We prove existence and uniqueness of a stationary distribution and absolute regularity for nonlinear GARCH and INGARCH models of order (p, q). In contrast to previous work we impose, besides a geometric drift condition, only a semi-contractive condition which allows us to include models which would be ruled out by a fully contractive condition. This results in a subgeometric rather than the more usual geometric decay rate of the mixing coefficients. The proofs are heavily based on a coupling of two versions of the processes.

Using a panel of 54 countries between 1980 and 2013, we find empirical support for the view that changes in the fiscal policy stance (year-on-year change in the cyclically adjusted primary balance) have a significant positive correlation with inflation volatility. An increase in the volatility of discretionary fiscal policies by one standard deviation raises inflation volatility by about 6%. Moreover, results using alternative inflation volatility proxies confirm that an expansionary fiscal stance increases price volatility. Another relevant outcome is that in a context of economic expansions (recessions) the harmful impact of fiscal activism on price volatility is soft (heightened), while the negative impact of fiscal activism on price stability is higher when fiscal policy is expansionary. Finally, fiscal activism fuels inflation volatility much more pronouncedly in emerging market economies vis-à-vis advanced economies.

In this paper, a discrete-time framework is proposed to value power exchange options with counterparty default risk, where counterparty risk is considered in a reduced-form setting and the variance processes of the underlying assets are captured by GARCH processes. In addition, the proposed model allows for the correlation between the intensity of default and the variances of the underlying assets by breaking down the total risk into systematic and idiosyncratic components. By dint of measure-change techniques and characteristic functions, we obtain the closed-form pricing formula for the value of power exchange options with counterparty default risk. Finally, numerical results are presented to show the power exchange option values.

Branching processes in random environments have been widely studied and applied to population growth systems to model the spread of epidemics, infectious diseases, cancerous tumor growth, and social network traffic. However, Ebola virus, tuberculosis infections, and avian flu grow or change at rates that vary with time—at peak rates during pandemic time periods, while at low rates when near extinction. The branching processes in generalized autoregressive conditional environments we propose provide a novel approach to branching processes that allows for such time-varying random environments and instances of peak growth and near extinction-type rates. Offspring distributions we consider to illustrate the model include the generalized Poisson, binomial, and negative binomial integer-valued GARCH models. We establish conditions on the environmental process that guarantee stationarity and ergodicity of the mean offspring number and environmental processes and provide equations from which their variances, autocorrelation, and cross-correlation functions can be deduced. Furthermore, we present results on fundamental questions of importance to these processes—the survival-extinction dichotomy, growth behavior, necessary and sufficient conditions for noncertain extinction, characterization of the phase transition between the subcritical and supercritical regimes, and survival behavior in each phase and at criticality.

Advanced machine learning techniques like Gaussian process regression and multi-task learning are novel in the area of wine price prediction; previous research in this area being restricted to parametric linear regression models when predicting wine prices. Using historical price data of the 100 wines in the Liv-Ex 100 index, the main contributions of this paper to the field are, firstly, a clustering of the wines into two distinct clusters based on autocorrelation. Secondly, an implementation of Gaussian process regression on these wines with predictive accuracy surpassing both the trivial and simple ARMA and GARCH time series prediction benchmarks. Lastly, an implementation of an algorithm which performs multi-task feature learning with kernels on the wine returns as an extension to our optimal Gaussian process regression model. Using the optimal covariance kernel from Gaussian process regression, we achieve predictive results which are comparable to that of Gaussian process regression. Altogether, our research suggests that there is potential in using advanced machine learning techniques in wine price prediction. (JEL Classifications: C6, G12)

This paper examines the supply response of the Greek pork market. A GARCH process is used to estimate expected price and price volatility, while price and supply equations are estimated jointly. In addition to the standard GARCH model, several different symmetric, asymmetric, and nonlinear GARCH models are estimated. The empirical results indicate that among the estimated GARCH models, the quadratic NAGARCH model seems to better describe producers' price volatility, which was found to be an important risk factor of the supply response function of the Greek pork market. Furthermore, the empirical findings show that feed price is an important cost factor of the supply response function and that high uncertainty restricts the expansion of the Greek pork sector. Finally, the model provides forecasts for quantity supplied, producers' price, and price volatility.

We consider the problem of stochastic comparison of general GARCH-like processes for different parameters and different distributions of the innovations. We identify several stochastic orders that are propagated from the innovations to the GARCH process itself, and we discuss their interpretations. We focus on the convex order and show that in the case of symmetric innovations it is also propagated to the cumulated sums of the GARCH process. More generally, we discuss multivariate comparison results related to the multivariate convex and supermodular orders. Finally, we discuss ordering with respect to the parameters in the GARCH(1, 1) case.

In this paper we study the fractional moments of the stationary solution to the stochastic recurrence equation Xt = AtXt−1 + Bt, t ∈ Z, where ((At, Bt))t∈Z is an independent and identically distributed bivariate sequence. We derive recursive formulae for the fractional moments E|X0|p, p ∈ R. Special attention is given to the case when Bt has an Erlang distribution. We provide various approximations to the moments E|X0|p and show their performance in a small numerical study.

Suppose that {Xt} is a Markov chain such as the state space model for a threshold GARCH time series. The regularity assumptions for a drift condition approach to establishing the ergodicity of {Xt} typically are ϕ-irreducibility, aperiodicity, and a minorization condition for compact sets. These can be very tedious to verify due to the discontinuous and singular nature of the Markov transition probabilities. We first demonstrate that, for Feller chains, the problem can at least be simplified to focusing on whether the process can reach some neighborhood that satisfies the minorization condition. The results are valid not just for the transition kernels of Markov chains but also for bounded positive kernels, opening the possibility for new ergodic results. More significantly, we show that threshold GARCH time series and related models of interest can often be embedded into Feller chains, allowing us to apply the conclusions above.

Daily financial returns (and daily stock returns, in particular) are commonly modeled as GARCH(1, 1) processes. Here we test this specification using new model evaluation technology developed by Ashley and Patterson that examines the ability of the estimated model to reproduce features of particular interest: various aspects of nonlinear serial dependence, in the present instance. Using daily returns to the CRSP equally weighted stock index, we find that the GARCH(1, 1) specification cannot be rejected; thus, this model appears to be reasonably adequate in terms of reproducing the kinds of nonlinear serial dependence addressed by the battery of nonlinearity tests used here.

There is only a sparse literature on the determination of real exchange rate volatility, and little attention has been given to the possible impact of EMU on volatility of real exchange rates of EU countries. A number of papers suggest a negative impact of exchange rate volatility on investment or growth, for advanced as well as developing countries, although we note that price and wage adjustment that might link to real exchange rate volatility is also part of the adjustment mechanism to macroeconomic shocks in EMU. We assess whether an effect of EMU on conditional volatility of real effective exchange rates can be detected, both for EMU and non EMU members. We find that the advent of EMU was accompanied by a reduction in conditional real exchange rate volatility for most EMU countries, as well as Sweden and Denmark that did not join EMU, but did not lead to a reduction in real rate volatility for Germany, Belgium, the Netherlands, nor, outside EMU, for the UK.