A Further Extension of Duration Dependent Models

The duration dependence of stock market cycles has been investigated using the Markov-switching model where the market conditions are unobservable. In the conventional modeling, restrictions are imposed that transition probability is a monotonic function of duration and the duration is truncated at a certain value. This paper proposes a model that is free from these arbitrary restrictions and nests the conventional models. In the model,the parameters that characterize the transition probability are formulated in the state space. Empirical results in several stock markets show that the duration structures differ greatly depending on countries. They are not necessarily monotonic functions of duration and, therefore, cannot be described by the conventional models.Duration, World stock markets, Markov-switching model, Nonparametric Model, Gibbs sampling, Marginal Likelihood

Listening to the Market: Estimating Credit Demand and Supply from Survey Data

The literature referring to the credit slowdown has been plagued by the identification problem of whether a decline in a bank's credit is derived from the demand or the supply side. This paper proposes an original approach in directly estimating the credit demand and the credit supply from survey data. Using the TANKAN and the recently published Senior Loan Officer survey data, the paper demonstrates that the observed lending amount did not change much during the period of study; however, the observed lending amount deviated, as one might expect, from the estimated credit demand and credit supply for every firm size. This credit mismatch presents evidence of credit market imperfections and is of interest for further investigation as a possible explanation of firms' liquidity constraints and banks' lending mechanisms.Credit demand, Credit supply, Survey data, Japanese Economy

spRap1 and spRif1, recruited to telomeres by Taz1, are essential for telomere function in fission yeast

AbstractTelomeres are essential for genome integrity. scRap1 (S. cerevisiae Rap1) directly binds to telomeric DNA [1–3] and regulates telomere length and telomere position effect (TPE) [4–6] by recruiting two different groups of proteins to its RCT (Rap1 C-terminal) domain [7]. The first group, Rif1 and Rif2, regulates telomere length [8, 9]. The second group, Sir3 and Sir4 [10], is involved in heterochromatin formation [11–13]. On the other hand, human TRF1 and TRF2, as well as their fission yeast homolog, Taz1, directly bind to telomeric DNA [14–16] and negatively regulate telomere length [16–20]. Taz1 also plays important roles in TPE and meiosis [16, 20, 21]. Human Rap1, the ortholog of scRap1, negatively regulates telomere length and appears to be recruited to telomeres by interacting with TRF2 [7]. Here, we describe two novel fission yeast proteins, spRap1 (S. pombe Rap1) and spRif1 (S. pombe Rif1), which are orthologous to scRap1 and scRif1, respectively. spRap1 and spRif1 are independently recruited to telomeres by interacting with Taz1. The rap1 mutant is severely defective in telomere length control, TPE, and telomere clustering toward the spindle pole body (SPB) at the premeiotic horsetail stage, indicating that spRap1 has critical roles in these telomere functions. The rif1 mutant also shows some defects in telomere length control and meiosis. Our results indicate that Taz1 provides binding sites for telomere regulators, spRap1 and spRif1, which perform the essential telomere functions. This study establishes the similarity of telomere organization in fission yeast and humans

A New Extension of Chubanov's Method to Symmetric Cones

We propose a new variant of Chubanov's method for solving the feasibility problem over the symmetric cone by extending Roos's method (2018) of solving the feasibility problem over the nonnegative orthant. The proposed method considers a feasibility problem associated with a norm induced by the maximum eigenvalue of an element and uses a rescaling focusing on the upper bound for the sum of eigenvalues of any feasible solution to the problem. Its computational bound is (i) equivalent to that of Roos's original method (2018) and superior to that of Louren\c{c}o et al.'s method (2019) when the symmetric cone is the nonnegative orthant, (ii) superior to that of Louren\c{c}o et al.'s method (2019) when the symmetric cone is a Cartesian product of second-order cones, (iii) equivalent to that of Louren\c{c}o et al.'s method (2019) when the symmetric cone is the simple positive semidefinite cone, and (iv) superior to that of Pena and Soheili's method (2017) for any simple symmetric cones under the feasibility assumption of the problem imposed in Pena and Soheili's method (2017). We also conduct numerical experiments that compare the performance of our method with existing methods by generating instances in three types: strongly (but ill-conditioned) feasible instances, weakly feasible instances, and infeasible instances. For any of these instances, the proposed method is rather more efficient than the existing methods in terms of accuracy and execution time.Comment: 44 pages; Department of Policy and Planning Sciences Discussion Paper Series No. 1378, University of Tsukub

Post-Processing with Projection and Rescaling Algorithms for Semidefinite Programming

We propose the algorithm that solves the symmetric cone programs (SCPs) by iteratively calling the projection and rescaling methods the algorithms for solving exceptional cases of SCP. Although our algorithm can solve SCPs by itself, we propose it intending to use it as a post-processing step for interior point methods since it can solve the problems more efficiently by using an approximate optimal (interior feasible) solution. We also conduct numerical experiments to see the numerical performance of the proposed algorithm when used as a post-processing step of the solvers implementing interior point methods, using several instances where the symmetric cone is given by a direct product of positive semidefinite cones. Numerical results show that our algorithm can obtain approximate optimal solutions more accurately than the solvers. When at least one of the primal and dual problems did not have an interior feasible solution, the performance of our algorithm was slightly reduced in terms of optimality. However, our algorithm stably returned more accurate solutions than the solvers when the primal and dual problems had interior feasible solutions.Comment: 78 page

Centering ADMM for the Semidefinite Relaxation of the QAP

We propose a new method for solving the semidefinite (SD) relaxation of the quadratic assignment problem (QAP), called Centering ADMM. Centering ADMM is an alternating direction method of multipliers (ADMM) combining the centering steps used in the interior-point method. The first stage of Centering ADMM updates the iterate so that it approaches the central path by incorporating a barrier function term into the objective function, as in the interior-point method. If the current iterate is sufficiently close to the central path with a sufficiently small value of the barrier parameter, the method switches to the standard version of ADMM. We show that Centering ADMM (not employing a dynamic update of the penalty parameter) has global convergence properties. To observe the effect of the centering steps, we conducted numerical experiments with SD relaxation problems of instances in QAPLIB. The results demonstrate that the centering steps are quite efficient for some classes of instances