Business cycle asymmetries: characterisation and testing based on Markov-switching autoregressions

Tests for business cycle asymmetries are developed for Markov-switching autoregressive models. The tests of deepness, steepness, and sharpness are Wald statistics, which have standard asymptotics. For the standard two-regime model of expansions and contractions, deepness is shown to imply sharpness (and vice versa), whereas the process is always nonsteep. Two and three-state models of U.S. GNP growth are used to illustrate the approach, along with models of U.S. investment and consumption growth. The robustness of the tests to model misspecification, and the effects of regime-dependent heteroscedasticity, are investigated.

Threshold autoregressive and Markov switching models: an application to commercial real estate

Although financial theory rests heavily upon the assumption that asset returns are normally distributed, value indices of commercial real estate display significant departures from normality. In this paper, we apply and compare the properties of two recently proposed regime switching models for value indices of commercial real estate in the US and the UK, both of which relax the assumption that observations are drawn from a single distribution with constant mean and variance. Statistical tests of the models' specification indicate that the Markov switching model is better able to capture the non-stationary features of the data than the threshold autoregressive model, although both represent superior descriptions of the data than the models that allow for only one state. Our results have several implications for theoretical models and empirical research in finance.

House price dynamics and their reaction to macroeconomic changes

This article applies a three-regime Markov switching model to investigate the impact of the macroeconomy on the dynamics of the residential real estate market in the US. Focusing on the period between 1960 and 2011, the methodology implemented allows for a clearer understanding of the drivers of the real estate market in “boom”, “steady-state” and “crash” regimes. Our results show that the sensitivity of the real estate market to economic changes is regime-dependent. The paper then proceeds to examine whether policymakers are able to influence a regime switch away from the crash regime. We find that a decrease in interest rate spreads could be an effective catalyst to precipitate such a change of state.

Futures trading, spot price volatility and market efficiency: evidence from European real estate securities futures

In 2007 futures contracts were introduced based upon the listed real estate market in Europe. Following their launch they have received increasing attention from property investors, however, few studies have considered the impact their introduction has had. This study considers two key elements. Firstly, a traditional Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model, the approach of Bessembinder & Seguin (1992) and the Gray’s (1996) Markov-switching-GARCH model are used to examine the impact of futures trading on the European real estate securities market. The results show that futures trading did not destabilize the underlying listed market. Importantly, the results also reveal that the introduction of a futures market has improved the speed and quality of information flowing to the spot market. Secondly, we assess the hedging effectiveness of the contracts using two alternative strategies (naïve and Ordinary Least Squares models). The empirical results also show that the contracts are effective hedging instruments, leading to a reduction in risk of 64 %.

On the predictive content of leading indicators: the case of U.S. real estate markets

This paper employs a probit and a Markov switching model using information from the Conference Board Leading Indicator and other predictor variables to forecast the signs of future rental growth in four key U.S. commercial rent series. We find that both approaches have considerable power to predict changes in the direction of commercial rents up to two years ahead, exhibiting strong improvements over a naïve model, especially for the warehouse and apartment sectors. We find that while the Markov switching model appears to be more successful, it lags behind actual turnarounds in market outcomes whereas the probit is able to detect whether rental growth will be positive or negative several quarters ahead.

Are mortgage lenders guilty of the housing bubble? A UK perspective

Existing theoretical models of house prices and credit rely on continuous rationality of consumers, an assumption that has been frequently questioned in recent years. Meanwhile, empirical investigations of the relationship between prices and credit are often based on national-level data, which is then tested for structural breaks and asymmetric responses, usually with subsamples. Earlier author argues that local markets are structurally different from one another and so the coefficients of any estimated housing market model should vary from region to region. We investigate differences in the price–credit relationship for 12 regions of the UK. Markov-switching is introduced to capture asymmetric market behaviours and turning points. Results show that credit abundance had a large impact on house prices in Greater London and nearby regions alongside a strong positive feedback effect from past house price movements. This impact is even larger in Greater London and the South East of England when house prices are falling, which are the only instances where the credit effect is more prominent than the positive feedback effect. A strong positive feedback effect from past lending activity is also present in the loan dynamics. Furthermore, bubble probabilities extracted using a discrete Kalman filter neatly capture market turning points.

Hidden Markov analysis describes dive patterns in semiaquatic animals

Existing methods of dive analysis, developed for fully aquatic animals, tend to focus on frequency of behaviors rather than transitions between them. They, therefore, do not account for the variability of behavior of semiaquatic animals, and the switching between terrestrial and aquatic environments. This is the first study to use hidden Markov models (HMM) to divide dives of a semiaquatic animal into clusters and thus identify the environmental predictors of transition between behavioral modes. We used 18 existing data sets of the dives of 14 American mink (Neovison vison) fitted with time-depth recorders in lowland England. Using HMM, we identified 3 behavioral states (1, temporal cluster of dives; 2, more loosely aggregated diving within aquatic activity; and 3, terminal dive of a cluster or a single, isolated dive). Based on the higher than expected proportion of dives in State 1, we conclude that mink tend to dive in clusters. We found no relationship between temperature and the proportion of dives in each state or between temperature and the rate of transition between states, meaning that in our study area, mink are apparently not adopting different diving strategies at different temperatures. Transition analysis between states has shown that there is no correlation between ambient temperature and the likelihood of mink switching from one state to another, that is, changing foraging modes. The variables provided good discrimination and grouped into consistent states well, indicating promise for further application of HMM and other state transition analyses in studies of semiaquatic animals.

Modelling heterotachy in phylogenetic inference by reversible-jump Markov chain Monte Carlo

The rate at which a given site in a gene sequence alignment evolves over time may vary. This phenomenon-known as heterotachy-can bias or distort phylogenetic trees inferred from models of sequence evolution that assume rates of evolution are constant. Here, we describe a phylogenetic mixture model designed to accommodate heterotachy. The method sums the likelihood of the data at each site over more than one set of branch lengths on the same tree topology. A branch-length set that is best for one site may differ from the branch-length set that is best for some other site, thereby allowing different sites to have different rates of change throughout the tree. Because rate variation may not be present in all branches, we use a reversible-jump Markov chain Monte Carlo algorithm to identify those branches in which reliable amounts of heterotachy occur. We implement the method in combination with our 'pattern-heterogeneity' mixture model, applying it to simulated data and five published datasets. We find that complex evolutionary signals of heterotachy are routinely present over and above variation in the rate or pattern of evolution across sites, that the reversible-jump method requires far fewer parameters than conventional mixture models to describe it, and serves to identify the regions of the tree in which heterotachy is most pronounced. The reversible-jump procedure also removes the need for a posteriori tests of 'significance' such as the Akaike or Bayesian information criterion tests, or Bayes factors. Heterotachy has important consequences for the correct reconstruction of phylogenies as well as for tests of hypotheses that rely on accurate branch-length information. These include molecular clocks, analyses of tempo and mode of evolution, comparative studies and ancestral state reconstruction. The model is available from the authors' website, and can be used for the analysis of both nucleotide and morphological data.

Inference on microsatellite mutation processes in the invasive mite, Varroa destructor, using reversible jump Markov chain Monte Carlo

Varroa destructor is a parasitic mite of the Eastern honeybee Apis cerana. Fifty years ago, two distinct evolutionary lineages (Korean and Japanese) invaded the Western honeybee Apis mellifera. This haplo-diploid parasite species reproduces mainly through brother sister matings, a system which largely favors the fixation of new mutations. In a worldwide sample of 225 individuals from 21 locations collected on Western honeybees and analyzed at 19 microsatellite loci, a series of de novo mutations was observed. Using historical data concerning the invasion, this original biological system has been exploited to compare three mutation models with allele size constraints for microsatellite markers: stepwise (SMM) and generalized (GSM) mutation models, and a model with mutation rate increasing exponentially with microsatellite length (ESM). Posterior probabilities of the three models have been estimated for each locus individually using reversible jump Markov Chain Monte Carlo. The relative support of each model varies widely among loci, but the GSM is the only model that always receives at least 9% support, whatever the locus. The analysis also provides robust estimates of mutation parameters for each locus and of the divergence time of the two invasive lineages (67,000 generations with a 90% credibility interval of 35,000-174,000). With an average of 10 generations per year, this divergence time fits with the last post-glacial Korea Japan land separation. (c) 2005 Elsevier Inc. All rights reserved.

Bayesian analysis of correlated evolution of discrete characters by reversible-jump Markov chain Monte Carlo

We describe a Bayesian method for investigating correlated evolution of discrete binary traits on phylogenetic trees. The method fits a continuous-time Markov model to a pair of traits, seeking the best fitting models that describe their joint evolution on a phylogeny. We employ the methodology of reversible-jump ( RJ) Markov chain Monte Carlo to search among the large number of possible models, some of which conform to independent evolution of the two traits, others to correlated evolution. The RJ Markov chain visits these models in proportion to their posterior probabilities, thereby directly estimating the support for the hypothesis of correlated evolution. In addition, the RJ Markov chain simultaneously estimates the posterior distributions of the rate parameters of the model of trait evolution. These posterior distributions can be used to test among alternative evolutionary scenarios to explain the observed data. All results are integrated over a sample of phylogenetic trees to account for phylogenetic uncertainty. We implement the method in a program called RJ Discrete and illustrate it by analyzing the question of whether mating system and advertisement of estrus by females have coevolved in the Old World monkeys and great apes.

Detecting recombination in 4-taxa DNA sequence alignments with Bayesian hidden Markov models and Markov chain Monte Carlo

This article presents a statistical method for detecting recombination in DNA sequence alignments, which is based on combining two probabilistic graphical models: (1) a taxon graph (phylogenetic tree) representing the relationship between the taxa, and (2) a site graph (hidden Markov model) representing interactions between different sites in the DNA sequence alignments. We adopt a Bayesian approach and sample the parameters of the model from the posterior distribution with Markov chain Monte Carlo, using a Metropolis-Hastings and Gibbs-within-Gibbs scheme. The proposed method is tested on various synthetic and real-world DNA sequence alignments, and we compare its performance with the established detection methods RECPARS, PLATO, and TOPAL, as well as with two alternative parameter estimation schemes.

Estimation of Hidden Markov Models parameters using differential evolution

Hidden Markov Models (HMMs) have been successfully applied to different modelling and classification problems from different areas over the recent years. An important step in using HMMs is the initialisation of the parameters of the model as the subsequent learning of HMM’s parameters will be dependent on these values. This initialisation should take into account the knowledge about the addressed problem and also optimisation techniques to estimate the best initial parameters given a cost function, and consequently, to estimate the best log-likelihood. This paper proposes the initialisation of Hidden Markov Models parameters using the optimisation algorithm Differential Evolution with the aim to obtain the best log-likelihood.