Our recent research focuses on the following 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.
Mixture autoregressive models are useful for modelling time series that exhibit nonlinearities and regime switching behaviour in the underlying data generating dynamics. They can be described as collections of (typically) linear (vector) autoregressive models referred to as regimes. At each point of time, the process generates an observation from one of its regimes, which is randomly selected according to the probabilities given by the mixing weights. For example, in the Gaussian mixture autoregressive (GMAR) model (Kalliovirta, Meitz, and Saikkonen, 2015), the mixing weights are, for a pth order model, defined as the relative weighted likelihoods of the regimes corresponding to the previous p observations. This specification of the mixing weights is intuitively appealing and accommodates data-driven switching dynamics, but it also leads to attractive theoretical properties such as ergodicity and full knowledge of the stationary distribution of p consecutive observations.
Our research develops new mixture (vector)autoregressive models and studies their theoretical properties, including the structural analysis of these models. Accompanying open source software is also often developed to facilitate numerical analysis of the introduced models.
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.