DYNAMIC PROBABILISTIC FORECASTING WITH UNCERTAINTY

2021 ◽  
Author(s):  
FRED ESPEN BENTH ◽  
GLEDA KUTROLLI ◽  
SILVANA STEFANI
Keyword(s):  
Stochastic Processes ◽  
Model Uncertainty ◽  
Empirical Studies ◽  
Probability Density Functions ◽  
Density Functions ◽  
Option Prices ◽  
Probabilistic Forecasting ◽  
New Class ◽  
Probability Densities ◽  
Equity Indices

In this paper, we introduce a dynamical model for the time evolution of probability density functions incorporating uncertainty in the parameters. The uncertainty follows stochastic processes, thereby defining a new class of stochastic processes with values in the space of probability densities. The purpose is to quantify uncertainty that can be used for probabilistic forecasting. Starting from a set of traded prices of equity indices, we do some empirical studies. We apply our dynamic probabilistic forecasting to option pricing, where our proposed notion of model uncertainty reduces to uncertainty on future volatility. A distribution of option prices follows, reflecting the uncertainty on the distribution of the underlying prices. We associate measures of model uncertainty of prices in the sense of Cont.

scholarly journals OPTIMAL CONTROL OF PROBABILITY DENSITY FUNCTIONS OF STOCHASTIC PROCESSES

2010 ◽  
Vol 15 (4) ◽  
pp. 393-407 ◽  
Author(s):  
Mario Annunziato ◽  
Alfio Borzì
Keyword(s):  
Optimal Control ◽  
Stochastic Processes ◽  
Probability Density ◽  
Control Strategy ◽  
Time Windows ◽  
Probability Density Functions ◽  
Density Functions ◽  
Optimal Control Strategy ◽  
Control Laws ◽  
Fokker Planck

A Fokker‐Planck framework for the formulation of an optimal control strategy of stochastic processes is presented. Within this strategy, the control objectives are defined based on the probability density functions of the stochastic processes. The optimal control is obtained as the minimizer of the objective under the constraint given by the Fokker‐Planck model. Representative stochastic processes are considered with different control laws and with the purpose of attaining a final target configuration or tracking a desired trajectory. In this latter case, a receding‐horizon algorithm over a sequence of time windows is implemented.

scholarly journals Weighted Means of Likelihood Ratio as Indices Measuring Similarity Between Densities

2021 ◽  
Author(s):  
Hideyoshi Ko
Keyword(s):  
Numerical Simulations ◽  
Density Estimation ◽  
Likelihood Ratio ◽  
Numerical Optimization ◽  
Probability Density Functions ◽  
Nonparametric Density Estimation ◽  
Short Paper ◽  
Density Functions ◽  
Weighted Means ◽  
Probability Densities

Abstract Criteria for similarity between probability density functions are important in the field of statistics such as density estimation. In this short paper, a set of indices measuring similarity between probability densities is proposed using the weighted means of the likelihood ratio function. Numerical simulations demonstrate that the estimates of these indices are easily obtained from observations and could be useful for both parametric and nonparametric density estimation with numerical optimization.

scholarly journals Monitoring the post-containment COVID-19 crisis in Guadeloupe: Early-warning signals of destabilisation through bootstrapped probability density functions

2020 ◽  
Author(s):  
Meriem ALLALI ◽  
Patrick Portecop ◽  
Michel Carles ◽  
Dominique Gibert
Keyword(s):  
Probability Density ◽  
Early Warning ◽  
Warning Signal ◽  
Probability Density Functions ◽  
Density Functions ◽  
Control Points ◽  
Epidemic Spread ◽  
Data Clusters ◽  
Probability Densities ◽  
Simulated Case

We propose a method to detect early-warning information in relation with subtle changes occurring in the trend of evolution in data time series of the COVID-19 epidemic spread (e.g. daily new cases). The method is simple and easy to implement on laptop computers. It is designed to be able to provide reliable results even with very small amounts of data (i.e. ≈ 10 − 20). The results are given as compact graphics easy to interpret. The data are separated into two subsets: the old data used as control points to statistically define a "trend" and the recent data that are tested to evaluate their conformity with this trend. The trend is characterised by bootstrapping in order to obtain probability density functions of the expected misfit of each data point. The probability densities are used to compute distance matrices where data clusters and outliers are easily visually recognised. In addition to be able to detect very subtle changes in trend, the method is also able to detect outliers. A simulated case is analysed where R0 is slowly augmented (i.e. from 1.5 to 2.0 in 20 days) to pass from a stable damped control of the epidemic spread to an exponentially diverging situation. The method is able to give an early warning signal as soon as the very beginning of the R0 variation. Application to the data of Guadeloupe shows that a small destabilising event occurred in the data near April 30, 2020. This may be due to an increase of R0 ≈ 0.7 around April 13-15, 2020.

OPTIMUM MULTICHANNEL VELOCITY FILTERS

Geophysics ◽  
1968 ◽  
Vol 33 (1) ◽  
pp. 11-35 ◽  
Author(s):  
R. L. Sengbush ◽  
M. R. Foster
Keyword(s):  
Power Spectrum ◽  
Probability Density ◽  
Noise Suppression ◽  
Minimum Mean Square Error ◽  
Probability Density Functions ◽  
Linear Functions ◽  
Density Functions ◽  
Coherent Noise ◽  
Special Cases ◽  
Probability Densities

Optimum systems have been developed to correspond to the sub‐optimum moveout discrimination systems presented previously by several authors. The seismic data on the lth trace is assumed to be additive signal S with moveout [Formula: see text], coherent noise N with moveout [Formula: see text], and incoherent noise [Formula: see text], expressed [Formula: see text] where S, N, and [Formula: see text] are independent, second order stationary random processes and [Formula: see text] and [Formula: see text] are random variables with prescribed probability density functions. The signal estimate S⁁ is produced by filtering each trace with its corresponding filter [Formula: see text] and summing the outputs [Formula: see text] We choose the system of filters [Formula: see text] to make the signal estimate optimum in the Wiener sense (minimum mean‐square error of the signal ensemble). For the special cases discussed, the moveouts are linear functions of the trace number l determined by the moveout/trace τ for signal and [Formula: see text] for noise. Thus, the optimum system is determined by the probability densities of τ and [Formula: see text] together with the noise/signal power spectrum ratios [Formula: see text] and [Formula: see text]. In comparison, suboptimum systems are controlled completely by the cut‐off moveout/trace [Formula: see text]. Events whose moveout/trace falls within [Formula: see text] of the expected dip moveout/trace are accepted, and those falling outside this range are suppressed. Suboptimum systems can be derived from optimum systems by choosing probability densities for τ and [Formula: see text] that are uniform within the above ranges and letting [Formula: see text] be very large. Optimum systems have increased flexibility over suboptimum systems due to control over the probability density functions and the power spectrum ratios and allow increased noise suppression in selected regions of f‐k space.

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