Nonlinearity and Temporal Dependence

Nonlinearities in the drift and diffusion coefficients influence temporal dependence in scalar diffusion models. We study this link using two notions of temporal dependence: beta-mixing and rho-mixing. We show that beta-mixing and rho-mixing with exponential decay are essentially equivalent concepts for scalar diffusions. For stationary diffusions that fail to be rho-mixing, we show that they are still beta-mixing except that the decay rates are slower than exponential. For such processes we find transformations of the Markov states that have finite variances but infinite spectral densities at frequency zero. Some have spectral densities that diverge at frequency zero in a manner similar to that of stochastic processes with long memory. Finally we show how nonlinear, state-dependent, Poisson sampling alters the unconditional distribution as well as the temporal dependence.Mixing, Diffusion, Strong dependence, Long memory, Poisson sampling

Nonlinearity and Temporal Dependence

Nonlinearities in the drift and diffusion coefficients influence temporal dependence in scalar diffusion models. We study this link using two notions of temporal dependence: β−mixing and ρ−mixing. Weshow that β−mixing and ρ−mixing with exponential decay are essentially equivalent concepts for scalar diffusions. For stationary diffusions that fail to be ρ−mixing, we show that they are still β−mixing except that the decay rates are slower than exponential. For such processes we find transformations of the Markov states that have finite variances but infinite spectral densities at frequency zero. Some have spectral densities that diverge at frequency zero in a manner similar to that of stochastic processes with long memory. Finally we show how nonlinear, state-dependent, Poisson sampling alters the unconditional distribution as well as the temporal dependence. Les non-linéarités dans les coefficients de mouvement et de diffusion ont une incidence sur la dépendance temporelle dans le cas des modèles de diffusion scalaire. Nous examinons ce lien en recourant à deux notions de dépendance temporelle : mélange β et mélange ρ. Nous démontrons que le mélange β et le mélange ρ avec dégradation exponentielle constituent des concepts fondamentalement équivalents en ce qui a trait aux diffusions scalaires. Pour ce qui est des diffusions stationnaires qui ne se classent pas dans le mélange ρ, nous démontrons quâelles appartiennent quand même au mélange β, sauf que les taux de dégradation sont lents plutôt quâexponentiels. Pour ce genre de processus, nous recourons à des transformations des états de Markov dont les variations sont finies, mais dont les densités spectrales sont infinies à la fréquence zéro. Certains états ont des densités spectrales qui divergent à la fréquence zéro de la même façon que dans le cas des processus stochastiques à mémoire longue. En terminant, nous indiquons la façon dont lâéchantillonnage de Poisson qui est non linéaire et dépendant de lâétat modifie la distribution inconditionnelle et la dépendance temporelle.Mixing, Diffusion, Strong dependence, Long memory, Poisson sampling., mélange, diffusion, forte dépendance, mémoire longue, échantillonnage de Poisson.

Nonlinearity and Temporal Dependence

Nonlinearities in the drift and diffusion coefficients influence temporal dependence in diffusion models. We study this link using three measures of temporal dependence: rho-mixing, beta-mixing and alpha-mixing. Stationary diffusions that are rho-mixing have mixing coefficients that decay exponentially to zero. When they fail to be rho-mixing, they are still beta-mixing and alpha-mixing; but coefficient decay is slower than exponential. For such processes we find transformations of the Markov states that have finite variances but infinite spectral densities at frequency zero. The resulting spectral densities behave like those of stochastic processes with long memory. Finally we show how state-dependent, Poisson sampling alters the temporal dependence.Diffusion, Strong dependence, Long memory, Poisson sampling, Quadratic forms

Principal Components and Long Run Implications of Multivariate Diffusions

We investigate a method for extracting nonlinear principal components. These principal components maximize variation subject to smoothness and orthogonality constraints; but we allow for a general class of constraints and multivariate densities, including densities without compact support and even densities with algebraic tails. We provide primitive sufficient conditions for the existence of these principal components. We characterize the limiting behavior of the associated eigenvalues, the objects used to quantify the incremental importance of the principal components. By exploiting the theory of continuous-time, reversible Markov processes, we give a different interpretation of the principal components and the smoothness constraints. When the diffusion matrix is used to enforce smoothness, the principal components maximize long-run variation relative to the overall variation subject to orthogonality constraints. Moreover, the principal components behave as scalar autoregressions with heteroskedastic innovations; this supports semiparametric identification of a multivariate reversible diffusion process and tests of the overidentifying restrictions implied by such a process from low frequency data. We also explore implications for stationary, possibly non-reversible diffusion processes

Nonlinearity and Temporal Dependence

Nonlinearities in the drift and diffusion coefficients influence temporal dependence in scalar diffusion models. We study this link using two notions of temporal dependence: beta-mixing and rho-mixing. We show that beta-mixing and rho-mixing with exponential decay are essentially equivalent concepts for scalar diffusions. For stationary diffusions that fail to be rho-mixing, we show that they are still beta-mixing except that the decay rates are slower than exponential. For such processes we find transformations of the Markov states that have finite variances but infinite spectral densities at frequency zero. Some have spectral densities that diverge at frequency zero in a manner similar to that of stochastic processes with long memory. Finally we show how nonlinear, state-dependent, Poisson sampling alters the unconditional distribution as well as the temporal dependence

Robust Identification of Investor Beliefs

This paper develops a new method informed by data and models to recover information about investor beliefs. Our approach uses information embedded in forward-looking asset prices in conjunction with asset pricing models. We step back from presuming rational expectations and entertain potential belief distortions bounded by a statistical measure of discrepancy. Additionally, our method allows for the direct use of sparse survey evidence to make these bounds more informative. Within our framework, market-implied beliefs may differ from those implied by rational expectations due to behavioral/psychological biases of investors, ambiguity aversion, or omitted permanent components to valuation. Formally, we represent evidence about investor beliefs using a novel nonlinear expectation function deduced using model-implied moment conditions and bounds on statistical divergence. We illustrate our method with a prototypical example from macro-finance using asset market data to infer belief restrictions for macroeconomic growth rates

Ultra-low-velocity anomaly inside the Pacific Slab near the 410-km discontinuity

The upper boundary of the mantle transition zone, known as the “410-km discontinuity”, is attributed to the phase transformation of the mineral olivine (α) to wadsleyite (β olivine). Here we present observations of triplicated P-waves from dense seismic arrays that constrain the structure of the subducting Pacific slab near the 410-km discontinuity beneath the northern Sea of Japan. Our analysis of P-wave travel times and waveforms at periods as short as 2 s indicates the presence of an ultra-low-velocity layer within the cold slab, with a P-wave velocity that is at least ≈20% lower than in the ambient mantle and an apparent thickness of ≈20 km along the wave path. This ultra-low-velocity layer could contain unstable material (e.g., poirierite) with reduced grain size where diffusionless transformations are favored

Sacubitril/valsartan reduces serum uric acid concentration, an independent predictor of adverse outcomes in PARADIGM-HF

Aims: Elevated serum uric acid concentration (SUA) has been associated with an increased risk of cardiovascular disease, but this may be due to unmeasured confounders. We examined the association between SUA and outcomes as well as the effect of sacubitril/valsartan on SUA in patients with heart failure with reduced ejection fraction (HFrEF) in PARADIGM-HF. Methods and results: The association between SUA and the primary composite outcome of cardiovascular death or heart failure (HF) hospitalization, its components, and all-cause mortality was examined using Cox regression analyses among 8213 patients using quintiles (Q1–Q5) of SUA adjusted for baseline prognostic variables including estimated glomerular filtration rate (eGFR), diuretic dose, and log N-terminal pro-brain natriuretic peptide. Change in SUA from baseline over 12 months was also evaluated in each treatment group. Patients in Q5 (SUA ≥8.6 mg/dL) compared with Q1 (<5.4 mg/dL) were younger (62.8 vs. 64.2 years), more often male (88.7% vs. 63.1%), had lower systolic blood pressure (119 vs. 123 mmHg), lower eGFR (57.4 vs. 76.6 mL/min/1.73 m2), and greater diuretic use. Higher SUA was associated with a higher risk of the primary outcome (adjusted hazard ratios) Q5 vs. Q1 = 1.28 [95% confidence intervals (1.09–1.50), P = 0.003], cardiovascular death [1.44 (1.11–1.77), P = 0.001], HF hospitalization [1.37 (1.11–1.70), P = 0.004], and all-cause mortality [1.36 (1.13–1.64), P = 0.001]. Compared with enalapril, sacubitril/valsartan reduced SUA by 0.24 (0.17–0.32) mg/dL over 12 months (P < 0.0001). Sacubitril/valsartan improved outcomes, irrespective of SUA concentration. Conclusion: Serum uric acid concentration was an independent predictor of worse outcomes after multivariable adjustment in patients with HFrEF. Compared with enalapril, sacubitril/valsartan reduced SUA and improved outcomes irrespective of SUA