Guillaume Chevillon

Non-Parametric Direct Multi-Step Estimation for Forecasting Economic Processes

We evaluate the asymptotic and finite-sample properties of direct multi-step estimation (DMS) for forecasting at several horizons. For forecast accuracy gains from DMS in finite samples, mis-specification and non-stationarity of the DGP are necessary, but when a model is well-specified, iterating the one-step ahead forecasts may not be asymptotically preferable. If a model is mis-specified for a non-stationary DGP, omitting either negative residual serial correlation or regime shifts, DMS can forecast more accurately. Monte Carlo simulations clarify the non-linear dependence of the estimation and forecast biases on the parameters of the DGP, and explain existing results.

Direct Multi-Step Estimation and Forecasting

This paper surveys the literature on multi-step forecasting when the model or the estimation method focuses directly on the link between the forecast origin and the horizon of interest. Among diverse contributions, we show how the current consensual concepts have emerged. We present an exhaustive overview of the existing results, including a conclusive review of the circumstances favourable to direct multi-step forecasting, namely different forms of non-stationarity and appropriate model design. We also provide a unifying framework which allows us to analyse the sources of forecast errors and hence of accuracy improvements from direct over iterated multi-step forecasting. Copyright 2007 The Author. Journal compilation

Physical Market Determinants of the Price of Crude Oil and the Market Premium

We analyze the determinants of the real price of crude oil by means of an equilibrium correction model over the last two decades where we focus on the aspects of the physical market that impact on the clearing price. We find that two cointegrating relations affect the changes in prices: one refers to OPECs behavior, attempting to control prices using its market power and quotas; the other to the coverage rate of OECD expected future demand using inventory behaviors. We derive a forecasting equation for the change in oil prices which we use to assess the speculative elements of the price increases of the period 2000-05. We show that worries alien to the physical markets were the causes of the increase in oil prices and we quantify their overall impact.

Inference in the Presence of Stochastic and Deterministic Trends

The focus of this paper is inference about stochastic and deterministic trends when both types are present. We show that, contrary to asymptotic theory and the existing literature, the parameters of the deterministic components must be taken into account in finite samples. We analyze the ubiquitous Likelihood Ratio test for the rank of cointegration in vector processes. Here, we directly control the parameters of the data generating process so that a local-asymptotic framework accounts for small sample interactions between stochastic and deterministic trends. We show that the usual corrections are invalid as they take no account of the relative magnitudes of these two types of trends. Block-local models provide an embedding framework which provides a rationale for consistent estimation and testing of the whole set of parameters. In an empirical application to European GDP series, we show that using usual corrections leads to underestimating the number of stochastic trends.

Learning Generates Long Memory

We consider a prototypical representative-agent forward-looking model, and study the low frequency variability of the data when the agents beliefs about the model are updated through linear learning algorithms. We find that learning in this context can generate strong persistence. The degree of persistence depends 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. When the learning algorithm is recursive least squares, long memory arises when the coefficient on expectations is sufficiently large. In algorithms with discounting, long memory provides a very good approximation to the low-frequency variability of the data. Hence long memory arises endogenously, due to the self-referential nature of the model, without any persistence in the exogenous shocks. This is distinctly different from the case of rational expectations, where the memory of the endogenous variable is determined exogenously. Finally, this property of learning is used to shed light on some well-known empirical puzzles.

Robust cointegration testing in the presence of weak trends, with an application to the human origin of global warming

Standard tests for the rank of cointegration of a vector autoregressive process present distributions that are affected by the presence of deterministic trends. We consider the recent approach of Demetrescu et al. (2009) who recommend testing a composite null. We assess this methodology in the presence of trends (linear or broken) whose magnitude is small enough not to be detectable at conventional significance levels. We model them using local asymptotics and derive the properties of the test statistics. We show that whether the trend is orthogonal to the cointegrating vector has a major impact on the distributions but that the test combination approach remains valid. We apply of the methodology to the study of cointegration properties between global temperatures and the radiative forcing of human gas emissions. We find new evidence of Granger Causality.

Robust Inference in Structural Vars with Long-Run Restrictions

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. The method is based on a combination of the Anderson-Rubin test with instruments derived by filtering potentially non-stationary variables to make them near stationary. We apply our method to obtain robust confidence bands on impulse responses in two leading applications in the literature.

Long Memory Through Marginalization of Large Systems and Hidden Cross-Section Dependence

This paper shows that large dimensional vector autoregressive (VAR) models of finite order can generate long memory 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 consider the implications of our findings for the variances of asset returns where the so-called golden-rule of realized variances states that they tend always to exhibit fractional integration of a degree close to 0:4.

Detecting and Forecasting Large Deviations and Bubbles in a Near-Explosive Random Coefficient Model

This paper proposes a Near Explosive Random-Coefficient autoregressive model for asset pricing which accommodates both the fundamental asset value and the recurrent presence of autonomous deviations or bubbles. Such a process can be stationary with or without fat tails, unit-root nonstationary or exhibit temporary exponential growth. We develop the asymptotic theory to analyze ordinary least-squares (OLS) estimation. One important theoretical observation is that the estimator distribution in the random coefficient model is qualitatively different from its distribution in the equivalent fixed coefficient model. We conduct recursive and full-sample inference by inverting the asymptotic distribution of the OLS test statistic, a common procedure in the presence of localizing parameters. This methodology allows to detect the presence of bubbles and establish probability statements on their apparition and devolution. We apply our methods to the study of the dynamics of the Case-Shiller index of U.S. house prices. Focusing in particular on the change in the price level, we provide an early detection device for turning points of booms and bust of the housing market.

Local-Explosive Approximations to Null Distributions of the Johansen Cointegration Test, with an Application to Cyclical Concordance in the Euro Area

This paper considers approximating the nite sample null-distribution of a test statistic as its asymptotic distribution under a local alternative. We focus on the Likelihood Ratio test for the rank of cointegration and use nonlinearities that represent some nite sample distributional features. Reliable approximations are obtained using a class of locally explosive models. An empirical evaluation of the concordance of European business cycles through cointegration shows that some standard corrections lead to underestimating the number of cointegrating relations and induce volatile results.