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on Econometric Time Series |
| By: | Arnaud Dufays; Aristide Houndetoungan; Alain Co\"en |
| Abstract: | Change-point processes are one flexible approach to model long time series. We propose a method to uncover which model parameter truly vary when a change-point is detected. Given a set of breakpoints, we use a penalized likelihood approach to select the best set of parameters that changes over time and we prove that the penalty function leads to a consistent selection of the true model. Estimation is carried out via the deterministic annealing expectation-maximization algorithm. Our method accounts for model selection uncertainty and associates a probability to all the possible time-varying parameter specifications. Monte Carlo simulations highlight that the method works well for many time series models including heteroskedastic processes. For a sample of 14 Hedge funds (HF) strategies, using an asset based style pricing model, we shed light on the promising ability of our method to detect the time-varying dynamics of risk exposures as well as to forecast HF returns. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.05329&r=ets |
| By: | Nigar Hashimzade; Oleg Kirsanov; Tatiana Kirsanova; Junior Maih |
| Abstract: | This paper presents a framework for empirical analysis of dynamic macroeconomic models using Bayesian filtering, with a specific focus on the state-space formulation of New Keynesian Dynamic Stochastic General Equilibrium (NK DSGE) models with multiple regimes. We outline the theoretical foundations of model estimation, provide the details of two families of powerful multiple-regime filters, IMM and GPB, and construct corresponding multiple-regime smoothers. A simulation exercise, based on a prototypical NK DSGE model, is used to demonstrate the computational robustness of the proposed filters and smoothers and evaluate their accuracy and speed. We show that the canonical IMM filter is faster than the commonly used Kim and Nelson (1999) filter and is no less, and often more, accurate. Using it with the matching smoother improves the precision in recovering unobserved variables by about 25%. Furthermore, applying it to the U.S. 1947-2023 macroeconomic time series, we successfully identify significant past policy shifts including those related to the post-Covid-19 period. Our results demonstrate the practical applicability and potential of the proposed routines in macroeconomic analysis. |
| Keywords: | Markov switching models, filtering, smoothing |
| JEL: | C11 C32 C54 E52 |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10941&r=ets |
| By: | Jooyoung Cha |
| Abstract: | Impulse response analysis studies how the economy responds to shocks, such as changes in interest rates, and helps policymakers manage these effects. While Vector Autoregression Models (VARs) with structural assumptions have traditionally dominated the estimation of impulse responses, local projections, the projection of future responses on current shock, have recently gained attention for their robustness and interpretability. Including many lags as controls is proposed as a means of robustness, and including a richer set of controls helps in its interpretation as a causal parameter. In both cases, an extensive number of controls leads to the consideration of high-dimensional techniques. While methods like LASSO exist, they mostly rely on sparsity assumptions - most of the parameters are exactly zero, which has limitations in dense data generation processes. This paper proposes a novel approach that incorporates high-dimensional covariates in local projections without relying on sparsity constraints. Adopting the Orthogonal Greedy Algorithm with a high-dimensional AIC (OGA+HDAIC) model selection method, this approach offers advantages including robustness in both sparse and dense scenarios, improved interpretability by prioritizing cross-sectional explanatory power, and more reliable causal inference in local projections. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.07743&r=ets |
| By: | Chotipong Charoensom |
| Abstract: | This paper proposes an approach to develop regime switching models where latent process determining the switching is endogenously controlled by the model shocks with free functional forms. The linear endogeneity assumption in the conventional endogenous regime switching models can therefore be relaxed. A recursive filter technique is applied to proceed maximum likelihood estimation in order to estimate the model parameters. A nonlinear endogenous two-regime switching mean-volatility model is conducted in numerical examples to investigate the model performance. In the examples, the endogeneity in switching allows heterogeneous effects of the shock signs (asymmetric endogeneity) and of the states being before the switching determination (state-dependent endogeneity). Monte Carlo simulations show that the conventional switching model ignoring the nonlinear endogeneity leads to the volatility biases. The estimates tend to be over or under their true value depending on how the endogeneity characteristics are. In particular, the true model that accounts the nonlinear endogeneity effectively provides the more precise estimates. The same model is also applied to real data of excess returns on US stock market, and the estimation results informatively describe the effects influencing the regime shifts. |
| Keywords: | Nonlinear endogeneity; Regime switching; Maximum likelihood estimation; Asymmetric endogeneity; State-dependent endogeneity |
| JEL: | C13 C32 |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:pui:dpaper:217&r=ets |
| By: | Jungjun Choi; Ming Yuan |
| Abstract: | This paper studies the principal components (PC) estimator for high dimensional approximate factor models with weak factors in that the factor loading ($\boldsymbol{\Lambda}^0$) scales sublinearly in the number $N$ of cross-section units, i.e., $\boldsymbol{\Lambda}^{0\top} \boldsymbol{\Lambda}^0 / N^\alpha$ is positive definite in the limit for some $\alpha \in (0, 1)$. While the consistency and asymptotic normality of these estimates are by now well known when the factors are strong, i.e., $\alpha=1$, the statistical properties for weak factors remain less explored. Here, we show that the PC estimator maintains consistency and asymptotical normality for any $\alpha\in(0, 1)$, provided suitable conditions regarding the dependence structure in the noise are met. This complements earlier result by Onatski (2012) that the PC estimator is inconsistent when $\alpha=0$, and the more recent work by Bai and Ng (2023) who established the asymptotic normality of the PC estimator when $\alpha \in (1/2, 1)$. Our proof strategy integrates the traditional eigendecomposition-based approach for factor models with leave-one-out analysis similar in spirit to those used in matrix completion and other settings. This combination allows us to deal with factors weaker than the former and at the same time relax the incoherence and independence assumptions often associated with the later. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.05789&r=ets |
| By: | Fabrizio Ghezzi; Eduardo Rossi; Lorenzo Trapani |
| Abstract: | We study online changepoint detection in the context of a linear regression model. We propose a class of heavily weighted statistics based on the CUSUM process of the regression residuals, which are specifically designed to ensure timely detection of breaks occurring early on during the monitoring horizon. We subsequently propose a class of composite statistics, constructed using different weighing schemes; the decision rule to mark a changepoint is based on the largest statistic across the various weights, thus effectively working like a veto-based voting mechanism, which ensures fast detection irrespective of the location of the changepoint. Our theory is derived under a very general form of weak dependence, thus being able to apply our tests to virtually all time series encountered in economics, medicine, and other applied sciences. Monte Carlo simulations show that our methodologies are able to control the procedure-wise Type I Error, and have short detection delays in the presence of breaks. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.04433&r=ets |