Maximum likelihood estimation of skew-t copulas with its applications to stock returns

The multivariate Student-t copula family is used in statistical finance and other areas when there is tail dependence in the data. It often is a good-fitting copula but can be improved on when there is tail asymmetry. Multivariate skew-t copula families can be considered when there is tail dependence and tail asymmetry, and we show how a fast numerical implementation for maximum likelihood estimation is possible. For the copula implicit in a multivariate skew-t distribution, the fast implementation makes use of (i) monotone interpolation of the univariate marginal quantile function and (ii) a re-parametrization of the correlation matrix. Our numerical approach is tested with simulated data with data-driven parameters. A real data example involves the daily returns of three stock indices: the Nikkei225, S&P500 and DAX. With both unfiltered returns and GARCH/EGARCH filtered returns, we compare the fits of the Azzalini–Capitanio skew-t, generalized hyperbolic skew-t, Student-t, skew-Normal and Normal copulas.     

Non-traditional analysis of stock returns

SUMMARY An investigation of the prices of eight individual stocks showed that pricechange returns are significantly less complex than are time-dependent returns. Timedependent returns computed every 15, 30 and 45 minutes were found to be more complex, using a complexity measure. Complexity is quantified by measuring the number of times that the estimated correlation dimension of an observed series is multiplied by when its original sequence is randomly shuffled.     

Jump-diffusion models of German stock returns

This paper discusses the statistical properties of jump-diffusion processes and reports on parameter estimates for the DAX stock index and 48 German stocks with traded options. It is found that a Poisson-type jump-diffusion process can explain the high levels of kurtosis and skewness of observed return distributions of German stocks. Furthermore, we demonstrate that the return dynamics of the DAX include a statistically significant jump component except for a few sample subperiods. This finding is seen to be inconsistent with asset pricing models assuming that the jump component of the stock's return is unsystematic and diversifiable in the market portfolio.     

Penalized likelihood inference in extreme value analyses

Models for extreme values are usually based on detailed asymptotic argument, for which strong ergodic assumptions such as stationarity, or prescribed perturbations from stationarity, are required. In most applications of extreme value modelling such assumptions are not satisfied, but the type of departure from stationarity is either unknown or complex, making asymptotic calculations unfeasible. This has led to various approaches in which standard extreme value models are used as building blocks for conditional or local behaviour of processes, with more general statistical techniques being used at the modelling stage to handle the non-stationarity. This paper presents another approach in this direction based on penalized likelihood. There are some advantages to this particular approach: the method has a simple interpretation; computations for estimation are relatively straightforward using standard algorithms; and a simple reinterpretation of the model enables broader inferences, such as confidence intervals, to be obtained using MCMC methodology. Methodological details together with applications to both athletics and environmental data are given.     

股票市场的货币政策效应的度量

近来的研究揭示股票价格的变动已经越来越成为金融当局关注的重点 ,股票市场已成为货币政策的重要传导渠道。钱小安 (1998)讨论了资产价格变化对货币供求与传导机制的影响 ;梁宇峰 (2 0 0 1)论述了资产价格泡沫对经济和金融体制的危害性 ;瞿强 (2 0 0 1)指出货币政策对资产价格要“关注” ,但不要“钉住”。中国人民银行研究局课题组 (2 0 0 2 )就股票市场的发展对货币政策的影响进行了实证研究 ,提出中央银行的货币政策操作应关注股票市场价格的波动。以上这些研究揭示了股票市场的发展对货币政策各方面的影响 ,说明货币政策关注股票市场的…     

The predictability of stock returns - a nonparametric approach

This paper reexamines the predictability of stock returns with a nonparametric model. We first identify, through a set of diagnostic tests, five lagged predictive factors from a linear model. Using these factors, we predict one-month-ahead stock index returns with a nonparametric approach. We find that our nonparametricmodel. We first identify, through a set of diagnostic tests, five lagged predictive factors from a linear model. Using these factors, we predict on -month-ahead stock index returns with a nonparametric approach. We find that our nonparametric model can correctly predict about 74% of stock index return signs. With various ex ante trading rules based on nonparametric predictions and transaction cost schedules, we then compare the performance of "managed" portfolios with that of the buy and hold portfolios. We fmd that the managed portfolios are mean-variance dominant over the buy-and-hold strategies when no or low transaction costs are assumed. When high transaction costs are assumed instead, the mean-variance dominance diminishes However,the Sharpe index of risk-adjusted portfolio performanceindicates that the managed portfolios significantly outperform the buy-and-hold strategies even for the high-transaction cost scenario. We show that the difference in performance between the managed portfolios and the buy-and-hold strategies can be partially explained by the January effect or the small firm effect. In sum, this paper demonstrates the merits of using a nonparametric approach for predicting stock returns and testing market efficiency.     

Dynamic component detection in a multifactor model for stock returns

Summary In this paper the factorial structure of some asset returns quoted at the Milan stock exchange is analyzed in order to detect the presence of a dynamic component. The maximum likelihood estimates of the dynamic model, for which a space-state representation and the Kalman filter were used, are compared with the estimates of the static model via the information criteria. There is no evidence of dynamic factors underlying the analyzed samples of asset returns, while one static factor seems to be relevant. Invited paper at the Conference held in Bologna, Italy, 27–28 May 1993, on ?Statistical Tests: Methodology and Econometric Applications?.     

Estimates of the parameters of type-II extreme value distribution from censored samples

Maximum likelihood estimators of a Type-II extreme value distribution are derived from doubly censored samples. The asymptotic variances and covariances of the maximum likelihood estimators are discussed and these are numerically evaluated for different censoring proportions q₁ = 0.0(0. l) (0.9) from below and q₂ = 0.0 (0. l) (0.9- q₁) from above. The asymptotic relative efficiencies of the parameter estimates revealed that lower order statistics are more important for estimating the parameters of Type-II extreme value distribution as compared to higher order statistics.     

More on the volatility-trading volume relationship in emerging markets: The Chinese stock market

This paper empirically investigates the characteristics in terms of volatility and trading volume relationships of the Chinese stock markets, and specifically of the stocks comprising the SSE180 index. Our results show that, contrary to previous evidence, both volatility and trading volume appear to be multi-fractal and highly intermittent, suggesting a common long-run behaviour in addition to the common short-term behaviour underlined by former studies. Moreover, the trading volume seems to have no explanatory power for volatility persistence when introduced in the conditional variance equation. Finally, the sign of the trading volume coefficients is mainly negative, hence showing a negative correlation between the two variables.     

A dynamic analysis of stock markets using a hidden Markov model

This paper proposes a framework to detect financial crises, pinpoint the end of a crisis in stock markets and support investment decision-making processes. This proposal is based on a hidden Markov model (HMM) and allows for a specific focus on conditional mean returns. By analysing weekly changes in the US stock market indexes over a period of 20 years, this study obtains an accurate detection of stable and turmoil periods and a probabilistic measure of switching between different stock market conditions. The results contribute to the discussion of the capabilities of Markov-switching models of analysing stock market behaviour. In particular, we find evidence that HMM outperforms threshold GARCH model with Student-t innovations both in-sample and out-of-sample, giving financial operators some appealing investment strategies.     

Likelihood procedure for testing changes in skew normal model with applications to stock returns

The skew normal distribution family is an attractive distribution family due to its mathematical tractability and inclusion of the normal distribution as the special case. It has wide applications in many applied fields such as finance, economics, and medical research. Such a distribution family has been studied extensively since it was introduced by Azzalini in 1985 Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics 12:171–178. [Google Scholar] for the first time. Yet, few work has been done on the study of change point problem related to this distribution family. In this article, we propose the likelihood ratio test (LRT) to detect changes in the parameters of the skew normal distribution associated with some asymptotic results of the test statistic. Simulations have been conducted under different scenarios to investigate the performance of the proposed method. Comparisons to some other existing method indicate the comparable power of the method in detecting changes in parameters of the skew normal distribution model. Applications on two real data: Brazilian and Tanzanian stock returns illustrate the detection procedure.     

A Markov regime‐switching model for crude‐oil markets: Comparison of composite likelihood and full likelihood

We use the two‐state Markov regime‐switching model to explain the behaviour of the WTI crude‐oil spot prices from January 1986 to February 2012. We investigated the use of methods based on the composite likelihood and the full likelihood. We found that the composite‐likelihood approach can better capture the general structural changes in world oil prices. The two‐state Markov regime‐switching model based on the composite‐likelihood approach closely depicts the cycles of the two postulated states: fall and rise. These two states persist for on average 8 and 15 months, which matches the observed cycles during the period. According to the fitted model, drops in oil prices are more volatile than rises. We believe that this information can be useful for financial officers working in related areas. The model based on the full‐likelihood approach was less satisfactory. We attribute its failure to the fact that the two‐state Markov regime‐switching model is too rigid and overly simplistic. In comparison, the composite likelihood requires only that the model correctly specifies the joint distribution of two adjacent price changes. Thus, model violations in other areas do not invalidate the results. The Canadian Journal of Statistics 41: 353–367; 2013 © 2013 Statistical Society of Canada     

Examining the interrelation dynamics between option and stock markets using the Markov-switching vector error correction model

This study examines the dynamics of the interrelation between option and stock markets using the Markov-switching vector error correction model. Specifically, we calculate the implied stock prices from the Black–Scholes 6 Black, F. and Scholes, M. 1973. The pricing of options and corporate liabilities. J. Polit. Econ., 81: 637–659. [Crossref], [Web of Science ®] [Google Scholar] model and establish a statistic framework in which the parameter of the price discrepancy between the observed and implied prices switches according to the phase of the volatility regime. The model is tested in the US S&P 500 stock market. The empirical findings of this work are consistent with the following notions. First, while option markets react more quickly to the newest stock–option disequilibrium shocks than spot markets, as found by earlier studies, we further indicate that the price adjustment process occurring in option markets is pronounced when the high variance condition is concerned, but less so during the stable period. Second, the degree of the co-movement between the observed and implied prices is significantly reduced during the high variance state. Last, the lagged price deviation between the observed and implied prices functions as an indicator of the variance-turning process.     

CVaR-EVT和BMM在极端金融风险管理中的应用研究

随着风险度量一致性原则的提出,研究发现金融机构广泛采用的VaR模型存在严重不足,尤其针对分布具有厚尾特征的极端金融风险无法有效度量。本文采用极值理论（EVT）解决VaR方法的尾部度量不足问题,利用CVaR-EVT和BMM模型分析美国、香港股票市场和我国沪深两市指数18年的日收益数据,研究发现：（1）在95％置信区间及点估计中,分位数为99%的CVaR-EVT所揭示的极端风险优于VaR的估计值;且BMM方法为实施长期极端风险管理提供了有力决策依据,其回报率受分段时区的影响,期间越长,风险估计值越高;（2）模型采用ML和BS方法统计估值显示,我国股票市场极端风险尾部估计值高于香港和美国市场;但是,国内市场逐步稳定,并呈现出跟进国际市场且差距缩小的发展趋势。     

Decomposing the predictive performance of the moving average trading rule of technical analysis: the contribution of linear and non-linear dependencies in stock returns

The main purpose of this work is to decompose the predictive performance of the moving average (MA) trading rule and find out the portion that could be attributed to the possible exploitation of linear and non-linear dependencies in stock returns. Data from the General Index of the Athens Stock Exchange, from the Standard and Poor-500 Index of the New York Stock Exchange and from the Austrian Traded Index of the Vienna Stock Exchange are filtered by linear filters so as the resulting simulated ‘returns’ exhibit no serial correlation. Applying MA trading rules to both the original and the simulated indices and using a new statistical testing procedure that takes into account the sensitivity of the performance of the trading rule as a function of the length of the MA it is found that the predictive performance of the trading rule is clearly weakened when applied to the simulated indices indicating that a substantial part of the rule's predictive performance is due to the exploitation of linear dependencies in stock returns. This weakening is uneven; in general the shorter the MA length the more pronounced the attenuation.     

CUSUM method in predicting regime shifts and its performance in different stock markets allowing for transaction fees

Statistical Process Control (SPC) is a scientific approach to quality improvement in which data are collected and used as evidence of the performance of a process, organisation or set of equipment. One of the SPC techniques, the cumulative sum (CUSUM) method, first developed by E.S. Page (1961), uses a series of cumulative sums of sample data for online process control. This paper reviews CUSUM techniques applied to financial markets in several different ways. The performance of the CUSUM method in predicting regime shifts in stock market indices is then studied in detail. Research in this field so far does not take the transaction fees of buying and selling into consideration. As the study in this paper shows, the performances of the CUSUM when taking account of transaction fees are quite different to those not taking transaction fees into account. The CUSUM plan is defined by parameters h and k. Choosing the parameters of the method should be based on studies that take transaction fees into account. The performances of the CUSUM in different stock markets are also compared in this paper. The results show that the same CUSUM plan has remarkably different performances in different stock markets.     

Maximum likelihood estimation in the presence of outiliers

This paper deals with the maximum likelihood estimation of parameters when the sample (x₁…x_n ) may heve k spuriously generated observations from another distribution, say G≠F, where F is the distribution of the target population. If G is stochastically larger than F, then these k observations may give rise to k extreme observations or ‘outliers’. This situation is often described by a so-called ‘k-outlier model’ in which in addition to the parameters involved in F and G, the set ν={ν₁,…,ν_k} of indices, for which x_νj , j=1,…,k, come from G, is also unknow.     

On the foundations of likelihood principle

According to the likelihood principle, if the designs produce proportional likelihood functions, one could make an identical inference about a parameter from the data irrespective of the design, which yields the data. If it comes to that, there are several counter-examples, and/or paradoxical consequences to likelihood principle. Besides, as we will see, contrary to a widely held opinion, such a principle is not a direct consequence of Bayes theorem. In particular, the piece of information about the design is one part of the evidence, and it is relevant for the prior. Later on, Jeffreys non-informative prior is used to show how different designs result in different priors. Another basic idea of the present paper is that (apart from other information) the equiprobability assumption is to be linked to the idea of the impartiality of design with respect to the parameter under consideration. The whole paper has remarkable implications on the foundations of statistics from the notion of sufficiency, the relevance of the stopping rule and of the randomization in survey sampling and in the experimental design, the difference between ignorable and non-ignorable designs, until a reconciliation of different approaches to the inductive reasoning in statistical inference.