Probabilistic forecasting of industrial electricity load with regime switching behavior

This paper suggests a novel inhomogeneous Markov switching approach for the probabilistic forecasting of industrial companies’ electricity loads, for which the load switches at random times between production and standby regimes. The model that we propose describes the transitions between the regimes using a hidden Markov chain with time-varying transition probabilities that depend on calendar variables. We model the demand during the production regime using an autoregressive moving-average (ARMA) process with seasonal patterns, whereas we use a much simpler model for the standby regime in order to reduce the complexity. The maximum likelihood estimation of the parameters is implemented using a differential evolution algorithm. Using the continuous ranked probability score (CRPS) to evaluate the goodness-of-fit of our model for probabilistic forecasting, it is shown that this model often outperforms classical additive time series models, as well as homogeneous Markov switching models. We also propose a simple procedure for classifying load profiles into those with and without regime-switching behaviors.     

Modeling node heterogeneity in latent space models for multidimensional networks

Multidimensional network data can have different levels of complexity, as nodes may be characterized by heterogeneous individual-specific features, which may vary across the networks. This article introduces a class of models for multidimensional network data, where different levels of heterogeneity within and between networks can be considered. The proposed framework is developed in the family of latent space models, and it aims to distinguish symmetric relations between the nodes and node-specific features. Model parameters are estimated via a Markov Chain Monte Carlo algorithm. Simulated data and an application to a real example, on fruits import/export data, are used to illustrate and comment on the performance of the proposed models.     

Latent Markov Modelling of Recidivism Data

This article discusses the application of latent Markov modelling for the analysis of recidivism data. We briefly examine the relations of Markov modelling with log–linear analysis, pointing out pertinent differences as well. We show how the restrictive Markov model may be more easily applicable by adding latent variables to the model, in which case the latent Markov model is a dynamic version of the latent class model. As an illustration, we apply latent Markov analysis on an empirical data set of juvenile prosecution careers, showing how the Markov analyses producing well-fitting and interpretable solutions. We end by comparing the possible contributions of Markov modelling in recidivism research, outlining its drawbacks as well. Recommendations and directions for future research conclude the article.     

A two-step approach for identifying seasonal autoregressive time series forecasting models

One of the most powerful and widely used methodologies for forecasting economic time series is the class of models known as seasonal autoregressive processes. In this article we present a new approach not only for identifying seasonal autoregressive models, but also the degree of differencing required to induce stationarity in the data. The identification method is iterative and consists in systematically fitting increasing order models to the data, and then verifying that the resulting residuals behave like white noise using a two stage autoregressive order determination criterion. Once the order of the process is determined the identified structure is tested to see if it can be simplified. The identification performance of this procedure is contrasted with other order selection procedures for models with ‘gaps.' We also illustrate the forecast performance of the identification method using monthly and quarterly economic data.     

The effect of seasonal adjustment on the properties of business cycle regimes

We study the impact of seasonal adjustment on the properties of business cycle expansion and recession regimes using analytical, simulation and empirical methods. Analytically, we show that the X‐11 adjustment filter both reduces the magnitude of change at turning points and reduces the depth of recessions, with specific effects depending on the length of the recession. A Monte Carlo analysis using Markov‐switching models confirms these properties, with particularly undesirable effects in delaying the recognition of the end of a recession. However, seasonal adjustment can help to clarify the true regime when this is well underway. These results continue to hold when a seasonally non‐stationary process with regime‐dependent mean is misspecified as one with deterministic seasonal effects. The empirical findings, based on four coincident US business cycle indicators, reinforce the analytical and simulation results by showing that seasonal adjustment leads to the identification of longer and shallower recessions than obtained using unadjusted data. Copyright © 2008 John Wiley & Sons, Ltd.     

Mixed Hidden Markov Models for Longitudinal Data: An Overview

In this paper we review statistical methods which combine hidden Markov models (HMMs) and random effects models in a longitudinal setting, leading to the class of so‐called mixed HMMs. This class of models has several interesting features. It deals with the dependence of a response variable on covariates, serial dependence, and unobserved heterogeneity in an HMM framework. It exploits the properties of HMMs, such as the relatively simple dependence structure and the efficient computational procedure, and allows one to handle a variety of real‐world time‐dependent data. We give details of the Expectation‐Maximization algorithm for computing the maximum likelihood estimates of model parameters and we illustrate the method with two real applications describing the relationship between patent counts and research and development expenditures, and between stock and market returns via the Capital Asset Pricing Model.     

Improving Markov switching models using realized variance

This paper proposes a class of models that jointly model returns and ex post variance measures under a Markov switching framework. Both univariate and multivariate return versions of the model are introduced. Estimation can be conducted under a fixed dimension state space or an infinite one. The proposed models can be seen as nonlinear common factor models subject to Markov switching and are able to exploit the information content in both returns and ex post volatility measures. Applications to equity returns compare the proposed models to existing alternatives. The empirical results show that the joint models improve density forecasts for returns and point predictions of return variance. Using the information in ex post volatility measures can increase the precision of parameter estimates, sharpen the inference on the latent state variable, and improve portfolio decisions.     

The ACR Model: A Multivariate Dynamic Mixture Autoregression*

This paper proposes and analyses the autoregressive conditional root (ACR) time‐series model. This multivariate dynamic mixture autoregression allows for non‐stationary epochs. It proves to be an appealing alternative to existing nonlinear models, e.g. the threshold autoregressive or Markov switching class of models, which are commonly used to describe nonlinear dynamics as implied by arbitrage in presence of transaction costs. Simple conditions on the parameters of the ACR process and its innovations are shown to imply geometric ergodicity, stationarity and existence of moments. Furthermore, consistency and asymptotic normality of the maximum likelihood estimators are established. An application to real exchange rate data illustrates the analysis.     

Space-varying Coefficient Simultaneous Autoregressive Models for the Structural Analysis of Residential Water Demand

Abstract

This study develops two space-varying coefficient simultaneous autoregressive (SVC-SAR) models for areal data and applies them to the discrete/continuous choice model, which is an econometric model based on the consumer's utility maximization problem. The space-varying coefficient model is a statistical model in which the coefficients vary depending on their location. This study introduces the simultaneous autoregressive model for the underlying spatial dependence across coefficients, where the coefficients for one observation are affected by the sum of those for the other observations. This model is named the SVC-SAR model. Because of its flexibility, we use the Bayesian approach and construct its estimation method based on the Markov chain Monte Carlo simulation. The proposed models are applied to estimate the Japanese residential water demand function, which is an example of the discrete/continuous choice model.     

Testing the Markov property with high frequency data

This paper develops a framework to nonparametrically test whether discrete-valued irregularly spaced financial transactions data follow a 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 the irregular spacing that characterizes transactions data. Under such an observation rule, the current price duration is independent of a previous price duration given the previous price realization. A simple nonparametric test then follows by examining whether this conditional independence property holds. Monte Carlo simulations suggest that the asymptotic test has huge size distortions, though a bootstrap-based variant entails reasonable size and power properties in finite samples. As for an empirical illustration, we investigate whether 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. We robustly reject the Markov assumption for two out of the five stocks under scrutiny. Finally, it is reassuring that our results are consistent with two alternative measures of asymmetric information.     

Exit problems in regime-switching models

This paper provides a general framework for pricing of perpetual American and real options in regime-switching Lévy models. In each state of the Markov chain, which determines switches from one Lévy process to another, the payoff stream is a monotone function of the Lévy process labeled by the state. This allows for additional switching within each state of the Markov chain (payoffs can be different in different regions of the real line). The pricing procedure is efficient even if the number of states is large provided the transition rates are not very large w.r.t. the riskless rates. The payoffs and riskless rates may depend on a state. Special cases are stochastic volatility models and models with stochastic interest rate; both must be modeled as finite-state Markov chains. As an application, we solve exit problems for a price-taking firm, and study the dependence of the exit threshold on the interest rate uncertainty.     

Estimation of copula-based semiparametric time series models

This paper studies the estimation of a class of copula-based semiparametric stationary Markov models. These models are characterized by nonparametric marginal distributions and parametric copula functions, while the copulas capture all the scale-free temporal dependence of the processes. Simple estimators of the marginal distribution and the copula parameter are provided, and their asymptotic properties are established under easily verifiable conditions. These results are used to obtain root-n consistent and asymptotically normal estimators of important features of the transition distribution such as the (nonlinear) conditional moments and conditional quantiles. The semiparametric conditional quantile estimators are automatically monotonic across quantiles, which is attractive for portfolio conditional value-at-risk calculations.     

Pseudo-likelihood estimation and bootstrap inference for structural discrete Markov decision models

This paper analyzes the higher-order properties of the estimators based on the nested pseudo-likelihood (NPL) algorithm and the practical implementation of such estimators for parametric discrete Markov decision models. We derive the rate at which the NPL algorithm converges to the MLE and provide a theoretical explanation for the simulation results in Aguirregabiria and Mira [Aguirregabiria, V., Mira, P., 2002. Swapping the nested fixed point algorithm: A class of estimators for discrete Markov decision models. Econometrica 70, 1519–1543], in which iterating the NPL algorithm improves the accuracy of the estimator. We then propose a new NPL algorithm that can achieve quadratic convergence without fully solving the fixed point problem in every iteration and apply our estimation procedure to a finite mixture model. We also develop one-step NPL bootstrap procedures for discrete Markov decision models. The Monte Carlo simulation evidence based on a machine replacement model of Rust [Rust, J., 1987. Optimal replacement of GMC bus engines: An empirical model of Harold Zurcher. Econometrica 55, 999–1033] shows that the proposed one-step bootstrap test statistics and confidence intervals improve upon the first order asymptotics even with a relatively small number of iterations.     

Stationary Markovian equilibrium in overlapping generation models with stochastic nonclassical production and Markov shocks

This paper provides new sufficient conditions for the existence and computation of Markovian equilibrium for a large class of OLG models with Markov shocks to production. The economies considered allow for a very large class of “reduced-form” production functions, including those that are nonclassical, encompassing stochastic OLG models with social security, income redistribution policies, taxation, valued fiat money, production nonconvexities, and monopolistic competition. Our approach combines aspects of both topological and order theoretic fixed point theory and provides globally stable successive approximations algorithms for computing extremal Markovian equilibrium objects.     

Dynasties versus pennant races: competitive balance in major league baseball

This paper examines the impact of competitive balance on attendance in Major League Baseball. Two types of competitive balance are included in a single‐equation model of attendance: intra‐seasonal balance and inter‐seasonal balance. The metric used to calibrate the first is the ratio of the actual standard deviation of season win percents divided by the ideal standard deviation. Inter‐seasonal balance is calibrated with Markov transitional probabilities of teams making the playoffs in consecutive seasons. The results indicate that intra‐seasonal balance does not significantly impact attendance, and that inter‐seasonal balance has significant but small impacts on attendance in the American League. Copyright © 2006 John Wiley & Sons, Ltd.     

Beta-product dependent Pitman–Yor processes for Bayesian inference

Multiple time series data may exhibit clustering over time and the clustering effect may change across different series. This paper is motivated by the Bayesian non-parametric modelling of the dependence between clustering effects in multiple time series analysis. We follow a Dirichlet process mixture approach and define a new class of multivariate dependent Pitman–Yor processes (DPY). The proposed DPY are represented in terms of vectors of stick-breaking processes which determine dependent clustering structures in the time series. We follow a hierarchical specification of the DPY base measure to account for various degrees of information pooling across the series. We discuss some theoretical properties of the DPY and use them to define Bayesian non-parametric repeated measurement and vector autoregressive models. We provide efficient Monte Carlo Markov Chain algorithms for posterior computation of the proposed models and illustrate the effectiveness of the method with a simulation study and an application to the United States and the European Union business cycle.     

Transition matrix models of consumer credit ratings

Although the corporate credit risk literature includes many studies modelling the change in the credit risk of corporate bonds over time, there has been far less analysis of the credit risk for portfolios of consumer loans. However, behavioural scores, which are calculated on a monthly basis by most consumer lenders, are the analogues of ratings in corporate credit risk. Motivated by studies of corporate credit risk, we develop a Markov chain model based on behavioural scores for establishing the credit risk of portfolios of consumer loans. Although such models have been used by lenders to develop models for the Basel Accord, nothing has been published in the literature on them. The model which we suggest differs in many respects from the corporate credit ones based on Markov chains — such as the need for a second order Markov chain, the inclusion of economic variables and the age of the loan. The model is applied using data on a credit card portfolio from a major UK bank.     

Stable seasonal pattern models for forecast revision: A comparative study

Many firms prepare forecasts at the beginning of each financial quarter that predict total sales over the upcoming quarter. Such forecasts may be used to make financial projections, or to plan manufacturing capacity and materials purchases. As weekly sales are recorded during the quarter, these quarterly forecasts are often revised, allowing plans and projections to be adjusted appropriately. A formal basis for these forecast revisions may be found in so-called stable seasonal pattern models, which are based on the observation that in many instances, the sales that accrue during a given period of a quarter follow a regular pattern. This paper discusses a number of stable seasonal pattern models – several from the literature, two that are novel – which have been evaluated for making forecast revisions at Sun Microsystems, Inc. Commonalities between the models are elucidated using a general theoretical framework, and a straightforward sample-based mechanism is described that affords great flexibility in the design and use of stable seasonal pattern models. The paper culminates in a detailed comparison of the performance of new and existing stable seasonal pattern models with respect to Sun's sales data.