Volume 12, Issue 2

The NoVaS methodology for prediction of stationary financial returns is reviewed, and the applicability of the NoVaS transformation for volatility estimation is illustrated using realized volatility as a proxy. The realm of applicability of the NoVaS methodology is then extended to non-stationary data (involving local stationarity and/or structural breaks) for one-step ahead point prediction of squared returns. In addition, a NoVaS-based algorithm is proposed for the construction of bootstrap prediction intervals for one-step ahead squared returns for both stationary and non-stationary data. It is shown that the “Time-varying” NoVaS is robust against possible nonstationarities in the data; this is true in terms of locally (but not globally) financial returns but also in change point problems where the NoVaS methodology adapts fast to the new regime that occurs after an unknown/undetected change point. Extensive empirical work shows that the NoVaS methodology generally outperforms the GARCH benchmark for (i) point prediction of squared returns, (ii) interval prediction of squared returns, and (iii) volatility estimation. With regard to target (i), earlier work had shown little advantage of using a nonzero α in the NoVaS transformation. However, in terms or targets (ii) and (iii), it appears that using the Generalized version of NoVaS—either Simple or Exponential—can be quite beneficial and well-worth the associated computational cost.

In this paper, new models are studied by proposing the family of generalized power series distributions with inflated parameter (IGPSD) for the innovation process of the INAR(1) model. The main properties of the process were established, such as mean, variance, autocorrelation and transition probability. The methods of estimation by Yule–Walker and the conditional maximum likelihood were used to estimate the parameters of the models. Two particular cases of the INAR(1)$\left(1\right)$ model with IGPSD innovation were studied, named IPoINAR(1)$\left(1\right)$ and IGeoINAR(1)$\left(1\right)$. Finally, in the real data example, a good performance of the proposed new models was observed.

We propose a Bayesian vector autoregressive (VAR) model for mixed-frequency data. Our model is based on the mean-adjusted parametrization of the VAR and allows for an explicit prior on the “steady states” (unconditional means) of the included variables. Based on recent developments in the literature, we discuss extensions of the model that improve the flexibility of the modeling approach. These extensions include a hierarchical shrinkage prior for the steady-state parameters, and the use of stochastic volatility to model heteroskedasticity. We put the proposed model to use in a forecast evaluation using US data consisting of 10 monthly and three quarterly variables. The results show that the predictive ability typically benefits from using mixed-frequency data, and that improvement can be obtained for both monthly and quarterly variables. We also find that the steady-state prior generally enhances the accuracy of the forecasts, and that accounting for heteroskedasticity by means of stochastic volatility usually provides additional improvements, although not for all variables.

The spatial lag model (SLM) has been widely studied in the literature for spatialised data modeling in various disciplines such as geography, economics, demography, regional sciences, etc. This is an extension of the classical linear model that takes into account the proximity of spatial units in modeling. In this paper, we propose a Bayesian estimation of the functional spatial lag (FSLM) model. The Bayesian MCMC technique is used as a method of estimation for the parameters of the model. A simulation study is conducted in order to compare the results of the Bayesian functional spatial lag model with the functional spatial lag model and the functional linear model. As an illustration, the proposed Bayesian functional spatial lag model is used to establish a relationship between the unemployment rate and the curves of illiteracy rate observed in the 45 departments of Senegal.