Bayesian fan charts for U.K. inflation: forecasting and sources of uncertainty in an evolving monetary system

We estimate a Bayesian vector autoregression for the U.K. with drifting coefficients and stochastic volatilities. We use it to characterize posterior densities for several objects that are useful for designing and evaluating monetary policy, including local approximations to the mean, persistence, and volatility of inflation. We present diverse sources of uncertainty that impinge on the posterior predictive density for inflation, including model uncertainty, policy drift, structural shifts and other shocks. We use a recently developed minimum entropy method to bring outside information to bear on inflation forecasts. We compare our predictive densities with the Bank of England's fan charts

Data-driven Economic NMPC using Reinforcement Learning

Reinforcement Learning (RL) is a powerful tool to perform data-driven optimal control without relying on a model of the system. However, RL struggles to provide hard guarantees on the behavior of the resulting control scheme. In contrast, Nonlinear Model Predictive Control (NMPC) and Economic NMPC (ENMPC) are standard tools for the closed-loop optimal control of complex systems with constraints and limitations, and benefit from a rich theory to assess their closed-loop behavior. Unfortunately, the performance of (E)NMPC hinges on the quality of the model underlying the control scheme. In this paper, we show that an (E)NMPC scheme can be tuned to deliver the optimal policy of the real system even when using a wrong model. This result also holds for real systems having stochastic dynamics. This entails that ENMPC can be used as a new type of function approximator within RL. Furthermore, we investigate our results in the context of ENMPC and formally connect them to the concept of dissipativity, which is central for the ENMPC stability. Finally, we detail how these results can be used to deploy classic RL tools for tuning (E)NMPC schemes. We apply these tools on both a classical linear MPC setting and a standard nonlinear example from the ENMPC literature

Dynamic Bayesian Predictive Synthesis in Time Series Forecasting

We discuss model and forecast combination in time series forecasting. A foundational Bayesian perspective based on agent opinion analysis theory defines a new framework for density forecast combination, and encompasses several existing forecast pooling methods. We develop a novel class of dynamic latent factor models for time series forecast synthesis; simulation-based computation enables implementation. These models can dynamically adapt to time-varying biases, miscalibration and inter-dependencies among multiple models or forecasters. A macroeconomic forecasting study highlights the dynamic relationships among synthesized forecast densities, as well as the potential for improved forecast accuracy at multiple horizons

The Determinants of Equity Risk and Their Forecasting Implications: A Quantile Regression Perspective

Several market and macro-level variables influence the evolution of equity risk in addition to the well-known volatility persistence. However, the impact of those covariates might change depending on the risk level, being different between low and high volatility states. By combining equity risk estimates, obtained from the Realized Range Volatility, corrected for microstructure noise and jumps, and quantile regression methods, we evaluate the forecasting implications of the equity risk determinants in different volatility states and, without distributional assumptions on the realized range innovations, we recover both the points and the conditional distribution forecasts. In addition, we analyse how the the relationships among the involved variables evolve over time, through a rolling window procedure. The results show evidence of the selected variables\u2019 relevant impacts and, particularly during periods of market stress, highlight heterogeneous effects across quantiles

Modelling short-term interest rate spreads in the euro money market

In the framework of a new money market econometric model, we assess the degree of precision achieved by the European Central Bank ECB) in meeting its operational target for the short-term interest rate and the impact of the U.S. sub-prime credit crisis on the euro money market during the second half of 2007. This is done in two steps. Firstly, the long-term behaviour of interest rates with one-week maturity is investigated by testing for co-breaking and for homogeneity of spreads against the minimum bid rate (MBR, the key policy rate). These tests capture the idea that successful steering of very short-term interest rates is inconsistent with the existence of more than one common trend driving the one-week interest rates and/or with nonstationarity of the spreads among interest rates of the same maturity (or measured against the MBR). Secondly, the impact of several shocks to the spreads (e.g. interest rate expectations, volumes of open market operations, interest rate volatility, policy interventions, and credit risk) is assessed by jointly modelling their behaviour. We show that, after August 2007, euro area commercial banks started paying a premium to participate in the ECB liquidity auctions. This puzzling phenomenon can be understood by the interplay between, on the one hand, adverse selection in the interbank market and, on the other hand, the broad range of collateral accepted by the ECB. We also show that after August 2007, the ECB steered the “risk-free” rate close to the policy rate, but has not fully off-set the impact of the credit events on other money market rates. JEL Classification: C32, E43, E50, E58, G15co-breaking, Credit risk, euro area, fractional co-integration, fractionally integrated factor vector autoregressive model, liquidity risk, long memory, money market interest rates, Structural change, sub-prime credit crisis

Performance analysis with network-enhanced complexities: On fading measurements, event-triggered mechanisms, and cyber attacks

Copyright © 2014 Derui Ding et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Nowadays, the real-world systems are usually subject to various complexities such as parameter uncertainties, time-delays, and nonlinear disturbances. For networked systems, especially large-scale systems such as multiagent systems and systems over sensor networks, the complexities are inevitably enhanced in terms of their degrees or intensities because of the usage of the communication networks. Therefore, it would be interesting to (1) examine how this kind of network-enhanced complexities affects the control or filtering performance; and (2) develop some suitable approaches for controller/filter design problems. In this paper, we aim to survey some recent advances on the performance analysis and synthesis with three sorts of fashionable network-enhanced complexities, namely, fading measurements, event-triggered mechanisms, and attack behaviors of adversaries. First, these three kinds of complexities are introduced in detail according to their engineering backgrounds, dynamical characteristic, and modelling techniques. Then, the developments of the performance analysis and synthesis issues for various networked systems are systematically reviewed. Furthermore, some challenges are illustrated by using a thorough literature review and some possible future research directions are highlighted.This work was supported in part by the National Natural Science Foundation of China under Grants 61134009, 61329301, 61203139, 61374127, and 61374010, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

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

VAR Forecasting Using Bayesian Variable Selection

This paper develops methods for automatic selection of variables in Bayesian vector autoregressions (VARs) using the Gibbs sampler. In particular, I provide computationally efficient algorithms for stochastic variable selection in generic linear and nonlinear models, as well as models of large dimensions. The performance of the proposed variable selection method is assessed in forecasting three major macroeconomic time series of the UK economy. Data-based restrictions of VAR coefficients can help improve upon their unrestricted counterparts in forecasting, and in many cases they compare favorably to shrinkage estimators.Forecasting; variable selection; time-varying parameters; Bayesian vector autoregression

Introducing shrinkage in heavy-tailed state space models to predict equity excess returns

We forecast S&P 500 excess returns using a flexible Bayesian econometric state space model with non-Gaussian features at several levels. More precisely, we control for overparameterization via novel global-local shrinkage priors on the state innovation variances as well as the time-invariant part of the state space model. The shrinkage priors are complemented by heavy tailed state innovations that cater for potential large breaks in the latent states. Moreover, we allow for leptokurtic stochastic volatility in the observation equation. The empirical findings indicate that several variants of the proposed approach outperform typical competitors frequently used in the literature, both in terms of point and density forecasts

A decision theoretic analysis of the unit root hypothesis using mixtures of elliptical models

This paper develops a formal decision theoretic approach to testing for a unit root in economic time series. The approach is empirically implemented by specifying a loss function based on predictive variances; models are chosen so as to minimize expected loss. In addition, the paper broadens the class of likelihood functions traditionally considered in the Bayesian unit root literature by: i) Allowing for departures from normality via the specification of a likelihood based on general elliptical densities; ii) allowing for structural breaks to occur; iii) allowing for moving average errors; and iv) using mixtures of various submodels to create a very flexible overall likelihood. Empirical results indicate that, while the posterior probability of trend-stationarity is quite high for most of the series considered, the unit root model is often selected in the decision theoretic analysis