A State Space Approach to Estimating the Integrated Variance and Microstructure Noise Component

We call the realized variance (RV) calculated with observed prices contaminated by microstructure noises (MNs) the noise-contaminated RV (NCRV) and refer to the component in the NCRV associated with the MNs as the MN component. This paper develops a method for estimating the integrated variance (IV) and MN component simultaneously, extending the state space method proposed by Barndorff-Nielsen and Shephard (2002). Our extension is based on the result obtained in Meddahi (2003), namely, when the true log-price process follows a general class of continuous-time stochastic volatility (SV) models, the IV follows an ARMA process. We represent the NCRV by a state space form and show that the state space form parameters are not identifiable; however, they can be expressed as functions of fewer identifiable parameters. We illustrate how to estimate these parameters. The proposed method is applied to yen/dollar exchange rate data. We find that the magnitude of the MN component is, on average, about 21%-48 % of the NCRV, depending on the sampling frequency.Realized Variance, Integrated Variance, Microstructure Noise

Pseudogap phenomenon in an ultracold Fermi gas with a p-wave pairing interaction

We investigate single-particle properties of a one-component Fermi gas with a tunable p-wave interaction. Including pairing fluctuations associated with this anisotropic interaction within a $T$-matrix theory, we calculate the single-particle density of states, as well as the spectral weight, above the superfluid transition temperature $T_{\rm c}$. Starting from the weak-coupling regime, we show that the so-called pseudogap first develops in these quantities with increasing the interaction strength. However, when the interaction becomes strong to some extent, the pseudogap becomes obscure to eventually disappear in the strong-coupling regime. This non-monotonic interaction dependence is quite different from the case of an s-wave interaction, where the pseudogap simply develops with increasing the interaction strength. The difference between the two cases is shown to originate from the momentum dependence of the p-wave interaction, which vanishes in the low momentum limit. We also identify the pseudogap regime in the phase diagram with respect to the temperature and the p-wave interaction strength. Since the pseudogap is a precursor phenomenon of the superfluid phase transition, our results would be useful for the research toward the realization of p-wave superfluid Fermi gases.Comment: 21 pages, 9 figure

Volume and heat kernel fluctuations for the three-dimensional uniform spanning tree

Let $\mathcal{U}$ be the uniform spanning tree on $\mathbb{Z}^{3}$. We show the occurrence of log-logarithmic fluctuations around the leading order for the volume of intrinsic balls in $\mathcal{U}$. As an application, we obtain similar fluctuations for the quenched heat kernel of the simple random walk on $\mathcal{U}$.Comment: 39 pages, 20 figure

A State Space Approach to Estimating the Integrated Variance under the Existence of Market Microstructure Noise

We call the realized variance (RV), calculated with observed prices contaminated by (market) microstructure noises (MNs), the noise-contaminated RV (NCRV), and refer to the bias component in the NCRV, associated with the MNs, as the MN component. This paper develops a state space method for estimating the integrated variance (IV) and MN component. We represent the NCRV by a state space form and show that the state space form parameters are not identifiable, however, they can be expressed as functions of identifiable parameters. We illustrate how to estimate these parameters. We apply the proposed method to yen/dollar exchange rate data, where we find that most of the variation in NCRV is of the MN component. The proposed method also serves as a convenient way for estimating a general class of continuous-time stochastic volatility (SV) models under the existence of MN.Realized Variance, Integrated Variance, Microstructure Noise, State Space, Identification, Exchange Rate

A State Space Approach to Estimating the Integrated Variance under the Existence of Market Microstructure Noise

Abstract We call the realized variance (RV) calculated with observed prices contaminated by (market) microstructure noises (MNs) the noise-contaminated RV (NCRV), referring to the bias component in the NCRV associated with the MNs as the MN component. This paper develops a state space method for estimating the integrated variance (IV) and MN component. We represent the NCRV by a state space form and show that the state space form parameters are not identifiable, however, they can be expressed as functions of identifiable parameters. We illustrate how to estimate these parameters. The proposed method also serves as a convenient way for estimating a general class of continuous-time stochastic volatility (SV) models under the existence of MN. We apply the proposed method to yen/dollar exchange rate data, where we find that most of the variation in NCRV is of the MN component.Realized Variance, Integrated Variance, Microstructure Noise, State Space, Identification, Exchange Rate

iGlarLixi reduces residual hyperglycemia in Japanese patients with type 2 diabetes uncontrolled on basal insulin: A post‐hoc analysis of the LixiLan JP‐L trial

IntroductionTreatments for type 2 diabetes targeting baseline glucose levels but not postprandial glucose can result in normalized fasting blood glucose but suboptimal overall glycemic control (high glycated hemoglobin): residual hyperglycemia. In Japanese patients with type 2 diabetes the predominant pathophysiology is a lower insulin secretory capacity, and residual hyperglycemia is common with basal insulin treatment. Single-injection, fixed-ratio combinations of glucagon-like peptide-1 receptor agonists and basal insulin have been developed. iGlarLixi (insulin glargine 100 units/mL [iGlar]: lixisenatide ratio of 1 unit:1 µg) is for specific use in Japan. Post-hoc analysis of the LixiLan JP-L trial (NCT02752412) compared the effect of iGlarLixi with iGlar on this specific subpopulation with residual hyperglycemia.Materials and MethodsOutcomes at week 26 (based on the last observation carried forward) were assessed in patients in the modified intent-to-treat population with baseline residual hyperglycemia.ResultsOverall, 83 (32.5%) patients in the iGlarLixi group and 79 (30.7%) patients in the iGlar group had baseline residual hyperglycemia. The proportion of patients with residual hyperglycemia at week 26 decreased to 15.7% in the iGlarLixi group, and increased to 36.9% in the iGlar group. Patients in the iGlarLixi group had significantly greater reductions in glycated hemoglobin compared with the iGlar group (−0.72% difference between groups; P < 0.0001).ConclusionsNew data from this post-hoc analysis of the JP-L trial show that treatment with the fixed-ratio combination iGlarLixi reduced the proportion of Japanese patients with residual hyperglycemia from baseline to week 26 and significantly reduced glycated hemoglobin vs similar doses of iGlar alone