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Change-point (CP) processes are one flexible approach to model long time series. We propose a method to uncover which model parameters truly vary when a CP 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 fourteen hedge fund (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.

We propose a new volatility process in which parameters vary over time according to an artificial neural network (ANN). We prove the process’s stationarity as well as the global identification of the parameters. Since ANNs require economic series as input variables, we develop a shrinkage approach to select which explanatory variables are relevant to forecast volatility. Empirically, the proposed model favorably compares with other flexible processes in terms of in-sample fit on six financial returns. It also delivers accurate short-term volatility predictions in terms of root mean squared errors and the predictive likelihood criterion. For long-term forecasts, it can be competitive with the Markov-switching generalized autoregressive conditional heteroskedastic (MS-GARCH) model if appropriate exogenous variables are used. Since our new type of time-varying parameter (TVP) process is based on a universal approximator, the approach can readily revisit and potentially improve many standard TVP applications.

Structural break time series models, which are commonly used in macroeconomics and finance, capture unknown structural changes by allowing for abrupt changes to model parameters. However, many specifications suffer from an over-parametrization issue, since typically all parameters have to change when a break occurs. We introduce a sparse change-point model to detect which parameters change over time. We propose a shrinkage prior distribution, which controls model parsimony by limiting the number of parameters that change from one structural break to another. We develop a Bayesian sampler for inference on the sparse change-point model. An extensive simulation study based on AR, ARMA and GARCH processes highlights the excellent performance of the sampler. We provide several empirical applications including an out-of-sample forecasting exercise showing that the Sparse change-point framework compares favorably with other recent time-varying parameter processes.

Change-point time series specifications constitute flexible models that capture unknown structural changes by allowing for switches in the model parameters. Nevertheless most models suffer from an ...

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.

Sequential Monte Carlo (SMC) methods are widely used for non-linear filtering purposes. However, the SMC scope encompasses wider applications such as estimating static model parameters so much that it is becoming a serious alternative to Markov-Chain Monte-Carlo (MCMC) methods. Not only do SMC algorithms draw posterior distributions of static or dynamic parameters but additionally they provide an estimate of the marginal likelihood. The tempered and time (TNT) algorithm, developed in this paper, combines (off-line) tempered SMC inference with on-line SMC inference for drawing realizations from many sequential posterior distributions without experiencing a particle degeneracy problem. Furthermore, it introduces a new MCMC rejuvenation step that is generic, automated and well-suited for multi-modal distributions. As this update relies on the wide heuristic optimization literature, numerous extensions are readily available. The algorithm is notably appropriate for estimating change-point models. As an example, we compare several change-point GARCH models through their marginal log-likelihoods over time.

Change-point time series specifications constitute flexible models that capture unknown structural changes by allowing for switches in the model parameters. Nevertheless most models suffer from an over-parametrization issue since typically only one latent state variable drives the switches in all parameters. This implies that all parameters have to change when a break happens. To gauge whether and where there are structural breaks in realized variance, we introduce the sparse change-point HAR model. The approach controls for model parsimony by limiting the number of parameters which evolve from one regime to another. Sparsity is achieved thanks to employing a nonstandard shrinkage prior distribution. We derive a Gibbs sampler for inferring the parameters of this process. Simulation studies illustrate the excellent performance of the sampler. Relying on this new framework, we study the stability of the HAR model using realized variance series of several major international indices between January 2000 and August 2015.

Markov-switching models are usually specified under the assumption that all the parameters change when a regime switch occurs. Relaxing this hypothesis and being able to detect which parameters evolve over time is relevant for interpreting the changes in the dynamics of the series, for specifying models parsimoniously, and may be helpful in forecasting. We propose the class of sticky infinite hidden Markov-switching autoregressive moving average models, in which we disentangle the break dynamics of the mean and the variance parameters. In this class, the number of regimes is possibly infinite and is determined when estimating the model, thus avoiding the need to set this number by a model choice criterion. We develop a new Markov chain Monte Carlo estimation method that solves the path dependence issue due to the moving average component. Empirical results on macroeconomic series illustrate that the proposed class of models dominates the model with fixed parameters in terms of point and density forecasts. Appendix available at: https://ssrn.com/abstract=2965668

Sequential Monte Carlo (SMC) methods are widely used for filtering purposes of non-linear economic or financial models. Nevertheless the SMC scope encompasses wider applications such as estimating static model parameters so much that it is becoming a serious alternative to Markov- Chain Monte-Carlo (MCMC) methods. Not only SMC algorithms draw posterior distributions of static or dynamic parameters but additionally provide an estimate of the normalizing constant. The tempered and time (TNT) algorithm, developed in the paper, combines (off-line) tempered SMC inference with on-line SMC inference for estimating many slightly different distributions. The method encompasses the Iterated Batch Importance Sampling (IBIS) algorithm and more generally the Resample Move (RM) algorithm. Besides the number of particles, the TNT algorithm self-adjusts its calibrated parameters and relies on a new MCMC kernel that allows for particle interactions. The algorithm is well suited for efficiently back-testing models. We conclude by comparing in-sample and out-of-sample performances of complex volatility models.

We present an estimation and forecasting method, based on a differential evolution MCMC method, for inference in GARCH models subjected to an unknown number of structural breaks at unknown dates. We treat break dates as parameters and determine the number of breaks by computing the marginal likelihoods of competing models. We allow for both recurrent and non-recurrent (change-point) regime specifications. We illustrate the estimation method through simulations and apply it to seven financial time series of daily returns. We find structural breaks in the volatility dynamics of all series and recurrent regimes in nearly all series. Finally, we carry out a forecasting exercise to evaluate the usefulness of structural break models.

GARCH volatility models with fixed parameters are too restrictive for long time series due to breaks in the volatility process. Flexible alternatives are Markov-switching GARCH and change-point GARCH models. They require estimation by MCMC methods due to the path dependence problem. An unsolved issue is the computation of their marginal likelihood, which is essential for determining the number of regimes or change-points. We solve the problem by using particle MCMC, a technique proposed by Andrieu, Doucet, and Holenstein (2010). We examine the performance of this new method on simulated data, and we illustrate its use on several return series.