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.

Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels

Monte Carlo algorithms often aim to draw from a distribution π by simulating a Markov chain with transition kernel P such that π is invariant under P. However, there are many situations for which it is impractical or impossible to draw from the transition kernel P. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace P by an approximation Pˆ. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how ’close’ the chain given by the transition kernel Pˆ is to the chain given by P . We apply these results to several examples from spatial statistics and network analysis.

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.

Decomposition of surface electromyographic signal using Hidden Markov Model

The detection of physiological signals from the motor system (electromyographic signals) is being utilized in the practice clinic to guide the therapist in a more precise and accurate diagnosis of motor disorders. In this context, the process of decomposition of EMG (electromyographic) signals that includes the identification and classification of MUAP (Motor Unit Action Potential) of a EMG signal, is very important to help the therapist in the evaluation of motor disorders. The EMG decomposition is a complex task due to EMG features depend on the electrode type (needle or surface), its placement related to the muscle, the contraction level and the health of the Neuromuscular System. To date, the majority of researches on EMG decomposition utilize EMG signals acquired by needle electrodes, due to their advantages in processing this type of signal. However, relatively few researches have been conducted using surface EMG signals. Thus, this article aims to contribute to the clinical practice by presenting a technique that permit the decomposition of surface EMG signal via the use of Hidden Markov Models. This process is supported by the use of differential evolution and spectral clustering techniques. The developed system presented coherent results in: (1) identification of the number of Motor Units actives in the EMG signal; (2) presentation of the morphological patterns of MUAPs in the EMG signal; (3) identification of the firing sequence of the Motor Units. The model proposed in this work is an advance in the research area of decomposition of surface EMG signals.

The uniqueness of signature problem in the non-Markov setting

We establish a general framework for a class of multidimensional stochastic processes over [0,1] under which with probability one, the signature (the collection of iterated path integrals in the sense of rough paths) is well-defined and determines the sample paths of the process up to reparametrization. In particular, by using the Malliavin calculus we show that our method applies to a class of Gaussian processes including fractional Brownian motion with Hurst parameter H>1/4, the Ornstein–Uhlenbeck process and the Brownian bridge.

A semi-Markov multistate model for estimation of the mean quality-adjusted survival for non-progressive processes

We discuss the estimation of the expected value of the quality-adjusted survival, based on multistate models. We generalize an earlier work, considering the sojourn times in health states are not identically distributed, for a given vector of covariates. Approaches based on semiparametric and parametric (exponential and Weibull distributions) methodologies are considered. A simulation study is conducted to evaluate the performance of the proposed estimator and the jackknife resampling method is used to estimate the variance of such estimator. An application to a real data set is also included.

Using Normative Markov Decision Processes for Evaluating Electronic Contracts: A Case Study in a Simulated Aerospace Aftermarket

Before signing electronic contracts, a rational agent should estimate the expected utilities of these contracts and calculate the violation risks related to them. In order to perform such pre-signing procedures, this agent has to be capable of computing a policy taking into account the norms and sanctions in the contracts. In relation to this, the contribution of this work is threefold. First, we present the Normative Markov Decision Process, an extension of the Markov Decision Process for explicitly representing norms. In order to illustrate the usage of our framework, we model an example in a simulated aerospace aftermarket. Second, we specify an algorithm for identifying the states of the process which characterize the violation of norms. Finally, we show how to compute policies with our framework and how to calculate the risk of violating the norms in the contracts by adopting a particular policy.

Desenvolvimento de arquitetura para sistemas de reconhecimento automático de voz baseados em modelos ocultos de Markov

Este trabalho foi realizado dentro da área de reconhecimento automático de voz (RAV). Atualmente, a maioria dos sistemas de RAV é baseada nos modelos ocultos de Markov (HMMs) [GOM 99] [GOM 99b], quer utilizando-os exclusivamente, quer utilizando-os em conjunto com outras técnicas e constituindo sistemas híbridos. A abordagem estatística dos HMMs tem mostrado ser uma das mais poderosas ferramentas disponíveis para a modelagem acústica e temporal do sinal de voz. A melhora da taxa de reconhecimento exige algoritmos mais complexos [RAV 96]. O aumento do tamanho do vocabulário ou do número de locutores exige um processamento computacional adicional. Certas aplicações, como a verificação de locutor ou o reconhecimento de diálogo podem exigir processamento em tempo real [DOD 85] [MAM 96]. Outras aplicações tais como brinquedos ou máquinas portáveis ainda podem agregar o requisito de portabilidade, e de baixo consumo, além de um sistema fisicamente compacto. Tais necessidades exigem uma solução em hardware. O presente trabalho propõe a implementação de um sistema de RAV utilizando hardware baseado em FPGAs (Field Programmable Gate Arrays) e otimizando os algoritmos que se utilizam no RAV. Foi feito um estudo dos sistemas de RAV e das técnicas que a maioria dos sistemas utiliza em cada etapa que os conforma. Deu-se especial ênfase aos Modelos Ocultos de Markov, seus algoritmos de cálculo de probabilidades, de treinamento e de decodificação de estados, e sua aplicação nos sistemas de RAV. Foi realizado um estudo comparativo dos sistemas em hardware, produzidos por outros centros de pesquisa, identificando algumas das suas características mais relevantes. Foi implementado um modelo de software, descrito neste trabalho, utilizado para validar os algoritmos de RAV e auxiliar na especificação em hardware. Um conjunto de funções digitais implementadas em FPGA, necessárias para o desenvolvimento de sistemas de RAV é descrito. Foram realizadas algumas modificações nos algoritmos de RAV para facilitar a implementação digital dos mesmos. A conexão, entre as funções digitais projetadas, para a implementação de um sistema de reconhecimento de palavras isoladas é aqui apresentado. A implementação em FPGA da etapa de pré-processamento, que inclui a pré-ênfase, janelamento e extração de características, e a implementação da etapa de reconhecimento são apresentadas finalmente neste trabalho.

Improving mutual fund market timing measures: a markov switching approach

Market timing performance of mutual funds is usually evaluated with linear models with dummy variables which allow for the beta coefficient of CAPM to vary across two regimes: bullish and bearish market excess returns. Managers, however, use their predictions of the state of nature to deÞne whether to carry low or high beta portfolios instead of the observed ones. Our approach here is to take this into account and model market timing as a switching regime in a way similar to Hamilton s Markov-switching GNP model. We then build a measure of market timing success and apply it to simulated and real world data.

Dynamic hedging in Markov regimes

This dissertation proposes a bivariate markov switching dynamic conditional correlation model for estimating the optimal hedge ratio between spot and futures contracts. It considers the cointegration between series and allows to capture the leverage efect in return equation. The model is applied using daily data of future and spot prices of Bovespa Index and R$/US$ exchange rate. The results in terms of variance reduction and utility show that the bivariate markov switching model outperforms the strategies based ordinary least squares and error correction models.

Testing the Markov property with ultra high frequency financial data

This paper develops a framework to test whether discrete-valued irregularly-spaced financial transactions data follow a subordinated Markov process. For that purpose, we consider a specific optional sampling in which a continuous-time Markov process is observed only when it crosses some discrete level. This framework is convenient for it accommodates not only the irregular spacing of transactions data, but also price discreteness. Further, it turns out that, under such an observation rule, the current price duration is independent of previous price durations given the current price realization. A simple nonparametric test then follows by examining whether this conditional independence property holds. Finally, we investigate whether or not bid-ask spreads follow Markov processes using transactions data from the New York Stock Exchange. The motivation lies on the fact that asymmetric information models of market microstructures predict that the Markov property does not hold for the bid-ask spread. The results are mixed in the sense that the Markov assumption is rejected for three out of the five stocks we have analyzed.

Um modelo "time-varying markov-Switching" para crescimento econômico e algoritmo de estimação

Este trabalho elabora um modelo para investigação do padrão de variação do crescimento econômico, entre diferentes países e através do tempo, usando um framework Markov- Switching com matriz de transição variável. O modelo desenvolvido segue a abordagem de Pritchett (2003), explicando a dinâmica do crescimento a partir de uma coleção de diferentes estados – cada qual com seu sub-modelo e padrão de crescimento – através dos quais os países oscilam ao longo do tempo. A matriz de transição entre os diferentes estados é variante no tempo, dependendo de variáveis condicionantes de cada país e a dinâmica de cada estado é linear. Desenvolvemos um método de estimação generalizando o Algoritmo EM de Diebold et al. (1993) e estimamos um modelo-exemplo em painel com a matriz de transição condicionada na qualidade das instituições e no nível de investimento. Encontramos três estados de crescimento: crescimento estável, ‘milagroso’ e estagnação - virtualmente coincidentes com os três primeiros de Jerzmanowski (2006). Os resultados mostram que a qualidade das instituições é um importante determinante do crescimento de longo prazo enquanto o nível de investimento tem papel diferenciado: contribui positivamente em países com boa qualidade de instituições e tem papel pouco relevante para os países com instituições medianas ou piores.

A time-varying markov-switching model for economic growth

This paper investigates economic growth’s pattern of variation across and within countries using a Time-Varying Transition Matrix Markov-Switching Approach. The model developed follows the approach of Pritchett (2003) and explains the dynamics of growth based on a collection of different states, each of which has a sub-model and a growth pattern, by which countries oscillate over time. The transition matrix among the different states varies over time, depending on the conditioning variables of each country, with a linear dynamic for each state. We develop a generalization of the Diebold’s EM Algorithm and estimate an example model in a panel with a transition matrix conditioned on the quality of the institutions and the level of investment. We found three states of growth: stable growth, miraculous growth, and stagnation. The results show that the quality of the institutions is an important determinant of long-term growth, whereas the level of investment has varying roles in that it contributes positively in countries with high-quality institutions but is of little relevance in countries with medium- or poor-quality institutions.