Nonparametric predictive inference for stock returns

In finance, inferences about future asset returns are typically quantified with the use of parametric distributions and single-valued probabilities. It is attractive to use less restrictive inferential methods, including nonparametric methods which do not require distributional assumptions about variables, and imprecise probability methods which generalize the classical concept of probability to set-valued quantities. Main attractions include the flexibility of the inferences to adapt to the available data and that the level of imprecision in inferences can reflect the amount of data on which these are based. This paper introduces nonparametric predictive inference (NPI) for stock returns. NPI is a statistical approach based on few assumptions, with inferences strongly based on data and with uncertainty quantified via lower and upper probabilities. NPI is presented for inference about future stock returns, as a measure for risk and uncertainty, and for pairwise comparison of two stocks based on their future aggregate returns. The proposed NPI methods are illustrated using historical stock market data.     

Testing for a finite mixture model with two components

Summary.  We consider a finite mixture model with k components and a kernel distribution from a general one-parameter family. The problem of testing the hypothesis k =2 versus k 3 is studied. There has been no general statistical testing procedure for this problem. We propose a modified likelihood ratio statistic where under the null and the alternative hypotheses the estimates of the parameters are obtained from a modified likelihood function. It is shown that estimators of the support points are consistent. The asymptotic null distribution of the modified likelihood ratio test proposed is derived and found to be relatively simple and easily applied. Simulation studies for the asymptotic modified likelihood ratio test based on finite mixture models with normal, binomial and Poisson kernels suggest that the test proposed performs well. Simulation studies are also conducted for a bootstrap method with normal kernels. An example involving foetal movement data from a medical study illustrates the testing procedure.     

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.     

Bayesian mixture model averaging for identifying the different gene expressions of chickpea (Cicer arietinum) plant tissue

Identification of different gene expressions of chickpea (Cicer arietinum) plant tissue is needed in order to develop new varieties of chickpea plant which is resistant to disease through the insertion of genes. This plant is the third legume plant of the Leguminosae (Fabaceae) family and is much needed in the world due to its high-protein seeds and roots that contain symbiotic nitrogen-fixing bacteria. This paper has succeeded to demonstrate the work of Bayesian mixture model averaging (BMMA) approach to identify the different gene expressions of chickpea plant tissue in Indonesia. The results show that the best BMMA normal models contain from 727 (73%) up to 939 (94%) models from 1,000 generated mixture normal models. The fitted BMMA models to gene expression differences data on average is 0.2878511 for Kolmogorov–Smirnov (KS) and 0.1278080 for continuous rank probability score (CRPS). Based on these BMMA models, there are three groups of gene IDs: downregulated, regulated, and upregulated. The results of this grouping can be useful to find new varieties of chickpea plants that are more resistant to disease. The BMMA normal models coupled with Occam's window as a data-driven modeling have succeed to demonstrate the work of building the gene expression differences microarray experiments data.     

A Potts‐mixture spatiotemporal joint model for combined magnetoencephalography and electroencephalography data

We develop a new methodology for determining the location and dynamics of brain activity from combined magnetoencephalography (MEG) and electroencephalography (EEG) data. The resulting inverse problem is ill‐posed and is one of the most difficult problems in neuroimaging data analysis. In our development we propose a solution that combines the data from three different modalities, magnetic resonance imaging (MRI), MEG and EEG, together. We propose a new Bayesian spatial finite mixture model that builds on the mesostate‐space model developed by Daunizeau & Friston [Daunizeau and Friston, NeuroImage 2007; 38, 67–81]. Our new model incorporates two major extensions: (i) We combine EEG and MEG data together and formulate a joint model for dealing with the two modalities simultaneously; (ii) we incorporate the Potts model to represent the spatial dependence in an allocation process that partitions the cortical surface into a small number of latent states termed mesostates. The cortical surface is obtained from MRI. We formulate the new spatiotemporal model and derive an efficient procedure for simultaneous point estimation and model selection based on the iterated conditional modes algorithm combined with local polynomial smoothing. The proposed method results in a novel estimator for the number of mixture components and is able to select active brain regions, which correspond to active variables in a high‐dimensional dynamic linear model. The methodology is investigated using synthetic data and simulation studies and then demonstrated on an application examining the neural response to the perception of scrambled faces. R software implementing the methodology along with several sample datasets are available at the following GitHub repository https://github.com/v2south/PottsMix . The Canadian Journal of Statistics 47: 688–711; 2019 © 2019 Statistical Society of Canada