Bayesian inference in cointegrated systems

In this paper I deal with Bayesian methods for conducting inference on important features of (potentially) cointegrated VAR models involving I(1) variables. Firstly, (informal) inference is made on the cointegrating rank of the system. Secondly, posterior analysis is used to verify the validity of over-identifying restrictions on the cointegration parameters. Thirdly, posterior distributions are obtained for impulse response functions and predictive densities at different horizons. The relevant posterior distributions are obtained by means of Monte Carlo integration. The analysis is based on the use of simple weakly informative priors. Two applications on simulated data and on the Danish money demand data are presented.     

Causality: a Statistical View

Statistical aspects of causality are reviewed in simple form and the impact of recent work discussed. Three distinct notions of causality are set out and implications for densities and for linear dependencies explained. The importance of appreciating the possibility of effect modifiers is stressed, be they intermediate variables, background variables or unobserved confounders. In many contexts the issue of unobserved confounders is salient. The difficulties of interpretation when there are joint effects are discussed and possible modifications of analysis explained. The dangers of uncritical conditioning and marginalization over intermediate response variables are set out and some of the problems of generalizing conclusions to populations and individuals explained. In general terms the importance of search for possibly causal variables is stressed but the need for caution is emphasized.     

Heterogeneous learning

There is by now a large literature characterising conditions under which learning schemes converge to rational expectations equilibria (REEs). It has been claimed that these results depend on the assumption of homogeneous agents and homogeneous learning. This paper analyses the stability of REEs under heterogeneous adaptive learning, for the class of self-referential linear stochastic models. Agents may differ in their initial perceptions about the evolution of the economy, the degrees of inertia in revising their expectations, or the learning rules they use. General conditions are provided for local stability of an REE. In general, it is not possible to show that stability under homogeneous learning implies stability under heterogeneous learning. To illustrate how to apply the results, several examples are provided.     

Public capital, endogenous growth, and endogenous fluctuations

Cazzavillan [Cazzavillan, G., 1996. Public spending, endogenous growth, and endogenous fluctuations. Journal of Economic Theory 71, 394–415] studies a discrete-time, one-sector endogenous growth model with a flow of publicly enjoyable goods and productive services financed through income taxation. He demonstrates how equilibrium paths are indeterminate, for a large range of the consumption externality of public spending. This study extends [Cazzavillan, 1996] by considering an otherwise identical production function, except with public capital stock as an input. The results support the robustness of multiple growth paths even in a one-sector growth model with public capital stock, and modify the set of the consumption externality of public spending, in determining growth dynamics in a similar model with non-accumulated public spending.     

Bayesian time series analysis of periodic behaviour and spectral structure

Analysis, model selection and forecasting in univariate time series models can be routinely carried out for models in which the model order is relatively small. Under an ARMA assumption, classical estimation, model selection and forecasting can be routinely implemented with the Box–Jenkins time domain representation. However, this approach becomes at best prohibitive and at worst impossible when the model order is high. In particular, the standard assumption of stationarity imposes constraints on the parameter space that are increasingly complex. One solution within the pure AR domain is the latent root factorization in which the characteristic polynomial of the AR model is factorized in the complex domain, and where inference questions of interest and their solution are expressed in terms of the implied (reciprocal) complex roots; by allowing for unit roots, this factorization can identify any sustained periodic components. In this paper, as an alternative to identifying periodic behaviour, we concentrate on frequency domain inference and parameterize the spectrum in terms of the reciprocal roots, and, in addition, incorporate Gegenbauer components. We discuss a Bayesian solution to the various inference problems associated with model selection involving a Markov chain Monte Carlo (MCMC) analysis. One key development presented is a new approach to forecasting that utilizes a Metropolis step to obtain predictions in the time domain even though inference is being carried out in the frequency domain. This approach provides a more complete Bayesian solution to forecasting for ARMA models than the traditional approach that truncates the infinite AR representation, and extends naturally to Gegenbauer ARMA and fractionally differenced models.     

A Partially Observed Model for Micromovement of Asset Prices with Bayes Estimation via Filtering

A general micromovement model that describes transactional price behavior is proposed. The model ties the sample characteristics of micromovement and macromovement in a consistent manner. An important feature of the model is that it can be transformed to a filtering problem with counting process observations. Consequently, the complete information of price and trading time is captured and then utilized in Bayes estimation via filtering for the parameters. The filtering equations are derived. A theorem on the convergence of conditional expectation of the model is proved. A consistent recursive algorithm is constructed via the Markov chain approximation method to compute the approximate posterior and then the Bayes estimates. A simplified model and its recursive algorithm are presented in detail. Simulations show that the computed Bayes estimates converge to their true values. The algorithm is applied to one month of intraday transaction prices for Microsoft and the Bayes estimates are obtained.     

The Effect of Market Regimes on Style Allocation

We analyse time-varying risk premia and the implications for portfolio choice. Using Markov Chain Monte Carlo (MCMC) methods, we estimate a multivariate regime-switching model for the Carhart (1997) four-factor model. We find two clearly separable regimes with different mean returns, volatilities, and correlations. In the High-Variance Regime, only value stocks deliver a good performance, whereas in the Low-Variance Regime, the market portfolio and momentum stocks promise high returns. Regime-switching induces investors to change their portfolio style over time depending on the investment horizon, the risk aversion, and the prevailing regime. Value investing seems to be a rational strategy in the High-Variance Regime, momentum investing in the Low-Variance Regime. An empirical out-of-sample backtest indicates that this switching strategy can be profitable, but the overall forecasting ability for the regime-switching model seems to be weak compared to the iid model.     

Adjustable-rate mortgages,household mobility,and homeownership: A simulation study

A semi-Markov model is used to evaluate the effects of adjustable-rate mortgages on housing tenure decisions of recent movers and steady-state homeownership rates. Simulations were undertaken based on household data from the Panel Study of Income Dynamics together with information on FRM-ARM rate spreads and Treasury yield curves. Results suggest that under most interest rate patterns that prevailed in the 1980s, ARMS had little effect on the relative cost of owning to renting and, as a result, had little effect on mover tenure choice and home sales. Moreover, despite some minor projected increase in the percentage of movers that choose to own when ARMs are available, ARM effects on steady-state owner-occupancy rates appear to be largely mitigated by an ARM-induced tilt toward a relatively more mobile steady-state pool of owner-occupiers.     

Performance of cumulative sum schemes for monitoring low count-level processes

In many instances attributes data must be used to monitor a manufacturing (or other) process that, in normal conditions, should operate at very low count levels for defects. Lucas (1989) has directed attention to this problem, and has investigated a new control scheme for low count-level processes. An alternative scheme is proposed, based on a Cumulative Sum (CUSUM) of the number (termed Run-Length) of successive samples having zero count-levels between samples having at least one count. Using the criterion of Average Run Length (the average number of samples until a signal is generated) comparisons of the Lucas scheme and the Run-Length CUSUM scheme indicate that ARL values for the Run-Length CUSUM can be up to 50% lower.     

Dynamical analysis of corporate bonds based on the yield spread term-quality surface

Our aim of this research is to propose a model which estimates implied relative credit reliability from the yield spread of defaultable bonds and evaluates their spread risk. We introduce “yield spread term-quality surface” (YSTQS) which is defined on the space of duration and credit reliability of the issuers, and express their yield spread. First, we review the general pricing theorem of defaultable bonds with unpredictable recovery in the no-arbitrage context based on the external hazard rates. Second, we show that the dynamics of state variables determine the shape of the YSTQS, and they drive the YSTQS if the loss-adjusted hazard rates are described by a function of them. Finally, we show an empirical analysis of our model with daily yield spread, duration, and the credit ratings of corporate bonds.