Central banks have different objectives in the short and long run. Governments operate simultaneously at different timescales. Many economic processes are the result of the actions of several agents, who have different term objectives. Therefore, a macroeconomic time series is a combination of components operating on different frequencies. Several questions about economic time series are connected to the understanding of the behavior of key variables at different frequencies over time, but this type of information is difficult to uncover using pure time-domain or pure frequency-domain methods.To our knowledge, for the first time in an economic setup, we use cross-wavelet tools to show that the relation between monetary policy variables and macroeconomic variables has changed and evolved with time. These changes are not homogeneous across the different frequencies.

a b s t r a c tWe consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump-diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman's optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton-Jacobi-Belman equation, which turns out to be a partial integro-differential equation due to the extra terms arising from the Lévy process and the Markov process. As an application of our results, we study a finite horizon consumptioninvestment problem for a jump-diffusion financial market consisting of one risk-free asset and one risky asset whose coefficients are assumed to depend on the state of a continuous time finite state Markov process. We provide a detailed study of the optimal strategies for this problem, for the economically relevant families of power utilities and logarithmic utilities.

The purpose of this article is to provide insight on a partnership between Matosinhos City Hall that coordinates educational programs including physical education and the School of Higher Education of Porto. For the past 2 years, the institutions have worked together to develop a local curriculum for physical education teachers to foster life skills development and transfer in their students. In this article, we provide an overview about (a) how the partnership was developed, (b) how establishing fundamental pedagogical components provided the platform for later explicit life skills teaching, (c) the facilitators and barriers that emerged from these efforts, and (d) plans to integrate an explicit approach to sport-based life skills development and transfer.