The finite sample power of long-horizon predictive tests in models with financial bubbles

Mathematical modeling for a new portfolio selection problem in bubble condition, using a new risk measure

“…In the objective function (20), Z is in the denominator, Z must not be zero, because if it gets zero, the fraction is not defined and the model will be unacceptable, so the value of Z must be nonzero. As a result, the value of Z is assumed to be larger than a nonzero ε value (Guastaroba et al, [31]; Mansini et al, [32,33]).…”

“…  Equations (45) to (51) are in fact the same non-linear programming models' equations (20) to (26), which have become linear programming by changing the introduced variables. This model, based on the concept of new risk introduced in this study, offers a new approach to measure risk and also a relaxed linear programming model.…”

“…They studied the global dynamics of capital stocks and assets' values. Maynard and Ren [20] assessed the power of long-horizon predictive tests in a model that contains financial asset bubbles. Michaelides et al [21] developed a non-linearities in financial bubbles.…”

Long‐run predictability tests are even worse than you thought

“…However, while this might seem a reasonable intuitive justification for long‐horizon regressions, econometric specifications where this intuition actually bears fruit have proven fairly elusive. Attempts to design econometric models under the alternative of return predictability, which lead to power gains for long‐horizon tests over short‐horizon tests, have met with at most limited success (Hjalmarsson, 2012; Maynard & Ren, 2014; 2019). Related studies on the relationship between long‐ and short‐run results (e.g., Boudoukh et al, 2008; Hjalmarsson, 2008; McLoughlin,, 2019) also highlight that there seems to be little to be learned from the long run, given the short run.…”