A multiple error-correction model of housing supply

This paper considers supply dynamics in the context of the Irish residential market. The analysis, in a multiple error-correction framework, reveals that although developers did respond to disequilibrium in supply, the rate of adjustment was relatively slow. In contrast, however, disequilibrium in demand did not impact upon supply, suggesting that inelastic supply conditions could explain the prolonged nature of the boom in the Irish market. Increased elasticity in the later stages of the boom may have been a contributory factor in the extent of the house price falls observed in recent years.

Conditioning of the weak-constraint variational data assimilation problem for numerical weather prediction

4-Dimensional Variational Data Assimilation (4DVAR) assimilates observations through the minimisation of a least-squares objective function, which is constrained by the model flow. We refer to 4DVAR as strong-constraint 4DVAR (sc4DVAR) in this thesis as it assumes the model is perfect. Relaxing this assumption gives rise to weak-constraint 4DVAR (wc4DVAR), leading to a different minimisation problem with more degrees of freedom. We consider two wc4DVAR formulations in this thesis, the model error formulation and state estimation formulation. The 4DVAR objective function is traditionally solved using gradient-based iterative methods. The principle method used in Numerical Weather Prediction today is the Gauss-Newton approach. This method introduces a linearised `inner-loop' objective function, which upon convergence, updates the solution of the non-linear `outer-loop' objective function. This requires many evaluations of the objective function and its gradient, which emphasises the importance of the Hessian. The eigenvalues and eigenvectors of the Hessian provide insight into the degree of convexity of the objective function, while also indicating the difficulty one may encounter while iterative solving 4DVAR. The condition number of the Hessian is an appropriate measure for the sensitivity of the problem to input data. The condition number can also indicate the rate of convergence and solution accuracy of the minimisation algorithm. This thesis investigates the sensitivity of the solution process minimising both wc4DVAR objective functions to the internal assimilation parameters composing the problem. We gain insight into these sensitivities by bounding the condition number of the Hessians of both objective functions. We also precondition the model error objective function and show improved convergence. We show that both formulations' sensitivities are related to error variance balance, assimilation window length and correlation length-scales using the bounds. We further demonstrate this through numerical experiments on the condition number and data assimilation experiments using linear and non-linear chaotic toy models.

Bayesian estimation of co-integrating thresholds in the term structure of interest rates.

Threshold Error Correction Models are used to analyse the term structure of interest Rates. The paper develops and uses a generalisation of existing models that encompasses both the Band and Equilibrium threshold models of [Balke and Fomby ((1997) Threshold cointegration. Int Econ Rev 38(3):627–645)] and estimates this model using a Bayesian approach. Evidence is found for threshold effects in pairs of longer rates but not in pairs of short rates. The Band threshold model is supported in preference to the Equilibrium model.

Property company performance and real interest rates: a regime-switching approach

Linear models of property market performance may be misspecified if there exist distinct states where the market drivers behave in different ways. This paper examines the applicability of non-linear regime-based models. A Self Exciting Threshold Autoregressive (SETAR) model is applied to property company share data, using the real rate of interest to define regimes. Distinct regimes appear exhibiting markedly different market behaviour. The model both casts doubt on the specification of conventional linear models and offers the possibility of developing effective trading rules for real estate equities.

Does consumption-wealth ratio signal stock returns? VECM results for Germany

This paper studies the signalling effect of the consumption−wealth ratio (cay) on German stock returns via vector error correction models (VECMs). The effect of cay on U.S. stock returns has been recently confirmed by Lettau and Ludvigson with a two−stage method. In this paper, performance of the VECMs and the two−stage method are compared in both German and U.S. data. It is found that the VECMs are more suitable to study the effect of cay on stock returns than the two−stage method. Using the Conditional−Subset VECM, cay signals real stock returns and excess returns in both data sets significantly. The estimated coefficient on cay for stock returns turns out to be two times greater in U.S. data than in German data. When the two−stage method is used, cay has no significant effect on German stock returns. Besides, it is also found that cay signals German wealth growth and U.S. income growth significantly.

The impact of liquidity on senior credit index spreads during the subprime crisis

This paper examines the effects of liquidity during the 2007–09 crisis, focussing on the Senior Tranche of the CDX.NA.IG Index and on Moody's AAA Corporate Bond Index. It aims to understand whether the sharp increase in the credit spreads of these AAA-rated credit indices can be explained by worse credit fundamentals alone or whether it also reflects a lack of depth in the relevant markets, the scarcity of risk-capital, and the liquidity preference exhibited by investors. Using cointegration analysis and error correction models, the paper shows that during the crisis lower market and funding liquidity are important drivers of the increase in the credit spread of the AAA-rated structured product, whilst they are less significant in explaining credit spread changes for a portfolio of unstructured credit instruments. Looking at the experience of the subprime crisis, the study shows that when the conditions under which securitisation can work properly (liquidity, transparency and tradability) suddenly disappear, investors are left highly exposed to systemic risk.

Implicit equal-weights particle filter

Filter degeneracy is the main obstacle for the implementation of particle filter in non-linear high-dimensional models. A new scheme, the implicit equal-weights particle filter (IEWPF), is introduced. In this scheme samples are drawn implicitly from proposal densities with a different covariance for each particle, such that all particle weights are equal by construction. We test and explore the properties of the new scheme using a 1,000-dimensional simple linear model, and the 1,000-dimensional non-linear Lorenz96 model, and compare the performance of the scheme to a Local Ensemble Kalman Filter. The experiments show that the new scheme can easily be implemented in high-dimensional systems and is never degenerate, with good convergence properties in both systems.

Nonlinear system identification using particle swarm optimisation tuned radial basis function models

A novel particle swarm optimisation (PSO) tuned radial basis function (RBF) network model is proposed for identification of non-linear systems. At each stage of orthogonal forward regression (OFR) model construction process, PSO is adopted to tune one RBF unit's centre vector and diagonal covariance matrix by minimising the leave-one-out (LOO) mean square error (MSE). This PSO aided OFR automatically determines how many tunable RBF nodes are sufficient for modelling. Compared with the-state-of-the-art local regularisation assisted orthogonal least squares algorithm based on the LOO MSE criterion for constructing fixed-node RBF network models, the PSO tuned RBF model construction produces more parsimonious RBF models with better generalisation performance and is often more efficient in model construction. The effectiveness of the proposed PSO aided OFR algorithm for constructing tunable node RBF models is demonstrated using three real data sets.

Linear-wavelet models applied to the identification of a two-link manipulator

This paper shows that a wavelet network and a linear term can be advantageously combined for the purpose of non linear system identification. The theoretical foundation of this approach is laid by proving that radial wavelets are orthogonal to linear functions. A constructive procedure for building such nonlinear regression structures, termed linear-wavelet models, is described. For illustration, sim ulation data are used to identify a model for a two-link robotic manipulator. The results show that the introduction of wavelets does improve the prediction ability of a linear model.

Optimal piecewise locally linear modeling

Associative memory networks such as Radial Basis Functions, Neurofuzzy and Fuzzy Logic used for modelling nonlinear processes suffer from the curse of dimensionality (COD), in that as the input dimension increases the parameterization, computation cost, training data requirements, etc. increase exponentially. Here a new algorithm is introduced for the construction of a Delaunay input space partitioned optimal piecewise locally linear models to overcome the COD as well as generate locally linear models directly amenable to linear control and estimation algorithms. The training of the model is configured as a new mixture of experts network with a new fast decision rule derived using convex set theory. A very fast simulated reannealing (VFSR) algorithm is utilized to search a global optimal solution of the Delaunay input space partition. A benchmark non-linear time series is used to demonstrate the new approach.

Can we explain the dynamics of the UK FTSE 100 stock and stock index futures markets?

If stock and stock index futures markets are functioning properly price movements in these markets should best be described by a first order vector error correction model with the error correction term being the price differential between the two markets (the basis). Recent evidence suggests that there are more dynamics present than should be in effectively functioning markets. Using self-exciting threshold autoregressive (SETAR) models, this study analyses whether such dynamics can be related to different regimes within which the basis can fluctuate in a predictable manner without triggering arbitrage. These findings reveal that the basis shows strong evidence of autoregressive behaviour when its value is between the two thresholds but that the extra dynamics disappear once the basis moves above the upper threshold and their persistence is reduced, although not eradicated, once the basis moves below the lower threshold. This suggests that once nonlinearity associated with transactions costs is accounted for, stock and stock index futures markets function more effectively than is suggested by linear models of the pricing relationship.

Measures of observation impact in non-Gaussian data assimilation

ABSTRACT Non-Gaussian/non-linear data assimilation is becoming an increasingly important area of research in the Geosciences as the resolution and non-linearity of models are increased and more and more non-linear observation operators are being used. In this study, we look at the effect of relaxing the assumption of a Gaussian prior on the impact of observations within the data assimilation system. Three different measures of observation impact are studied: the sensitivity of the posterior mean to the observations, mutual information and relative entropy. The sensitivity of the posterior mean is derived analytically when the prior is modelled by a simplified Gaussian mixture and the observation errors are Gaussian. It is found that the sensitivity is a strong function of the value of the observation and proportional to the posterior variance. Similarly, relative entropy is found to be a strong function of the value of the observation. However, the errors in estimating these two measures using a Gaussian approximation to the prior can differ significantly. This hampers conclusions about the effect of the non-Gaussian prior on observation impact. Mutual information does not depend on the value of the observation and is seen to be close to its Gaussian approximation. These findings are illustrated with the particle filter applied to the Lorenz ’63 system. This article is concluded with a discussion of the appropriateness of these measures of observation impact for different situations.

Ensemble clustering in deterministic ensemble Kalman filters

Ensemble clustering (EC) can arise in data assimilation with ensemble square root filters (EnSRFs) using non-linear models: an M-member ensemble splits into a single outlier and a cluster of M−1 members. The stochastic Ensemble Kalman Filter does not present this problem. Modifications to the EnSRFs by a periodic resampling of the ensemble through random rotations have been proposed to address it. We introduce a metric to quantify the presence of EC and present evidence to dispel the notion that EC leads to filter failure. Starting from a univariate model, we show that EC is not a permanent but transient phenomenon; it occurs intermittently in non-linear models. We perform a series of data assimilation experiments using a standard EnSRF and a modified EnSRF by a resampling though random rotations. The modified EnSRF thus alleviates issues associated with EC at the cost of traceability of individual ensemble trajectories and cannot use some of algorithms that enhance performance of standard EnSRF. In the non-linear regimes of low-dimensional models, the analysis root mean square error of the standard EnSRF slowly grows with ensemble size if the size is larger than the dimension of the model state. However, we do not observe this problem in a more complex model that uses an ensemble size much smaller than the dimension of the model state, along with inflation and localisation. Overall, we find that transient EC does not handicap the performance of the standard EnSRF.

On a stochastic Trotter formula with application to spontaneous localization models

We consider the relation between so called continuous localization models—i.e. non-linear stochastic Schrödinger evolutions—and the discrete GRW-model of wave function collapse. The former can be understood as scaling limit of the GRW process. The proof relies on a stochastic Trotter formula, which is of interest in its own right. Our Trotter formula also allows to complement results on existence theory of stochastic Schrödinger evolutions by Holevo and Mora/Rebolledo.