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on Econometric Time Series |
| By: | Donald W. K. Andrews (Yale University); Ming Li (National University of Singapore) |
| Abstract: | This paper considers nonparametric estimation and inference in first-order autoregressive (AR(1)) models with deterministically time- varying parameters. A key feature of the proposed approach is to allow for time-varying stationarity in some time periods, time-varying nonstationarity (i.e., unit root or local-to-unit root behavior) in other periods, and smooth transitions between the two. The estimation of the AR parameter at any time point is based on a local least squares regression method, where the relevant initial condition is endogenous. We obtain limit distributions for the AR parameter estimator and t-statistic at a given point T in time when the parameter exhibits unit root, local-to-unity, or stationary/stationary-like behavior at time T. These results are used to construct confidence intervals and median- unbiased interval estimators for the AR parameter at any specified point in time. The confidence intervals have correct uniform asymptotic coverage probability regardless of the time-varying stationarity/ nonstationary behavior of the observations. |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2389&r= |
| By: | Lajos Horvath; Lorenzo Trapani; Shixuan Wang |
| Abstract: | In this paper, we develop two families of sequential monitoring procedure to (timely) detect changes in a GARCH(1, 1) model. Whilst our methodologies can be applied for the general analysis of changepoints in GARCH(1, 1) sequences, they are in particular designed to detect changes from stationarity to explosivity or vice versa, thus allowing to check for volatility bubbles. Our statistics can be applied irrespective of whether the historical sample is stationary or not, and indeed without prior knowledge of the regime of the observations before and after the break. In particular, we construct our detectors as the CUSUM process of the quasi-Fisher scores of the log likelihood function. In order to ensure timely detection, we then construct our boundary function (exceeding which would indicate a break) by including a weighting sequence which is designed to shorten the detection delay in the presence of a changepoint. We consider two types of weights: a lighter set of weights, which ensures timely detection in the presence of changes occurring early, but not too early after the end of the historical sample; and a heavier set of weights, called Renyi weights which is designed to ensure timely detection in the presence of changepoints occurring very early in the monitoring horizon. In both cases, we derive the limiting distribution of the detection delays, indicating the expected delay for each set of weights. Our theoretical results are validated via a comprehensive set of simulations, and an empirical application to daily returns of individual stocks. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.17885&r= |
| By: | Daichi Hiraki; Siddhartha Chib; Yasuhiro Omori |
| Abstract: | In this paper we consider the simulation-based Bayesian analysis of stochastic volatility in mean (SVM) models. Extending the highly efficient Markov chain Monte Carlo mixture sampler for the SV model proposed in Kim et al. (1998) and Omori et al. (2007), we develop an accurate approximation of the non-central chi-squared distribution as a mixture of thirty normal distributions. Under this mixture representation, we sample the parameters and latent volatilities in one block. We also detail a correction of the small approximation error by using additional Metropolis-Hastings steps. The proposed method is extended to the SVM model with leverage. The methodology and models are applied to excess holding yields in empirical studies, and the SVM model with leverage is shown to outperform competing volatility models based on marginal likelihoods. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.13986&r= |