The vector floor and ceiling model

This paper motivates and develops a nonlinear extension of the Vector Autoregressive model which we call the Vector Floor and Ceiling model. Bayesian and classical methods for estimation and testing are developed and compared in the context of an application involving U.S. macroeconomic data. In terms of statistical significance both classical and Bayesian methods indicate that the (Gaussian) linear model is inadequate. Using impulse response functions we investigate the economic significance of the statistical analysis. We find evidence of strong nonlinearities in the contemporaneous relationships between the variables and milder evidence of nonlinearity in the conditional mean

Time varying VARs with inequality restrictions

In many applications involving time-varying parameter VARs, it is desirable to restrict the VAR coe¢ cients at each point in time to be non-explosive. This is an example of a problem where inequality restrictions are imposed on states in a state space model. In this paper, we describe how existing MCMC algorithms for imposing such inequality restrictions can work poorly (or not at all) and suggest alternative algorithms which exhibit better performance. Furthermore, previous algorithms involve an approximation relating to a key integrating constant. Our algorithms are exact, not involving this approximation. In an application involving a commonly-used U.S. data set, we show how this approximation can be a poor one and present evidence that the algorithms proposed in this paper work well

Are apparent findings of nonlinearity due to structural instability in economic time series?

Many modelling issues and policy debates in macroeconomics depend on whether macroeconomic times series are best characterized as linear or nonlinear. If departures from linearity exist, it is important to know whether these are endogenously generated (as in, e.g., a threshold autoregressive model) or whether they merely reflect changing structure over time. We advocate a Bayesian approach and show how such an approach can be implemented in practice. An empirical exercise involving several macroeconomic time series shows that apparent findings of threshold type nonlinearities could be due to structural instability

The Vector Floor and Ceiling Model

This paper motivates and develops a nonlinear extension of the Vector Autoregressive model which we call the Vector Floor and Ceiling model. Bayesian and classical methods for estimation and testing are developed and compared in the context of an application involving U.S. macroeconomic data. In terms of statistical significance both classical and Bayesian methods indicate that the (Gaussian) linear model is inadequate. Using impulse response functions we investigate the economic significance of the statistical analysis. We find evidence of strong nonlinearities in the contemporaneous relationships between the variables and milder evidence of nonlinearity in the conditional mean.Nonlinearity; Bayesian; Vector Autoregression

A semi-invertible Oseledets Theorem with applications to transfer operator cocycles

Oseledets' celebrated Multiplicative Ergodic Theorem (MET) is concerned with the exponential growth rates of vectors under the action of a linear cocycle on R^d. When the linear actions are invertible, the MET guarantees an almost-everywhere pointwise splitting of R^d into subspaces of distinct exponential growth rates (called Lyapunov exponents). When the linear actions are non-invertible, Oseledets' MET only yields the existence of a filtration of subspaces, the elements of which contain all vectors that grow no faster than exponential rates given by the Lyapunov exponents. The authors recently demonstrated that a splitting over R^d is guaranteed even without the invertibility assumption on the linear actions. Motivated by applications of the MET to cocycles of (non-invertible) transfer operators arising from random dynamical systems, we demonstrate the existence of an Oseledets splitting for cocycles of quasi-compact non-invertible linear operators on Banach spaces.Comment: 26 page

Understanding Liquidity and Credit Risks in the Financial Crisis*

This paper develops a structured dynamic factor model for the spreads between London Interbank Offered Rate (LIBOR) and overnight index swap (OIS) rates for a panel of banks. Our model involves latent factors which relect liquidity and credit risk. Our empirical results show that surges in the short term LIBOR-OIS spreads during the 2007-2009 financial crisis were largely driven by liquidity risk. However, credit risk played a more significant role in the longer term (twelve-month) LIBOR-OIS spread. The liquidity risk factors are more volatile than the credit risk factor. Most of the familiar events in the financial crisis are linked more to movements in liquidity risk than credit risk.LIBOR-OIS spread, factor model, credit default swap, Bayesian

Representing the Process of Machine Tool Calibration in First-order Logic

Machine tool calibration requires a wide range of measurement techniques that can be carried out in many different sequences. Planning a machine tool calibration is typically performed by a subject expert with a great understanding of International standards and industrial best-practice guides. However, it is often the case that the planned sequence of measurements is not the optimal. Therefore, in an attempt to improve the process, intelligent computing methods can be designed for plan suggestion. As a starting point, this paper presents a way of converting expert knowledge into first-order logic that can be expressed in the PROLOG language. It then shows how queries can be executed against the logic to construct a knowledge-base of all the different measurements that can be performed during machine tool calibration