Volatility forecasting with double Markov switching GARCH models

This paper investigates inference and volatility forecasting using a Markov switching heteroscedastic model with a fat‐tailed error distribution to analyze asymmetric effects on both the conditional mean and conditional volatility of financial time series. The motivation for extending the Markov switching GARCH model, previously developed to capture mean asymmetry, is that the switching variable, assumed to be a first‐order Markov process, is unobserved. The proposed model extends this work to incorporate Markov switching in the mean and variance simultaneously. Parameter estimation and inference are performed in a Bayesian framework via a Markov chain Monte Carlo scheme. We compare competing models using Bayesian forecasting in a comparative value‐at‐risk study. The proposed methods are illustrated using both simulations and eight international stock market return series. The results generally favor the proposed double Markov switching GARCH model with an exogenous variable. Copyright © 2008 John Wiley & Sons, Ltd.     

Out‐of‐sample equity premium prediction: A scenario analysis approach

We propose two methods of equity premium prediction with single and multiple predictors respectively and evaluate their out‐of‐sample performance using US stock data with 15 popular predictors for equity premium prediction. The first method defines three scenarios in terms of the expected returns under the scenarios and assumes a Markov chain governing the occurrence of the scenarios over time. It employs predictive quantile regressions of excess return on a predictor for three quantiles to estimate the occurrence of the scenarios over an in‐sample period and the transition probabilities of the Markov chain, predicts the expected returns under the scenarios, and generates an equity premium forecast by combining the predicted expected returns under three scenarios with the estimated transition probabilities. The second method generates an equity premium forecast by combining the individual forecasts from the first method across all predictors. For most of predictors, the first method outperforms the benchmark method of historical average and the traditional predictive linear regression with a single predictor both statistically and economically, and the second method consistently performs better than several competing methods used in the literature. The performance of our methods is further examined under different scenarios and economic conditions, and is robust for two different out‐of‐sample periods and specifications of the scenarios.     

Quantile Double AR Time Series Models for Financial Returns

We develop a novel quantile double autoregressive model for modelling financial time series. This is done by specifying a generalized lambda distribution to the quantile function of the location‐scale double autoregressive model developed by Ling (2004, 2007). Parameter estimation uses Markov chain Monte Carlo Bayesian methods. A simulation technique is introduced for forecasting the conditional distribution of financial returns m periods ahead, and hence any for predictive quantities of interest. The application to forecasting value‐at‐risk at different time horizons and coverage probabilities for Dow Jones Industrial Average shows that our method works very well in practice. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive modelling and forecasting of offshore wind power fluctuations with Markov‐switching autoregressive models

Wind power production data at temporal resolutions of a few minutes exhibit successive periods with fluctuations of various dynamic nature and magnitude, which cannot be explained (so far) by the evolution of some explanatory variable. Our proposal is to capture this regime‐switching behaviour with an approach relying on Markov‐switching autoregressive (MSAR) models. An appropriate parameterization of the model coefficients is introduced, along with an adaptive estimation method allowing accommodation of long‐term variations in the process characteristics. The objective criterion to be recursively optimized is based on penalized maximum likelihood, with exponential forgetting of past observations. MSAR models are then employed for one‐step‐ahead point forecasting of 10 min resolution time series of wind power at two large offshore wind farms. They are favourably compared against persistence and autoregressive models. It is finally shown that the main interest of MSAR models lies in their ability to generate interval/density forecasts of significantly higher skill. Copyright © 2010 John Wiley & Sons, Ltd.     

吸收马氏链在供应链优化判断中的应用

本文构建了具有一般意义的企业供应链系统及各环节对利润贡献的算法，首次运用吸收马链吸收概率的计算原理，通过对该系统各链点遍历状态和不返回状态的转换计算，对企业供应链的优化判断提供了新的数理依据，同时进行了实证分析。     

Dynamic Latent Class Model Averaging for Online Prediction

We consider the problem of online prediction when it is uncertain what the best prediction model to use is. We develop a method called dynamic latent class model averaging, which combines a state‐space model for the parameters of each of the candidate models of the system with a Markov chain model for the best model. We propose a polychotomous regression model for the transition weights to assume that the probability of a change in time depends on the past through the values of the most recent time periods and spatial correlation among the regions. The evolution of the parameters in each submodel is defined by exponential forgetting. This structure allows the ‘correct’ model to vary over both time and regions. In contrast to existing methods, the proposed model naturally incorporates clustering and prediction analysis in a single unified framework. We develop an efficient Gibbs algorithm for computation, and we demonstrate the value of our framework on simulated experiments and on a real‐world problem: forecasting IBM's corporate revenue. Copyright © 2014 John Wiley & Sons, Ltd.     

Forecasting stock prices using a hierarchical Bayesian approach

The Ohlson model is evaluated using quarterly data from stocks in the Dow Jones Index. A hierarchical Bayesian approach is developed to simultaneously estimate the unknown coefficients in the time series regression model for each company by pooling information across firms. Both estimation and prediction are carried out by the Markov chain Monte Carlo (MCMC) method. Our empirical results show that our forecast based on the hierarchical Bayes method is generally adequate for future prediction, and improves upon the classical method. Copyright © 2005 John Wiley & Sons, Ltd.     

Intermittent demand forecasting in the Enterprise: Empirical verification

Forecasting methods are often valued by means of simulation studies. For intermittent demand items there are often very few non–zero observations, so it is hard to check any assumptions, because statistical information is often too weak to determine, for example, distribution of a variable. Therefore, it seems important to verify the forecasting methods on the basis of real data. The main aim of the article is an empirical verification of several forecasting methods applicable in case of intermittent demand. Some items are sold only in specific subperiods (in given month in each year, for example), but most forecasting methods (such as Croston's method) give non–zero forecasts for all periods. For example, summer work clothes should have non–zero forecasts only for summer months and many methods will usually provide non–zero forecasts for all months under consideration. This was the motivation for proposing and testing a new forecasting technique which can be applicable to seasonal items. In the article six methods were applied to construct separate forecasting systems: Croston's, SBA (Syntetos–Boylan Approximation), TSB (Teunter, Syntetos, Babai), MA (Moving Average), SES (Simple Exponential Smoothing) and SESAP (Simple Exponential Smoothing for Analogous subPeriods). The latter method (SESAP) is an author's proposal dedicated for companies facing the problem of seasonal items. By analogous subperiods the same subperiods in each year are understood, for example, the same months in each year. A data set from the real company was used to apply all the above forecasting procedures. That data set contained monthly time series for about nine thousand products. The forecasts accuracy was tested by means of both parametric and non–parametric measures. The scaled mean and the scaled root mean squared error were used to check biasedness and efficiency. Also, the mean absolute scaled error and the shares of best forecasts were estimated. The general conclusion is that in the analyzed company a forecasting system should be based on two forecasting methods: TSB and SESAP, but the latter method should be applied only to seasonal items (products sold only in specific subperiods). It also turned out that Croston's and SBA methods work worse than much simpler methods, such as SES or MA. The presented analysis might be helpful for enterprises facing the problem of forecasting intermittent items (and seasonal intermittent items as well).     

A Method of Retail Mortgage Stress Testing: Based on Time‐Frame and Magnitude Analysis

In this study, a non‐stationary Markov chain model and a vector autoregressive moving average with exogenous variables coupled with a logistic function (VARMAX‐L) are used to analyze and predict the stability of a retail mortgage portfolio, based on the stress test framework. The method introduced in this paper can be used to forecast the transition probabilities in a retail mortgage over pre‐specified states, given a shock with a certain magnitude. Hence this method provides a dynamic picture of the portfolio transition process through which one can assess its behavior over time. While the paper concentrates on retail mortgages, the methodology of this study can be adapted also to analyze other credit products in banks. Copyright © 2015 John Wiley & Sons, Ltd.     

Subset threshold autoregression

We develop in this paper an efficient way to select the best subset threshold autoregressive model. The proposed method uses a stochastic search idea. Differing from most conventional approaches, our method does not require us to fix the delay or the threshold parameters in advance. By adopting the Markov chain Monte Carlo techniques, we can identify the best subset model from a very large of number of possible models, and at the same time estimate the unknown parameters. A simulation experiment shows that the method is very effective. In its application to the US unemployment rate, the stochastic search method successfully selects lag one as the time delay and five best models from more than 4000 choices. Copyright © 2003 John Wiley & Sons, Ltd.     

Seasonality in the reproductive phenology ofFicus: Its evolution and consequences

Summary Ficus can only reproduce if they are pollinated by mutualistic wasps that breed within the figs. Pollen-loaded wasps enter the figs when the female flowers are receptive. Several weeks later, their offspring load pollen within the fig and then emerge. As individual trees typically produce crops of synchronous figs at long intervals, the shortlived wasps have to move to another, receptive, tree. The wasp population can only survive, and hence the fig population reproduce, if there are trees fruiting all over the year. When only few trees are present within a population gaps in the flowering sequence may lead to the extinction of the local pollinator population. Two models are presented. One investigates the number of trees necessary in order to sustain a local pollinator population when the tree population has a seasonal pattern of fruiting. The second model investigates how such a seasonal pattern may evolve within a fig population as a result of individual selection on the trees. It is shown that pollinator populations are fragilized under seasonal conditions. Hence, the breeding system ofFicus limits their expansion into highly seasonal habitats. Seasonal habitats may also lead to seasonal adjustment of male versus female investments and to the evolution of dioecy.     

Forecasting under model uncertainty: Non-homogeneous hidden Markov models with Pòlya-Gamma data augmentation

We consider finite state-space non-homogeneous hidden Markov models for forecasting univariate time series. Given a set of predictors, the time series are modeled via predictive regressions with state-dependent coefficients and time-varying transition probabilities that depend on the predictors via a logistic/multinomial function. In a hidden Markov setting, inference for logistic regression coefficients becomes complicated and in some cases impossible due to convergence issues. In this paper, we aim to address this problem utilizing the recently proposed Pólya-Gamma latent variable scheme. Also, we allow for model uncertainty regarding the predictors that affect the series both linearly — in the mean — and non-linearly — in the transition matrix. Predictor selection and inference on the model parameters are based on an automatic Markov chain Monte Carlo scheme with reversible jump steps. Hence the proposed methodology can be used as a black box for predicting time series. Using simulation experiments, we illustrate the performance of our algorithm in various setups, in terms of mixing properties, model selection and predictive ability. An empirical study on realized volatility data shows that our methodology gives improved forecasts compared to benchmark models.     

Subset selection of autoregressive time series models

We propose a solution to select promising subsets of autoregressive time series models for further consideration which follows up on the idea of the stochastic search variable selection procedure in George and McCulloch (1993). It is based on a Bayesian approach which is unconditional on the initial terms. The autoregression stepup is in the form of a hierarchical normal mixture model, where latent variables are used to identify the subset choice. The framework of our procedure is utilized by the Gibbs sampler, a Markov chain Monte Carlo method. The advantage of the method presented is computational: it is an alternative way to search over a potentially large set of possible subsets. The proposed method is illustrated with a simulated data as well as a real data. Copyright © 1999 John Wiley & Sons, Ltd.     

A Bayesian threshold nonlinearity test for financial time series

We propose in this paper a threshold nonlinearity test for financial time series. Our approach adopts reversible‐jump Markov chain Monte Carlo methods to calculate the posterior probabilities of two competitive models, namely GARCH and threshold GARCH models. Posterior evidence favouring the threshold GARCH model indicates threshold nonlinearity or volatility asymmetry. Simulation experiments demonstrate that our method works very well in distinguishing GARCH and threshold GARCH models. Sensitivity analysis shows that our method is robust to misspecification in error distribution. In the application to 10 market indexes, clear evidence of threshold nonlinearity is discovered and thus supporting volatility asymmetry. Copyright © 2005 John Wiley & Sons, Ltd.     

Adaptive prediction for stochastic processes with markov jump parameters

This paper is concerned with the adaptive prediction for stochastic processes with abruptly changing parameters modelled as a finite-state Markov chain. The Markov transition matrix is assumed to be known. For the coloured noise disturbance case, it is shown that the optimal prediction algorithm requires a bank of elemental predictors running in parallel with its number growing exponentially with time. If the noise disturbance is white, it is found that the number of the elemental predictors required increases exponentially with the prediction ahead step instead of time. A suboptimal predictor is proposed with substantial reduced storage and computational requirements. Simulation examples show the good performance of the proposed algorithms.     

Forecasting Latent Volatility through a Markov Chain Approximation Filter

We propose a new methodology for filtering and forecasting the latent variance in a two‐factor diffusion process with jumps from a continuous‐time perspective. For this purpose we use a continuous‐time Markov chain approximation with a finite state space. Essentially, we extend Markov chain filters to processes of higher dimensions. We assess forecastability of the models under consideration by measuring forecast error of model expected realized variance, trading in variance swap contracts, producing value‐at‐risk estimates as well as examining sign forecastability. We provide empirical evidence using two sources, the S&P 500 index values and its corresponding cumulative risk‐neutral expected variance (namely the VIX index). Joint estimation reveals the market prices of equity and variance risk implicit by the two probability measures. A further simulation study shows that the proposed methodology can filter the variance of virtually any type of diffusion process (coupled with a jump process) with a non‐analytical density function. Copyright © 2015 John Wiley & Sons, Ltd.     

Forecasting VaR models under Different Volatility Processes and Distributions of Return Innovations

This paper provides clear‐cut evidence that the out‐of‐sample VaR (value‐at‐risk) forecasting performance of alternative parametric volatility models, like EGARCH (exponential general autoregressive conditional heteroskedasticity) or GARCH, and Markov regime‐switching models, can be considerably improved if they are combined with skewed distributions of asset return innovations. The performance of these models is found to be similar to that of the EVT (extreme value theory) approach. The performance of the latter approach can also be improved if asset return innovations are assumed to be skewed distributed. The performance of the Markov regime‐switching model is considerably improved if this model allows for EGARCH effects, for all different volatility regimes considered. Copyright © 2014 John Wiley & Sons, Ltd.     

Bayesian Forecasting for Financial Risk Management,Pre and Post the Global Financial Crisis

Value‐at‐risk (VaR) forecasting via a computational Bayesian framework is considered. A range of parametric models is compared, including standard, threshold nonlinear and Markov switching generalized autoregressive conditional heteroskedasticity (GARCH) specifications, plus standard and nonlinear stochastic volatility models, most considering four error probability distributions: Gaussian, Student‐t, skewed‐t and generalized error distribution. Adaptive Markov chain Monte Carlo methods are employed in estimation and forecasting. A portfolio of four Asia–Pacific stock markets is considered. Two forecasting periods are evaluated in light of the recent global financial crisis. Results reveal that: (i) GARCH models outperformed stochastic volatility models in almost all cases; (ii) asymmetric volatility models were clearly favoured pre crisis, while at the 1% level during and post crisis, for a 1‐day horizon, models with skewed‐t errors ranked best, while integrated GARCH models were favoured at the 5% level; (iii) all models forecast VaR less accurately and anti‐conservatively post crisis. Copyright © 2011 John Wiley & Sons, Ltd.     

Evaluating volatility dynamics and the forecasting ability of Markov switching models

This paper uses Markov switching models to capture volatility dynamics in exchange rates and to evaluate their forecasting ability. We identify that increased volatilities in four euro‐based exchange rates are due to underlying structural changes. Also, we find that currencies are closely related to each other, especially in high‐volatility periods, where cross‐correlations increase significantly. Using Markov switching Monte Carlo approach we provide evidence in favour of Markov switching models, rejecting random walk hypothesis. Testing in‐sample and out‐of‐sample Markov trading rules based on Dueker and Neely (Journal of Banking and Finance, 2007) we find that using econometric methodology is able to forecast accurately exchange rate movements. When applied to the Euro/US dollar and the euro/British pound daily returns data, the model provides exceptional out‐of‐sample returns. However, when applied to the euro/Brazilian real and the euro/Mexican peso, the model loses power. Higher volatility exercised in the Latin American currencies seems to be a critical factor for this failure. Copyright © 2009 John Wiley & Sons, Ltd.     

Bayesian structure selection for vector autoregression model

A vector autoregression (VAR) model is powerful for analyzing economic data as it can be used to simultaneously handle multiple time series from different sources. However, in the VAR model, we need to address the problem of substantial coefficient dimensionality, which would cause some computational problems for coefficient inference. To reduce the dimensionality, one could take model structures into account based on prior knowledge. In this paper, group structures of the coefficient matrices are considered. Because of the different types of VAR structures, corresponding Markov chain Monte Carlo algorithms are proposed to generate posterior samples for performing inference of the structure selection. Simulation studies and a real example are used to demonstrate the performances of the proposed Bayesian approaches.