Our research primarily deals with theory and empirical applications of non-Gaussian econometric time series models. Currently we focus, in particular, on the following models:
- Noninvertible and noncausal time series models
- Vector autoregressive (VAR) models, including nonlinear, non-Gaussian and non-causal VAR models, cointegrated VAR models, as well as structural VAR models
- Univariate and multivariate Gaussian mixture autoregressive (GMAR) models
- Discrete and limited dependent time series models
Our theoretical work involves derivation of the properties of these models, and development of both classical and Bayesian methods of inference and forecasting related to them. Our empirical applications range from pricing financial risks to modelling the effects of monetary policy and forecasting the phases of the business cycle by means of financial information.
Noncausal autoregressive models containing both leads and lags of the included variables are useful in modelling expectations and capturing nonfundamentalness arising from missing variables in econometric time series models. So far, we have put forth both classical and Bayesian methods of inference and forecasting in univariate and multivariate noncausal reduced-form autoregressions. In ongoing research, we consider structural inference in these models.
Structural vector autoregressive (SVAR) models have turned out to be quite versatile in that they are applicable to a wide range of economic and financial research questions.The general idea of SVAR analysis is to fit a reduced-form vector autoregression (VAR) to a set of data, and by imposing restrictions on it, identify linear combinations of (at least some of) the components of its error term as independent or uncorrelated economic shocks. Our research on SVAR models concentrates on statistical identification, i.e., the use of the statistical properties of the data, such as non-Gaussianity, in identification. We are also considering structural analysis in the noncausal VAR model under non-Gaussianity.
In Gaussian mixture autoregressive (GMAR) model, the conditional distribution of each observation is a mixture of two or more Gaussian distributions. Which one of these conditional distributions (or linear AR processes) generates the observation, is governed by conditional probabilities referred to as mixing weights. These mixing weights are functions of a few past observations and it is their clever definition that gives the GMAR model its beneficial properties and structure. In particular, stationarity and ergodicity are straightforward to establish, and even an explicit expression for the stationary distribution can be obtained. These theoretical properties, not shared by other general nonlinear AR models proposed in the literature, in our experience, also translate into good performance in empirical applications. In addition to diverse regime shifts in the conditional mean and variance, the GMAR model is also capable of allowing for various nonnormal shapes such as bimodality in both the stationary and conditional distribution. It can also be quite effective in capturing conditional heteroskedasticity of the type encountered in monthly or quarterly macroeconomic data. This can make the GMAR model and its extensions viable alternatives in modelling the regimes in, say, economic policy or financial markets.
Linear and nonlinear econometric models are typically designed for continuous real-valued variables. However, the dependent variable can also be limited, such as discrete with only a limited number of possible outcomes, or censored so that only values from a certain range are possible. An example of the former is a binary time series (i.e. two possible values) measuring, e.g., the state of the business cycle (expansion or recession) or the state of the stock market (bear or bull market). Our goal is to introduce new econometric models suitable for these kinds of time series, and to develop estimation and forecasting tools related to them. In addition to the methodological advances, empirical applications utilising them provide new insights into the behaviour of the macroeconomy and financial markets, with implications for the development of theoretical financial and macroeconomic models, and practical decision making of practitioners.