Spatial-temporal forecasting the sunspot diagram

We attempt to forecast the Sun's sunspot butterfly diagram in both space (i.e. in latitude) and time, instead of the usual one-dimensional time series forecasts prevalent in the scientific literature. We use a prediction method based on the non-linear embedding of data series in high dimensions. We use this method to forecast both in latitude (space) and in time, using a full spatial-temporal series of the sunspot diagram from 1874 to 2015. The analysis of the results shows that it is indeed possible to reconstruct the overall shape and amplitude of the spatial-temporal pattern of sunspots, but that the method in its current form does not have real predictive power. We also apply a metric called structural similarity to compare the forecasted and the observed butterfly cycles, showing that this metric can be a useful addition to the usual root mean square error metric when analysing the efficiency of different prediction methods

Dynamo models and differential rotation in late-type rapidly rotating stars

Increasing evidence is becoming available about not only the surface differential rotation of rapidly rotating cool stars but, in a small number of cases, also about temporal variations, which possibly are analogous to the solar torsional oscillations. Given the present difficulties in resolving the precise nature of such variations, due to both the short length and poor resolution of the available data, theoretical input is vital to help assess the modes of behaviour that might be expected, and will facilitate interpretation of the observations. Here we take a first step in this direction by studying the variations in the convection zones of such stars, using a two dimensional axisymmetric mean field dynamo model operating in a spherical shell in which the only nonlinearity is the action of the azimuthal component of the Lorentz force of the dynamo generated magnetic field on the stellar angular velocity. We consider three families of models with different depths of dynamo-active regions. For moderately supercritical dynamo numbers we find torsional oscillations that penetrate all the way down to the bottom of the convection zones, similar to the case of the Sun. For larger dynamo numbers we find fragmentation in some cases and sometimes there are other dynamical modes of behaviour, including quasi-periodicity and chaos. We find that the largest deviations in the angular velocity distribution caused by the Lorentz force are of the order of few percent, implying that the original assumed `background' rotation field is not strongly distorted.Comment: Astronomy and Astrophysics, in pres

The influence of noise on scalings for in-out intermittency

We study the effects of noise on a recently discovered form of intermittency, referred to as in-out intermittency. This type of intermittency, which reduces to on-off in systems with a skew product structure, has been found in the dynamics of maps, ODE and PDE simulations that have symmetries. It shows itself in the form of trajectories that spend a long time near a symmetric state interspersed with short bursts away from symmetry. In contrast to on-off intermittency, there are clearly distinct mechanisms of approach towards and away from the symmetric state, and this needs to be taken into account in order to properly model the long time statistics. We do this by using a diffusion-type equation with delay integral boundary condition. This model is validated by considering the statistics of a two-dimensional map with and without the addition of noise.Comment: Submitted to Physical Review E, also available at http://www.eurico.web.co

Time-varying capital requirements in a general equilibrium model of liquidity dependence

This paper attempts to quantify business cycle effects of bank capital requirements. The authors use a general equilibrium model in which financing of capital goods production is subject to an agency problem. At the center of this problem is the interaction between entrepreneurs' moral hazard and liquidity provision by banks as analyzed by Holmstrom and Tirole (1998). They impose capital requirements on banks and calibrate the regulation using the Basel II risk-weight formula. Comparing business cycle properties of the model under this procyclical regulation with those under hypothetical countercyclical regulation, the authors find that output volatility is about 25 percent larger under procyclical regulation and that this volatility difference implies a 1.7 percent reduction of the household's welfare. Even with more conservative parameter choices, the volatility and welfare differences under the two regimes remain nonnegligible.Bank capital ; Business cycles ; Bank reserves

Price-Level versus Inflation Targeting with Financial Market Imperfections

This paper compares price-level-path targeting (PT) with inflation targeting (IT) in a sticky-price, dynamic, general equilibrium model augmented with imperfections in both the debt and equity markets. Using a Bayesian approach, we estimate this model for the Canadian economy. We show that the model with both debt and equity market imperfections fits the data better and use it to compare PT versus the estimated current IT regime. We find that in general PT outperforms the current IT regime. However, the gain is lower when financial market imperfections are taken into account.Monetary policy framework; Inflation targets; Economic models

Private equity premium in a general equilibrium model of uninsurable investment risk

This paper studies the quantitative properties of a general equilibrium model where a continuum of heterogeneous entrepreneurs are subject to aggregate as well as idiosyncratic risks in the presence of a borrowing constraint. The calibrated model matches the highly skewed wealth and income distributions of entrepreneurs. The authors provide an accurate solution to the model despite the significant nonlinearities that are absent in the economy with uninsurable labor income risk. The model is capable of generating the average private equity premium of roughly 3 percent and a low risk-free rate. The model also produces procyclicality of the risk-free rate and countercyclicality of the average private equity premium. The countercyclicality of the average equity premium is largely driven by tightening (loosening) of financing constraints during recessions (booms).Risk ; Private equity ; Business cycles