Testing the Martingale Difference Hypothesis Using Neural Network Approximations

The martingale difference restriction is an outcome of many theoretical analyses in economics and finance. A large body of econometric literature deals with tests of that restriction. We provide new tests based on radial basis function neural networks. Our work is based on the test design of Blake and Kapetanios (2000, 2003a,b). However, unlike that work we can provide a formal theoretical justification for the validity of these tests using approximation results from Kapetanios and Blake (2007). These results take advantage of the link between the algorithms of Blake and Kapetanios (2000, 2003a,b) and boosting. We carry out a Monte Carlo study of the properties of the new tests and find that they have superior power performance to all existing tests of the martingale difference hypothesis we consider. An empirical application to the S&P500 constituents illustrates the usefulness of our new test.Martingale difference hypothesis, Neural networks, Boosting

Testing for Neglected Nonlinearity in Cointegrating Relationships

This paper proposes pure significance tests for the absence of nonlinearity in cointegrating relationships. No assumption of the functional form of the nonlinearity is made. It is envisaged that the application of such tests could form the first step towards specifying a nonlinear cointegrating relationship for empirical modelling. The asymptotic and small sample properties of our tests are investigated, where special attention is paid to the role of nuisance parameters and a potential resolution using the bootstrap.Cointegration, Nonlinearity, Neural networks, Bootstrap

Boosting Estimation of RBF Neural Networks for Dependent Data

This paper develops theoretical results for the estimation of radial basis function neural network specifications, for dependent data, that do not require iterative estimation techniques. Use of the properties of regression based boosting algorithms is made. Both consistency and rate results are derived. An application to nonparametric specification testing illustrates the usefulness of the results.Neural Networks, Boosting

Testing for ARCH in the Presence of Nonlinearity of Unknown Form in the Conditional Mean

Tests of ARCH are a routine diagnostic in empirical econometric and financial analysis. However, it is well known that misspecification of the conditional mean may lead to spurious rejections of the null hypothesis of no ARCH. Nonlinearity is a prime example of this phenomenon. There is little work on the extent of the effect of neglected nonlinearity on the properties of ARCH tests. This paper provides some such evidence and also new ARCH testing procedures that are robust to the presence of neglected nonlinearity. Monte Carlo evidence shows that the problem is serious and that the new methods alleviate this problem to a very large extent.Nonlinearity, ARCH, Neural networks

Time Consistent Policy in Markov Switching Models

In this paper we consider the quadratic optimal control problem with regime shifts and forward-looking agents. This extends the results of Zampolli (2003) who considered models without forward-looking expectations. Two algorithms are presented: The first algorithm computes the solution of a rational expectation model with random parameters or regime shifts. The second algorithm computes the time-consistent policy and the resulting Nash-Stackelberg equilibrium. The formulation of the problem is of general form and allows for model uncertainty and incorporation of policymaker’s judgement. We apply these methods to compute the optimal (non-linear) monetary policy in a small open economy subject to (symmetric or asymmetric) risks of change in some of its key parameters such as inflation inertia, degree of exchange rate pass-through, elasticity of aggregate demand to interest rate, etc.. We normally find that the time-consistent response to risk is more cautious. Furthermore, the optimal response is in some cases non-monotonic as a function of uncertainty. We also simulate the model under assumptions that the policymaker and the private sector hold the same beliefs over the probabilities of the structural change and different beliefs (as well as different assumptions about the knowledge of each other’s reaction function).monetary policy, regime switching, model uncertainty, time consistency

Inflation conservatism and monetary-fiscal policy interactions

Final version published in International Journal of Central Banking. Earlier version published as SSRN working paperThis paper investigates the stabilization bias that arises in a model of monetary and fiscal policy stabilization of the economy, when monetary authority puts higher weight on inflation stabilization than society. We demonstrate that inflation conservatism unambiguously leads to social welfare losses if the fiscal authority acts strategically under discretion. Although the precise form of monetary-fiscal interactions depends on the leadership structure, the choice of fiscal instrument, and the level of steady-state debt, the assessment of gains is robust to these assumptions. We develop an algorithm that computes leadership equilibria in a general framework of LQ RE models with strategic agents

Inflation-Conservatism and Monetary-Fiscal Policy Interactions

This paper investigates the stabilization bias that arises in a model of monetary and fiscal policy stabilization of the economy, when assuming that the monetary authority put higher weight on inflation stabilization than society. We demonstrate that inflation-conservatism unambiguously leads to social welfare losses if the fiscal authority acts strategically. Although the precise form of monetary-fiscal interactions depends on the choice of fiscal instrument and on the level of steady state debt, the assessment of gains is robust to these assumptions. We also study how the outcome of stabilization depends on the leadership structure. We develop an algorithm that computes leadership equilibria as well in much wider spectrum of problems with strategic agentsMonetary and Fiscal Policy, Policy Delegation, Discretion, Leadership Equilibria

Revisiting two-step Forbush decreases

Interplanetary coronal mass ejections (ICMEs) and their shocks can sweep out galactic cosmic rays (GCRs), thus creating Forbush decreases (FDs). The traditional model of FDs predicts that an ICME and its shock decrease the GCR intensity in a two-step profile. This model, however, has been the focus of little testing. Thus, our goal is to discover whether a passing ICME and its shock inevitably lead to a two-step FD, as predicted by the model. We use cosmic ray data from 14 neutron monitors and, when possible, high time resolution GCR data from the spacecraft International Gamma Ray Astrophysical Laboratory (INTEGRAL). We analyze 233 ICMEs that should have created two-step FDs. Of these, only 80 created FDs, and only 13 created two-step FDs. FDs are thus less common than predicted by the model. The majority of events indicates that profiles of FDs are more complicated, particularly within the ICME sheath, than predicted by the model. We conclude that the traditional model of FDs as having one or two steps should be discarded. We also conclude that generally ignored small-scale interplanetary magnetic field structure can contribute to the observed variety of FD profiles

Solving rational expectations models: a practical approach using Scilab®

This Handbook is about useful numerical methods for models commonly used in central banks. The linear general equilibrium model with rational expectations is a natural part of the central bank economist's toolkit. The appropriate modelling of monetary policy in these models is even more so. This Handbook aims to get people familiar with the methods and then to use them on their own problems by demonstrating exactly how to do it in as simple a way as possible.  The Handbook is structured so that the exercises and suggested variations should help the reader to both understand the techniques being used and the Scilab code itself. The Scilab code forms a useful library of routines than can be reused by economists wishing to investigate the properties of their models. The Handbook first introduces a basic New Keynesian (NK) model, briefly discussing each of the equations that comprise the system. Then is shows how to put the model into state space, how to solve the model for a given calibration, and present results for the model in terms of impulse responses and moments. The remainder of the Handbook builds on this by considering how to handle variations on this simple model, with modifications to the IS curve, the Phillips Curve, the policy rule and extending to an open economy. We also examine alternative forms of modelling monetary policy, in particular how to calculate optimal policies and to optimise the coefficients of a simple policy rule.DSGE; model solution; policy design;

Multipoint, high time resolution galactic cosmic ray observations associated with two interplanetary coronal mass ejections

[1] Galactic cosmic rays (GCRs) play an important role in our understanding of the interplanetary medium (IPM). The causes of their short timescale variations, however, remain largely unexplored. In this paper, we compare high time resolution, multipoint space-based GCR data to explore structures in the IPM that cause these variations. To ensure that features we see in these data actually relate to conditions in the IPM, we look for correlations between the GCR time series from two instruments onboard the Polar and INTEGRAL (International Gamma Ray Astrophysical Laboratory) satellites, respectively inside and outside Earth\u27s magnetosphere. We analyze the period of 18–24 August 2006 during which two interplanetary coronal mass ejections (ICMEs) passed Earth and produced a Forbush decrease (Fd) in the GCR flux. We find two periods, for a total of 10 h, of clear correlation between small-scale variations in the two GCR time series during these 7 days, thus demonstrating that such variations are observable using space-based instruments. The first period of correlation lasted 6 h and began 2 h before the shock of the first ICME passed the two spacecraft. The second period occurred during the initial decrease of the Fd, an event that did not conform to the typical one- or two-step classification of Fds. We propose that two planar magnetic structures preceding the first ICME played a role in both periods: one structure in driving the first correlation and the other in initiating the Fd