Trend‐cycle Estimation Using Fuzzy Transform and Its Application for Identifying Bull and Bear Phases in Markets

This paper is focused on one of the fundamental problems in financial time‐series analysis; namely, the identification of the historical bull and bear phases. We start with the proof that the trend‐cycle can be well estimated using the technique of a higher degree fuzzy transform. Then, we suggest a mathematical definition of the bull and bear phases and provide a novel technique for their identification. As a consequence, the turning points (i.e. the points where the market changes its phase) are detected. We illustrate our methodology on several examples.  

US stock returns: are there seasons of excesses?

This article explores the existence of seasonality in the tails of stock returns. We use a parametric model to describe the returns, and obtain a proxy of the innovation distribution via a pre-processing model. Then, we develop a change-point algorithm capturing changes in the tails of the innovations. We confirm the good performance of the procedure through extensive Monte Carlo experiments. An empirical investigation using US stocks data shows that while the lower tail of the innovations is approximately constant over the year, the upper tail is larger in Winter than in Summer, in 9 out of 12 industries.  

Revisiting the intertemporal risk–return relation: asymmetrical effect of unexpected volatility shocks

We suggest that an unexpected volatility shock is an important risk factor to induce the intertemporal relation, and the conflicting findings on the relation could be attributable to an omitting variable bias resulting from ignoring the effect of an unexpected volatility shock on the relation. With the effect of an unexpected volatility shock incorporated in estimation, we find a strong positive intertemporal relation for the US monthly excess returns for 1926:12–2008:12. We also find a significant link between the asymmetric mean-reversion and the intertemporal relation in that the quicker reversion of negative returns is attributed to the negative intertemporal relation under a prior negative return shock.  

Bayesian testing volatility persistence in stochastic volatility models with jumps

Whether or not there is a unit root persistence in volatility of financial assets has been a long-standing topic of interest to financial econometricians and empirical economists. The purpose of this article is to provide a Bayesian approach for testing the volatility persistence in the context of stochastic volatility with Merton jump and correlated Merton jump. The Shanghai Composite Index daily return data is used for empirical illustration. The result of Bayesian hypothesis testing strongly indicates that the volatility process doesn’t have unit root volatility persistence in this stock market.  

基于灰色-ARIMA的金融时间序列智能混合预测研究

提出了一种基于灰色-ARIMA的金融时间序列智能混合预测模型。首先建立金融时间序列灰色预测模型,并采用PSO算法对灰色模型的三个参数进行优化;利用ARIMA算法对预测模型的残差进行分析,同时采用遗传算法对ARIMA的系数进行优化;最后用ARIMA的残差预测结果对灰色预测模型进行补偿。结果表明,以较好的精度拟合一段时期内MA107的时间序列,预测误差控制在5%以上,与单纯的灰色预测算法和神经网络算法相比,在平均绝对误差、均方根误差和趋势准确率三项评价指标上,具有明显优势。  

Asset allocation when guarding against catastrophic losses: a comparison between the structure variable and joint probability methods

We apply a bivariate approach to the asset allocation problem for investors seeking to minimize the probability of large losses. It involves modelling the tails of joint distributions using techniques motivated by extreme value theory. We compare results with a corresponding univariate approach using simulated and financial data. Through an examination of a simulated and real financial data set we show that the estimated risks using the bivariate and univariate approaches are in close agreement for a wide range of losses and allocations. This is important since the bivariate approach is significantly more computationally expensive. We therefore suggest that the univariate approach be used for the typical level of loss that an investor may want to guard against. This univariate approach is effective even if there are more than two assets. The software written in support of this work is available on demand and we describe its use in the appendix.  

The next tick on Nasdaq

The Nasdaq stock market provides information about buying and selling interest in its limit order book. Using a vector autoregressive model of trades and returns, I assess the effect of the entire order book on the next tick. I also determine the influence of individual market makers and electronic networks and find evidence that the identity of market participants can be useful information. Finally, I produce a set of dynamic market price responses to buy and sell orders, and I find that these estimates vary with standard measures of liquidity.  

Analysing liquidity and absorption limits of electronic markets with volume durations

This paper focuses on the liquidity of electronic stock markets applying a sequential estimation approach of models for volume duration with increasing threshold values. A modified ACD model with a Box–Tukey transformation and a flexible generalized beta distribution is proposed to capture the changing cluster structure of duration processes. The estimation results with German XETRA data reveal the market's absorption limit for high volumes of shares, expanding the time costs of illiquidity when trading these quantities.  

Random matrix ensembles of time-lagged correlation matrices: derivation of eigenvalue spectra and analysis of financial time-series

We derive the exact form of the eigenvalue spectra of correlation matrices derived from a set of time-shifted, finite Brownian random walks (time-series). These matrices can be seen as real, asymmetric random matrices where the time-shift superimposes some structure. We demonstrate that, for large matrices, the associated eigenvalue spectrum is circular symmetric in the complex plane. This fact allows us to exactly compute the eigenvalue density via an inverse Abel-transform of the density of the symmetrized problem. We demonstrate the validity of this approach numerically. Theoretical findings are then compared with eigenvalue densities obtained from actual high-frequency (5 min) data of the S&P 500 and the observed deviations are discussed. We identify various non-trivial, non-random patterns and find asymmetric dependencies associated with eigenvalues departing strongly from the Gaussian prediction in the imaginary part. For the same time-series, with the market contribution removed, we observe strong clustering of stocks into causal sectors. We finally comment on the stability of the observed patterns.