Modelling multiple time series via common factors

We propose a new method for estimating common factors of multiple time series. One distinctive feature of the new approach is that it is applicable to some nonstationary time series. The unobservable (nonstationary) factors are identified via expanding the white noise space step by step; therefore solving a high-dimensional optimization problem by several low-dimensional subproblems. Asymptotic properties of the estimation were investigated. The proposed methodology was illustrated with both simulated and real data sets

Normal mixture quasi maximum likelihood estimation for non-stationary TGARCH(1,1) models

Although quasi maximum likelihood estimator based on Gaussian density (G-QMLE) is widely used to estimate GARCH-type models, it does not perform successfully when error distribution is either skewed or leptokurtic. This paper proposes normal mixture quasi-maximum likelihood estimator (NM-QMLE) for non-stationary TGARCH(1,1) models. We show that, under mild regular conditions, there is no consistent estimator for the intercept, and the proposed estimator for any other parameter is consistent

Dimension reduction for stationary multivariate time series data

Chang et al. (2016) extended PCA by finding a linear transformation of the original variables such that the transformed series is segmented into uncorrelated subseries with lower dimensions. This method is called TS-PCA. In our current research, we will extend TS-PCA by reducing the dimension of the transformed subseries further by applying GDPCA by Pena and Yohai (2016) to the results from TS-PCA, and possibly reach a further dimension reduction. Hence, the proposed method is a combination of TS-PCA and GDPCA

Bayesian analysis of multiple thresholds autoregressive model

Bayesian analysis of threshold autoregressive (TAR) model with various possible thresholds is considered. A method of Bayesian stochastic search selection is introduced to identify a threshold-dependent sequence with highest probability. All model parameters are computed by a hybrid Markov chain Monte Carlo (MCMC) method, which combines Metropolis-Hastings (M-H) algorithm and Gibbs sampler. The main innovation of the method introduced here is to estimate the TAR model without assuming the fixed number of threshold values, thus is more flexible and useful. Simulation experiments and a real data example lend further support to the proposed approach

On the distributivity of T-power based implications

Due to the fact that Zadeh's quantifiers constitute the usual method to modify fuzzy propositions, the so-called family of T-power based implications was proposed. In this paper, the four basic distributive laws related to T-power based fuzzy implications and fuzzy logic operations (t-norms and t-conorms) are deeply studied. This study shows that two of the four distributive laws of the T-power based implications have a unique solution, while the other two have multiple solutions

Testing a linear ARMA Model against threshold-ARMA models : a Bayesian approach

We introduce a Bayesian approach to test linear autoregressive moving-average (ARMA) models against threshold autoregressive moving-average (TARMA) models. Firstly, the marginal posterior densities of all parameters, including the threshold and delay, of a TARMA model are obtained by using Gibbs sampler with Metropolis-Hastings algorithm. Secondly, reversible-jump Markov chain Monte Carlo (RJMCMC) method is adopted to calculate the posterior probabilities for ARMA and TARMA models: Posterior evidence in favor of TARMA models indicates threshold nonlinearity. Finally, based on RJMCMC scheme and Akaike information criterion (AIC) or Bayesian information criterion (BIC), the procedure for modeling TARMA models is exploited. Simulation experiments and a real data example show that our method works well for distinguishing a ARMA from a TARMA model and for building TARMA models

Generalized principal component analysis for moderately non-stationary vector time series

This paper extends the principal component analysis (PCA) to moderately non-stationary vector time series. We propose a method that searches for a linear transformation of the original series such that the transformed series is segmented into uncorrelated subseries with lower dimensions. A columns' rearrangement method is proposed to regroup transformed series based on their relationships. We discuss the theoretical properties of the proposed method for fixed and large dimensional cases. Many simulation studies show our approach is suitable for moderately non-stationary data. Illustrations on real data are provided

A scalar dynamic conditional correlation model : structure and estimation

The dynamic conditional correlation (DCC) model has been popularly used for modeling conditional correlation of multivariate time series since Engle (2002). However, the stationarity conditions are established only most recently and the asymptotic theory of parameter estimation for the DCC model has not been discussed fully. In this paper, we propose an alternative model, namely the scalar dynamic conditional correlation (SDCC) model. Sufficient and easy-checking conditions for stationarity, geometric ergodicity and β-mixing with exponential decay rates are provided. We then show the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) of the model parameters under regular conditions. The asymptotic results are illustrated by Monte Carlo experiments. As a real data example, the proposed SDCC model is applied to analysing the daily returns of the FSTE 100 index and FSTE 100 futures. Our model improves the performance of the DCC model in the sense that the LiMcleod statistic of the SDCC model is much smaller and the hedging efficiency is higher

Moving dynamic principal component analysis for non-stationary multivariate time series

This paper proposes an extension of principal component analysis (PCA) to non-stationary multivariate time series data. A criterion for determining the number of final retained components is proposed. An advance correlation matrix is developed to evaluate dynamic relationships among the chosen components. The theoretical properties of the proposed method are given. Many simulation experiments show our approach performs well on both stationary and non-stationary data. Real data examples are also presented as illustrations. We develop four packages using the statistical software R that contain the needed functions to obtain and assess the results of the the proposed method