Estimation in a Hazard Regression Model with Smooth Transitions over Unknown Regimes

Modified profile likelihood for panel data models

Hierarchical Bayesian autoregressive smooth transition time series models

Hierarchical Bayesian smooth transition autoregressive models provide accurate forecasts by accommodating nonlinear regime-switching dynamics while delivering robust uncertainty quantification, which makes them well suited for infectious disease surveillance and public health decision-making in resource-limited, high-uncertainty settings.

Robust estimation of Markov-switching GARCH models

The study of volatility is important in several areas of finance, and GARCH models have been widely used in the literature due to their ability to capture key stylised facts of financial time series. However, in some cases, financial time series exhibit structural changes in volatility dynamics, for which standard GARCH models may be inadequate; in such situations, Markov-switching GARCH models provide a more suitable framework. On the other hand, outliers are often present in empirical data. This paper shows that conventional estimators can be strongly affected by outliers and proposes an estimator that is more robust to their presence. The simulation results and empirical applications indicate that the proposed robust estimator is competitive and useful under contamination, but not uniformly superior to the QML-t estimator.

Parametric Time‐Variation in the Unconditional Volatility: Estimation and Inference

We propose modeling time‐variation in the unconditional volatility by augmenting the standard GARCH model by a deterministic time‐varying intercept. The model, called the additive time‐varying (ATV‐)GARCH model, can be interpreted as a reduced form of a model including covariates and can be derived from a multiplicative decomposition of volatility. It is globally nonstationary but can be locally approximated by a stationary GARCH process. We develop an asymptotic theory using the general theory of nonlinear locally stationary processes. As the main contribution of the paper, we obtain consistency and asymptotic normality of the quasi‐maximum likelihood estimator of the parameters of the ATV‐GARCH model under a moderate strengthening of the standard assumptions used in stationary GARCH models. An empirical application to Oracle Corporation stock returns demonstrates the usefulness of the model.

Modelling BSE Sensex Returns: A Markov Switching Autoregressive Approach

Using the Markov switching autoregressive (MSAR) model, this study examines the return behaviour of the BSE Sensex index from April 1999 to March 2025. The best model for the data was found to be the MSAR (2, 1) model, which includes a first-order autoregressive (AR) component and two different regimes. According to empirical findings, at a 1% significance level, the dependent variable’s first-order lag significantly increased returns in both Regimes 0 and 1. However, in Regime 1, the AR component demonstrated a considerable negative influence, which was not seen in Regime 0. According to the transition probability matrix (TPM), there was a 73.11% chance that the market would go from Regime 1 to Regime 0, and a 49.74% chance that it would move from Regime 0 to Regime 1. The findings imply that, although volatility is treated as being constant throughout regimes, regime transitions are mostly caused by modifications in the mean dynamics of returns. This suggests that although the variation is consistent across all regimes, the market fluctuates between distinct return patterns. This study adds to our understanding of the volatility of the Indian stock market by detaching light on the market dynamics and regime switching (RS) behaviour of the BSE Sensex.

Estimating and Testing Kinks in Panel Data Models

Many economic and financial relationships may change gradually rather than abruptly. We study panel data models in which the coefficient vector is continuous and piecewise linear in calendar time, with a finite number of unknown kink dates at which its slope changes. We propose a penalised least squares estimator that applies adaptive weighted group penalties to the second differences of the coefficient path, and develop asymptotic theory showing that it recovers both the number and the locations of the kinks with probability approaching one. To our knowledge, this is the first panel framework to estimate an unknown number of common kink dates in a time-varying coefficient path under fixed effects. We establish that endpoint slopes converge at the usual cubic regime-length rate and interior slopes at rates determined by their own and adjacent regime lengths. We also develop a coefficient-by-coefficient extension allowing individual regressors to kink at different dates. Monte Carlo evidence supports the good finite sample properties, and we illustrate the method through an application in macro-finance, specifically the relationship between debt and growth.