cointegration which allow for the possibility of regime shifts. We propose ADF-, Zα-, and Zt-type tests designed to test the null of no cointegration against the alternative of cointegration in the presence of a possible regime shift. In particular we consider cases where the intercept and/or slope coefficients have a single break of unknown timing. A formal proof is provided for the limiting distributions of the various tests for the…

重新思考单变量单位根检验：利用协变量提高功效AI 解读

In the context of testing for a unit root in a univariate time series, the convention is to ignore information in related time series. This paper shows that this convention is quite costly, as large power gains can be achieved by including correlated stationary covariates in the regression equation. The paper derives the asymptotic distribution of ordinary least-squares estimates of the largest autoregressive root and its t-statistic. The asymptotic distribution is not the…

非平稳波动率下的回归AI 解读

A new asymptotic theory of regression is introduced for possibly nonstationary time series. The regressors are assumed to be generated by a linear process with martingale difference innovations. The conditional variances of these martingale differences are specified as autoregressive stochastic volatility processes with autoregressive roots that are local to unity. The author finds conditions under which the least squares estimates are consistent and asymptotically normal. A…

季节模式是否随时间保持不变？季节稳定性检验AI 解读

This paper introduces Lagrange multiplier tests of the null hypothesis of no unit roots at seasonal frequencies against the alternative of a unit root at either a single seasonal frequency or a set of seasonal frequencies. The tests complement those of D. Dickey, D. Hasza, and W. Fuller (1984) and S. Hylleberg, et al. (1990), which examine the null of seasonal unit roots. The authors derive an asymptotic distribution theory for the tests and investigate their size and power…

相依异质过程向随机积分的收敛AI 解读

This paper provides conditions to establish the weak convergence of stochastic integrals. The theorems are proved under the assumption that the innovations are strong mixing with uniformly bounded 2-h moments. Several applications of the results are given, relevant for the theories of estimation with I (1) processes, I (2) processes, processes with nonstationary variances, near-integrated processes, and continuous time approximations.

异方差协整AI 解读

This paper develops an asymptotic theory of estimation and inference in ‘cointegrated’ regression models with errors displaying nonstationary variances. Least squares estimates are shown to be consistent at a T12 rate. Hypothesis testing requires the use of a robust covariance matrix estimate, in contrast to earlier work on cointegrated regressions. The inference theory is not nuisance-free, but preliminary investigations indicate that approximation by the normal…

存在确定性趋势时协整向量的有效估计与检验AI 解读

Estimation and inference in cointegrated models is examined in the presence of deterministic trends in the data. It is suggested that trends be excluded in the levels regression for maximal efficiency. Fully modified test statistics are asymptotically chi-square. A chi-square test for the validity of trend exclusion is presented. The asymptotic distributions of standard cointegration test statistics are shown to depend both upon regressor trends and estimation detrending…

含 I(1) 过程回归中的参数不稳定性检验AI 解读

This article derives the large-sample distributions of Lagrange multiplier (LM) tests for parameter instability against several alternatives of interest in the context of cointegrated regression models. The fully modified estimator of Phillips and Hansen is extended to cover general models with stochastic and deterministic trends. The test statistics considered include the SupF test of Quandt, as well as the LM tests of Nyblom and of Nabeya and Tanaka. It is found that the…

This paper studies the asymptotic properties of instrumental variable (IV) estimates of multivariate cointegrating regressions and allows for deterministic and stochastic regressors as well as quite general deterministic processes in the data-generating mechanism. It is found that IV regressions are consistent even when the instruments are stochastically independent of the regressors. This phenomenon, which contrasts with traditional theory for stationary time series, is a…