Patterns on an ancient artifact: a coincidence?

The Phaistos Disk is an ancient artifact from Crete. At each side of the disk, a series of unknown signs is written along a spiral. Professional archaeologists expect that we will only learn what it is until similar objects are found. A statistical analysis in this article shows what it is not: it is not a one‐dimensional text, since there are relations between the signs in adjacent windings of the spiral. Three patterns of such relations have been identified. A Monte Carlo simulation of one of them has been performed, using a model of the spiral form. It is concluded that the probability of this pattern being coincidental is small, well below the conventional threshold.     

Bayesian inference in cointegrated systems

In this paper I deal with Bayesian methods for conducting inference on important features of (potentially) cointegrated VAR models involving I(1) variables. Firstly, (informal) inference is made on the cointegrating rank of the system. Secondly, posterior analysis is used to verify the validity of over-identifying restrictions on the cointegration parameters. Thirdly, posterior distributions are obtained for impulse response functions and predictive densities at different horizons. The relevant posterior distributions are obtained by means of Monte Carlo integration. The analysis is based on the use of simple weakly informative priors. Two applications on simulated data and on the Danish money demand data are presented.     

Performance of empirical Bayes estimators of random coefficients in multilevel analysis: Some results for the random intercept-only model

For a multilevel model with two levels and only a random intercept, the quality of different estimators of the random intercept is examined. Analytical results are given for the marginal model interpretation where negative estimates of the variance components are allowed for. Except for four or five level-2 units, the Empirical Bayes Estimator (EBE) has a lower average Bayes risk than the Ordinary Least Squares Estimator (OLSE). The EBEs based on restricted maximum likelihood (REML) estimators of the variance components have a lower Bayes risk than the EBEs based on maximum likelihood (ML) estimators. For the hierarchical model interpretation, where estimates of the variance components are restricted being positive, Monte Carlo simulations were done. In this case the EBE has a lower average Bayes risk than the OLSE, also for four or five level-2 units. For large numbers of level-1 (30) or level-2 units (100), the performances of REML-based and ML-based EBEs are comparable. For small numbers of level-1 (10) and level-2 units (25), the REML-based EBEs have a lower Bayes risk than ML-based EBEs only for high intraclass correlations (0.5).     

Evolving densities in continuous strategy games through particle simulations

Many cases of strategic interaction between agents involve a continuous set of choices. It is natural to model these problems as continuous space games. Consequently, the population of agents playing the game will be represented with a density function defined over the continuous set of strategy choices. Simulating evolutionary dynamics on continuous strategy spaces is a challenging problem. The classic approach of discretizing the strategy space is ineffective for multidimensional strategy spaces. We present a principled approach to simulation of adaptive dynamics in continuous space games using sequential Monte Carlo methods. Sequential Monte Carlo methods use a set of weighted random samples, also named particles to represent density functions over multidimensional spaces. Sequential Monte Carlo methods provide computationally efficient ways of computing the evolution of probability density functions. We employ resampling and smoothing steps to prevent particle degeneration problem associated with particle estimates. The resulting algorithm can be interpreted as an agent based simulation with elements of natural selection, regression to mean and mutation. We illustrate the performance of the proposed simulation technique using two examples: continuous version of the repeated prisoner dilemma game and evolution of bidding functions in first-price closed-bid auctions.     

Bayesian time series analysis of periodic behaviour and spectral structure

Analysis, model selection and forecasting in univariate time series models can be routinely carried out for models in which the model order is relatively small. Under an ARMA assumption, classical estimation, model selection and forecasting can be routinely implemented with the Box–Jenkins time domain representation. However, this approach becomes at best prohibitive and at worst impossible when the model order is high. In particular, the standard assumption of stationarity imposes constraints on the parameter space that are increasingly complex. One solution within the pure AR domain is the latent root factorization in which the characteristic polynomial of the AR model is factorized in the complex domain, and where inference questions of interest and their solution are expressed in terms of the implied (reciprocal) complex roots; by allowing for unit roots, this factorization can identify any sustained periodic components. In this paper, as an alternative to identifying periodic behaviour, we concentrate on frequency domain inference and parameterize the spectrum in terms of the reciprocal roots, and, in addition, incorporate Gegenbauer components. We discuss a Bayesian solution to the various inference problems associated with model selection involving a Markov chain Monte Carlo (MCMC) analysis. One key development presented is a new approach to forecasting that utilizes a Metropolis step to obtain predictions in the time domain even though inference is being carried out in the frequency domain. This approach provides a more complete Bayesian solution to forecasting for ARMA models than the traditional approach that truncates the infinite AR representation, and extends naturally to Gegenbauer ARMA and fractionally differenced models.     

The Effect of Market Regimes on Style Allocation

We analyse time-varying risk premia and the implications for portfolio choice. Using Markov Chain Monte Carlo (MCMC) methods, we estimate a multivariate regime-switching model for the Carhart (1997) four-factor model. We find two clearly separable regimes with different mean returns, volatilities, and correlations. In the High-Variance Regime, only value stocks deliver a good performance, whereas in the Low-Variance Regime, the market portfolio and momentum stocks promise high returns. Regime-switching induces investors to change their portfolio style over time depending on the investment horizon, the risk aversion, and the prevailing regime. Value investing seems to be a rational strategy in the High-Variance Regime, momentum investing in the Low-Variance Regime. An empirical out-of-sample backtest indicates that this switching strategy can be profitable, but the overall forecasting ability for the regime-switching model seems to be weak compared to the iid model.     

RECENT PROGRESS IN APPLIED BAYESIAN ECONOMETRICS

Abstract. Bayesian methods are widely used by theoretical econometricians and statisticians but have not won widespread acceptance from applied researchers. After briefly describing the basic of the Bayesian approach, we discuss several issues relating to the empirical application of Bayesian methods. The existing Bayesian empirical literature is also partially summarized. The remainder of the paper offers a non-technical survey of some recent computational advances in Bayesian econometrics. The overall goal is to persuade economists that Bayesian methods are both computationally feasible and easy to implement in empirical research.     

基于蒙特卡罗模拟的多标的资产期权定价研究

在单标的资产价格随机模型的基础上,推导了具相关性的多标的资产价格的随机过程公式,以此构造蒙特卡罗模拟高维欧式期权定价的随机模型,给出模拟算法,并分析了影响蒙特卡罗模拟效果的几个关键因素。模拟算例的结果显示模拟效果较好。     

基于超高频数据的日内风险价值度量研究

随着金融市场的快速发展,传统的以日为单位的风险价值（VaR）已无法满足金融风险管理的需求,计算持有期小于1天的日内风险价值（Intraday VaR）显得愈加重要。文中对日内风险价值测度的方法进行了梳理、细化和改进,对测度中细节给予更加充分的考虑,最后结合我国股市特点对日内风险价值测度进行了实证研究。     

A New Method for Identifying the Effects of Foreign Exchange Interventions

Central banks react even to intraday changes in the exchange rate; however, in most cases, intervention data are available only at a daily frequency. This temporal aggregation makes it difficult to identify the effects of interventions on the exchange rate. We apply the Bayesian Markov‐chain Monte Carlo (MCMC) approach to this endogeneity problem. We use “data augmentation” to obtain intraday intervention amounts and estimate the efficacy of interventions using the augmented data. Applying this new method to Japanese data, we find that an intervention of 1 trillion yen moves the yen/dollar rate by 1.8%, which is more than twice as much as the magnitude reported in previous studies applying ordinary least squares to daily observations. This shows the quantitative importance of the endogeneity problem due to temporal aggregation.