Work in progress 

Robustness of Multistep Forecasts and Predictive Regressions at Intermediate and Long Horizons

Publications

We propose a near explosive random coefficient autoregressive model (NERC) to obtain predictive probabilities of the apparition and devolution of bubbles. The distribution of the autoregressive coefficient of this model is allowed to be centred at an O(T^{−α}) distance of unity, with α ∈ (0,1). When the expectation of the autoregressive coefficient lies on the explosive side of unity, the NERC helps to model the temporary explosiveness of time series and obtain related predictive probabilities. We study the asymptotic properties of the NERC and provide a procedure for inference on the parameters. 

Long-run restrictions are a very popular method for identifying structural vector autoregressions, but they suffer from weak identification when the data is very persistent, i.e., when the highest autoregressive roots are near unity. Near unit roots introduce additional nuisance parameters and make standard weak-instrument-robust methods of inference inapplicable. We develop a method of inference that is robust to both weak identification and strong persistence.

This paper studies the low frequency dynamics in forward looking models where expectations are formed using perpetual learning such as constant gain least squares. We show that if the coefficient on expectations is sufficiently close to unity, perpetual learning induces strong persistence that is empirically indistinguishable from long memory. We apply this result to present value models of stock prices and exchange rates and find that perpetual learning can explain the long memory observed in the data.

(previously circulated as Long Memory through Marginalization of Large Systems and Hidden Cross-Section Dependence)

This paper shows that a large dimensional vector autoregressive model (VAR) of finite order can generate fractional integration in the marginalized univariate series. We derive high-level assumptions under which the final equation representation of a VAR(1) leads to univariate fractional white noises and verify the validity of these assumptions for two specific models. 

We study learning dynamics in a prototypical representative-agent forward-looking model in which agents’ beliefs are updated using linear learning algorithms. We show that learning in this model can generate long memory endogenously, without any persistence in the exogenous shocks, depending on the weights agents place on past observations when they update their beliefs, and on the magnitude of the feedback from expectations to the endogenous variable. This is distinctly different from the case of rational expectations, where the memory of the endogenous variable is determined exogenously.

In this paper, I consider how to improve forecasting techniques when the underlying data generating process is subject to stochastic shifts. I show how the improvement relates to the forecasting horizon.

Here I comment on a paper by B. Rossi and T. Sekhposyan. I assess in particular the conditions under which their methods for evaluating predictive densities can be generalized to multi-step ahead forecasts.

This article considers the issue of estimation and inference in models where agents' forward-looking expectations are formed via adaptive learning. We show that nonstandard dynamics result and invalidate standard techniques of inference. We provide valid methods and assess them by means of a three-equation new Keynesian macro model.

This papers evaluates the risk premium associated with the price of crude oil. The risk premium is defined as the difference between actual pricing and pricing based on historical demand and supply conditions

This article considers techniques for forecasting in a multivariate framework when the forecast horizon of interest varies and the economy is subject to breaks or change. This is mostly an empirical paper that assess how best to forecast the GDP of South Africa. 

This paper reviews existing results and provides a framework for understanding the interplay between the forecast horizon and the forecasting techniques.

We consider the optimal methods for forecasting as a function of the horizon at which it is wished to obtain a forecast.