Regression Driven F--Transform and Application to Smoothing of Financial Time Series

In this paper we propose to extend the definition of fuzzy transform in order to consider an interpolation of models that are richer than the standard fuzzy transform. We focus on polynomial models, linear in particular, although the approach can be easily applied to other classes of models. As an example of application, we consider the smoothing of time series in finance. A comparison with moving averages is performed using NIFTY 50 stock market index. Experimental results show that a regression driven fuzzy transform (RDFT) provides a smoothing approximation of time series, similar to moving average, but with a smaller delay. This is an important feature for finance and other application, where time plays a key role.Comment: IFSA-SCIS 2017, 5 pages, 6 figures, 1 tabl

A Bayesian Multivariate Functional Dynamic Linear Model

We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic linear models for multivariate time series to the functional data setting. We also develop Bayesian spline theory in a more general constrained optimization framework. The proposed methods identify a time-invariant functional basis for the functional observations, which is smooth and interpretable, and can be made common across multivariate observations for additional information sharing. The Bayesian framework permits joint estimation of the model parameters, provides exact inference (up to MCMC error) on specific parameters, and allows generalized dependence structures. Sampling from the posterior distribution is accomplished with an efficient Gibbs sampling algorithm. We illustrate the proposed framework with two applications: (1) multi-economy yield curve data from the recent global recession, and (2) local field potential brain signals in rats, for which we develop a multivariate functional time series approach for multivariate time-frequency analysis. Supplementary materials, including R code and the multi-economy yield curve data, are available online

Mixed effect model for absolute log returns of ultra high frequency data

The influence of covariates on absolute log returns of ultra high frequency data is analysed. Therefore we construct a mixed effect model for the absolute log returns. The parameters are estimated in a state space approach. To analyse the correlation in these irregularly spaced data empirically, the variogram, known mainly from spatial statistics, will be used. In a small simulation study the performance of the estimators will be analysed. In the end we apply the model to IBM trade data and analyse the influence of the covariates

Nonparametric estimation of conditional beta pricing models

We propose a new procedure to estimate and test conditional beta pricing models which allows for flexibility in the dynamics of assets' covariances with risk factors and market prices of risk (MPR). The method can be seen as a nonparametric version of the two-pass approach commonly employed in the context of unconditional models. In the first stage, conditional covariances are estimated nonparametrically for each asset and period using the time-series of previous data. In the second stage, time-varying MPR are estimated from the cross-section of returns and covariances, using the entire sample and allowing for heteroscedastic and cross-sectionally correlated errors. We prove the desirable properties of consistency and asymptotic normality of the estimators. Finally, an empirical application to the term structure of interest rates illustrates the method and highlights several drawbacks of existing parametric models

A General Framework for Observation Driven Time-Varying Parameter Models

We propose a new class of observation driven time series models that we refer to as Generalized Autoregressive Score (GAS) models. The driving mechanism of the GAS model is the scaled likelihood score. This provides a unified and consistent framework for introducing time-varying parameters in a wide class of non-linear models. The GAS model encompasses other well-known models such as the generalized autoregressive conditional heteroskedasticity, autoregressive conditional duration, autoregressive conditional intensity and single source of error models. In addition, the GAS specification gives rise to a wide range of new observation driven models. Examples include non-linear regression models with time-varying parameters, observation driven analogues of unobserved components time series models, multivariate point process models with time-varying parameters and pooling restrictions, new models for time-varying copula functions and models for time-varying higher order moments. We study the properties of GAS models and provide several non-trivial examples of their application.dynamic models, time-varying parameters, non-linearity, exponential family, marked point processes, copulas

Volatility forecasting

Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This chapter provides a selective survey of the most important theoretical developments and empirical insights to emerge from this burgeoning literature, with a distinct focus on forecasting applications. Volatility is inherently latent, and Section 1 begins with a brief intuitive account of various key volatility concepts. Section 2 then discusses a series of different economic situations in which volatility plays a crucial role, ranging from the use of volatility forecasts in portfolio allocation to density forecasting in risk management. Sections 3, 4 and 5 present a variety of alternative procedures for univariate volatility modeling and forecasting based on the GARCH, stochastic volatility and realized volatility paradigms, respectively. Section 6 extends the discussion to the multivariate problem of forecasting conditional covariances and correlations, and Section 7 discusses volatility forecast evaluation methods in both univariate and multivariate cases. Section 8 concludes briefly. JEL Klassifikation: C10, C53, G1

Managing uncertainty:financial, actuarial and statistical modelling.

present value; Value; Actuarial;