股指期货信息内含股价变动信息的挖掘 ――小波框架与支持向量回归的金融建模应用

 内容提要：中国股指期货的推出指日可待，交易者多了一种投资工具的同时也带来了新的风险。建立准确的金融时间序列预测模型是逐利及避险的方法之一，一直是学者专家研究的热点。本研究结合小波转换与支持向量回归，提出一个二阶段时间序列预测模型。先以离散小波框架将预测变量分解成不同尺度的多个子序列，揭示隐藏在预测变量内的信息，再以支持向量回归为工具，以这些子序列为预测变量建构SVR模型。本研究以日经225指数开盘价为预测目标，以期货开盘价为预测变量对模型进行实证研究，结果显示，该模型的预测绩效比单纯SVR模型及随机漫步模型好。未来可尝试以不同的基底函数作进一步研究。     

Estimation of Time-Varying Long Memory Parameter Using Wavelet Method

Stationary long memory processes have been extensively studied over the past decades. When we deal with financial, economic, or environmental data, seasonality and time-varying long-range dependence can often be observed and thus some kind of non-stationarity exists. To take into account this phenomenon, we propose a new class of stochastic processes: locally stationary k-factor Gegenbauer process. We present a procedure to estimate consistently the time-varying parameters by applying discrete wavelet packet transform. The robustness of the algorithm is investigated through a simulation study. And we apply our methods on Nikkei Stock Average 225 (NSA 225) index series.     

Volatility forecasting of financial time series using wavelet based exponential generalized autoregressive conditional heteroscedasticity model

Abstract

An improved forecasting model by merging two different computational models in predicting future volatility was proposed. The model integrates wavelet and EGARCH model where the pre-processing activity based on wavelet transform is performed with de-noising technique to eliminate noise in observed signal. The denoised signal is then feed into EGARCH model to forecast the volatility. The predictive capability of the proposed model is compared with the existing EGARCH model. The results show that the hybrid model has increased the accuracy of forecasting future volatility.     

Forecasting interest rates: a comparative assessment of some second-generation nonlinear models

Modeling and forecasting of interest rates has traditionally proceeded in the framework of linear stationary methods such as ARMA and VAR, but only with moderate success. We examine here three methods, which account for several specific features of the real world asset prices such as nonstationarity and nonlinearity. Our three candidate methods are based, respectively, on a combined wavelet artificial neural network (WANN) analysis, a mixed spectrum (MS) analysis and nonlinear ARMA models with Fourier coefficients (FNLARMA). These models are applied to weekly data on interest rates in India and their forecasting performance is evaluated vis-à-vis three GARCH models [GARCH (1,1), GARCH-M (1,1) and EGARCH (1,1)] as well as the random walk model. Both the WANN and MS methods show marked improvement over other benchmark models, and may thus hold out several potentials for real world modeling and forecasting of financial data.     

Modelling and forecasting by wavelets, and the application to exchange rates

This paper investigates the modelling and forecasting method for non-stationary time series. Using wavelets, the authors propose a modelling procedure that decomposes the series as the sum of three separate components, namely trend, harmonic and irregular components. The estimates suggested in this paper are all consistent. This method has been used for the modelling of US dollar against DM exchange rate data, and ten steps ahead (2 weeks) forecasting are compared with several other methods. Under the Average Percentage of forecasting Error (APE) criterion, the wavelet approach is the best one. The results suggest that forecasting based on wavelets is a viable alternative to existing methods.     

A new algorithm for maximum likelihood estimation in normal scale-mixture generalized autoregressive conditional heteroskedastic models

In this paper, we propose a new generalized autoregressive conditional heteroskedastic (GARCH) model using infinite normal scale-mixtures which can suitably avoid order selection problems in the application of finite normal scale-mixtures. We discuss its theoretical properties and develop a two-stage algorithm for the maximum likelihood estimator to estimate the mixing distribution non-parametric maximum likelihood estimator (NPMLE) as well as GARCH parameters (two-stage MLE). For the estimation of a mixing distribution, we employ a fast computational algorithm proposed by Wang [On fast computation of the non-parametric maximum likelihood estimate of a mixing distribution. J R Stat Soc Ser B. 2007;69:185–198] under the gradient characterization of the non-parametric mixture likelihood. The GARCH parameters are then estimated either using the expectation-mazimization algorithm or general optimization scheme. In addition, we propose a new forecasting algorithm of value-at-risk (VaR) using the two-stage MLE and the NPMLE. Through a simulation study and real data analysis, we compare the performance of the two-stage MLE with the existing ones including quasi-maximum likelihood estimator based on the standard normal density and the finite normal mixture quasi maximum estimated-likelihood estimator (cf. Lee S, Lee T. Inference for Box–Cox transformed threshold GARCH models with nuisance parameters. Scand J Stat. 2012;39:568–589) in terms of the relative efficiency and accuracy of VaR forecasting.     

Cross-correlating wavelet coefficients with applications to high-frequency financial time series

This paper uses a new concept in wavelet analysis to explore a financial transaction data set including returns, durations, and volume. The concept is based on a decomposition of the Allan covariance of two series into cross-covariances of wavelet coefficients, which allows a natural interpretation of cross-correlations in terms of frequencies. It is applied to financial transaction data including returns, durations between transactions, and trading volume. At high frequencies, we find significant spillover from durations to volume and a strong contemporaneous relation between durations and returns, whereas a strong causality between volume and volatility exists at various frequencies.     

Value-at-risk forecasting based on Gaussian mixture ARMA–GARCH model

In this paper, we develop a new forecasting algorithm for value-at-risk (VaR) based on ARMA–GARCH (autoregressive moving average–generalized autoregressive conditional heteroskedastic) models whose innovations follow a Gaussian mixture distribution. For the parameter estimation, we employ the conditional least squares and quasi-maximum-likelihood estimator (QMLE) for ARMA and GARCH parameters, respectively. In particular, Gaussian mixture parameters are estimated based on the residuals obtained from the QMLE of GARCH parameters. Our algorithm provides a handy methodology, spending much less time in calculation than the existing resampling and bias-correction method developed in Hartz et al. [Accurate value-at-risk forecasting based on the normal-GARCH model, Comput. Stat. Data Anal. 50 (2006), pp. 3032–3052]. Through a simulation study and a real-data analysis, it is shown that our method provides an accurate VaR prediction.     

基于混频模型的CPI短期预测研究

传统的CPI预测模型都是基于相同频率的月度数据,金融市场的高频日度数据需要转化为月度数据才能使用。这会忽略日度变量所包含的CPI短期走势信息。为充分利用这些信息,本文基于自回归混频数据抽样模型同时考察了金融市场一阶矩收益和二阶矩波动的日度信息对CPI的短期走势预测的影响。结果表明,股票收益、短期利率和长短期利差变化量仅在收益水平上对CPI短期走势产生影响,而长期利率、粮食和能源商品市场的收益和波动都有助于CPI短期预测,而且收益对CPI的影响要比波动更加持久。相对于传统的月度时间序列建模方法,本文的混频CPI模型具有更好的样本内解释能力和样本外预测能力。另外,引入二阶矩波动的日度信息在一定程度上能更多地降低预测偏差。     

Dynamic financial distress prediction based on Kalman filtering

In models for predicting financial distress, ranging from traditional statistical models to artificial intelligence models, scholars have primarily paid attention to improving predictive accuracy as well as the progressivism and intellectualization of the prognostic methods. However, the extant models use static or short-term data rather than time-series data to draw inferences on future financial distress. If financial distress occurs at the end of a progressive process, then omitting time series of historical financial ratios from the analysis ignores the cumulative effect of previous financial ratios on the current consequences. This study incorporated the cumulative characteristics of financial distress by using the characteristics of a state space model that is able to perform long-term forecasts to dynamically predict an enterprise's financial distress. Kalman filtering is used to estimate the model parameters. Thus, the model constructed in this paper is a dynamic financial prediction model that has the benefit of forecasting over the long term. Additionally, current data are used to forecast the future annual financial position and to judge whether the establishment will be in financial distress.     

Robust interval forecasting algorithm based on a probabilistic cluster model

For substantiation of managerial decisions the forecasting results of dynamic indicators are used. Therefore, forecasting accuracy of these indicators must be acceptable. Consequently, forecasting algorithms are constantly improved to get the acceptable accuracy. This paper considers a variant of the method of forecasting binary outcomes. This method allows prediction of whether or not a future value of the indicator exceeds a predetermined value. This method ‘interval forecasting’ was named. In this paper a robust interval forecasting algorithm based on a probabilistic cluster model is proposed. The algorithm’s accuracy was compared with an algorithm based on logistic regression. The indicators with different statistical properties were chosen. The obtained results have shown the accuracy of both the algorithms is approximately similar in most cases. However, the cases when the algorithm based on logistic regression demonstrated unacceptable accuracy, unlike the presented algorithm have been identified. Thus, this new algorithm is more accurate.     

An Interest-rate Model Analysis Based on Data Augmentation Bayesian Forecasting

In this paper, the author presents an efficient method of analyzing an interest-rate model using a new approach called 'data augmentation Bayesian forecasting.' First, a dynamic linear model estimation was constructed with a hierarchically-incorporated model. Next, an observational replication was generated based on the one-step forecast distribution derived from the model. A Markov-chain Monte Carlo sampling method was conducted on it as a new observation and unknown parameters were estimated. At that time, the EM algorithm was applied to establish initial values of unknown parameters while the 'quasi Bayes factor' was used to appreciate parameter candidates. 'Data augmentation Bayesian forecasting' is a method of evaluating the transition and history of 'future,' 'present' and 'past' of an arbitrary stochastic process by which an appropriate evaluation is conducted based on the probability measure that has been sequentially modified with additional information. It would be possible to use future prediction results for modifying the model to grasp the present state or re-evaluate the past state. It would be also possible to raise the degree of precision in predicting the future through the modification of the present and the past. Thus, 'data augmentation Bayesian forecasting' is applicable not only in the field of financial data analysis but also in forecasting and controlling the stochastic process.     

Bayesian Dynamic Factor Models and Portfolio Allocation

We discuss the development of dynamic factor models for multivariate financial time series, and the incorporation of stochastic volatility components for latent factor processes. Bayesian inference and computation is developed and explored in a study of the dynamic factor structure of daily spot exchange rates for a selection of international currencies. The models are direct generalizations of univariate stochastic volatility models and represent specific varieties of models recently discussed in the growing multivariate stochastic volatility literature. We discuss model fitting based on retrospective data and sequential analysis for forward filtering and short-term forecasting. Analyses are compared with results from the much simpler method of dynamic variance-matrix discounting that, for over a decade, has been a standard approach in applied financial econometrics. We study these models in analysis, forecasting, and sequential portfolio allocation for a selected set of international exchange-rate-return time series. Our goals are to understand a range of modeling questions arising in using these factor models and to explore empirical performance in portfolio construction relative to discount approaches. We report on our experiences and conclude with comments about the practical utility of structured factor models and on future potential model extensions.     

Semi-parametric expected shortfall forecasting in financial markets

Bayesian methods have proved effective for quantile estimation, including for financial Value-at-Risk forecasting. Expected shortfall (ES) is a competing tail risk measure, favoured by the Basel Committee, that can be semi-parametrically estimated via asymmetric least squares. An asymmetric Gaussian density is proposed, allowing a likelihood to be developed, that facilitates both pseudo-maximum likelihood and Bayesian semi-parametric estimation, and leads to forecasts of quantiles, expectiles and ES. Further, the conditional autoregressive expectile class of model is generalised to two fully nonlinear families. Adaptive Markov chain Monte Carlo sampling schemes are developed for the Bayesian estimation. The proposed models are favoured in an empirical study forecasting eight financial return series: evidence of more accurate ES forecasting, compared to a range of competing methods, is found, while Bayesian estimated models tend to be more accurate. However, during a financial crisis period most models perform badly, while two existing models perform best.     

Bayesian Forecasting of Many Count-Valued Time Series

Abstract

We develop and exemplify application of new classes of dynamic models for time series of nonnegative counts. Our novel univariate models combine dynamic generalized linear models for binary and conditionally Poisson time series, with dynamic random effects for over-dispersion. These models estimate dynamic regression coefficients in both binary and nonzero count components. Sequential Bayesian analysis allows fast, parallel analysis of sets of decoupled time series. New multivariate models then enable information sharing in contexts when data at a more highly aggregated level provide more incisive inferences on shared patterns such as trends and seasonality. A novel multiscale approach—one new example of the concept of decouple/recouple in time series—enables information sharing across series. This incorporates cross-series linkages while insulating parallel estimation of univariate models, and hence enables scalability in the number of series. The major motivating context is supermarket sales forecasting. Detailed examples drawn from a case study in multistep forecasting of sales of a number of related items showcase forecasting of multiple series, with discussion of forecast accuracy metrics, comparisons with existing methods, and broader questions of probabilistic forecast assessment.     

Inference in molecular population genetics

Full likelihood-based inference for modern population genetics data presents methodological and computational challenges. The problem is of considerable practical importance and has attracted recent attention, with the development of algorithms based on importance sampling (IS) and Markov chain Monte Carlo (MCMC) sampling. Here we introduce a new IS algorithm. The optimal proposal distribution for these problems can be characterized, and we exploit a detailed analysis of genealogical processes to develop a practicable approximation to it. We compare the new method with existing algorithms on a variety of genetic examples. Our approach substantially outperforms existing IS algorithms, with efficiency typically improved by several orders of magnitude. The new method also compares favourably with existing MCMC methods in some problems, and less favourably in others, suggesting that both IS and MCMC methods have a continuing role to play in this area. We offer insights into the relative advantages of each approach, and we discuss diagnostics in the IS framework.     

应用不等权重支持向量机预测人民币汇率的变动

基于金融时间序列的近期数据对未来的影响会大于早期数据,对应用于金融时间序列预测的支持向量机方法进行改进,给出了不等权重支持向量机方法（USVM）及其多项式光滑化处理。将不等权重支持向量机方法应用于训练样本集的子集确定预测模型,实证分析表明USVM算法预测是有效的。     

Long memory and changepoint models: a spectral classification procedure

Time series within fields such as finance and economics are often modelled using long memory processes. Alternative studies on the same data can suggest that series may actually contain a ‘changepoint’ (a point within the time series where the data generating process has changed). These models have been shown to have elements of similarity, such as within their spectrum. Without prior knowledge this leads to an ambiguity between these two models, meaning it is difficult to assess which model is most appropriate. We demonstrate that considering this problem in a time-varying environment using the time-varying spectrum removes this ambiguity. Using the wavelet spectrum, we then use a classification approach to determine the most appropriate model (long memory or changepoint). Simulation results are presented across a number of models followed by an application to stock cross-correlations and US inflation. The results indicate that the proposed classification outperforms an existing hypothesis testing approach on a number of models and performs comparatively across others.     

Central Bank Macroeconomic Forecasting During the Global Financial Crisis: The European Central Bank and Federal Reserve Bank of New York Experiences

This article documents macroeconomic forecasting during the global financial crisis by two key central banks: the European Central Bank and the Federal Reserve Bank of New York. The article is the result of a collaborative effort between staff at the two institutions, allowing us to study the time-stamped forecasts as they were made throughout the crisis. The analysis does not exclusively focus on point forecast performance. It also examines methodological contributions, including how financial market data could have been incorporated into the forecasting process.     

A fast wavelet approach for recovering damaged images

A wavelet method is proposed for recovering damaged images. The proposed method combines wavelet shrinkage with preprocessing based on a binning process and an imputation procedure that is designed to extend the scope of wavelet shrinkage to data with missing values and perturbed locations. The proposed algorithm, termed as the BTW algorithm is simple to implement and efficient for recovering an image. Furthermore, this algorithm can be easily applied to wavelet regression for one-dimensional (1-D) signal estimation with irregularly spaced data. Simulation studies and real examples show that the proposed method can produce substantially effective results.