scholarly journals Methods for Estimating Continuous Time Rational Expectations Models From Discrete Time Data

1980 ◽  
Author(s):  
Lars Peter Hansen ◽  
Thomas J. Sargent
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Rational Expectations ◽  
Time Data

Evaluating the accuracy of biodiversity changes through geologic times: from simulation to solution

Paleobiology ◽  
2017 ◽  
Vol 43 (4) ◽  
pp. 667-692 ◽  
Author(s):  
Corentin Gibert ◽  
Gilles Escarguel
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Simple Algorithm ◽  
Time Discretization ◽  
Time Interval ◽  
Taxonomic Richness ◽  
Time Data ◽  
Worst Case ◽  
Data Set ◽  
Reconstructed Signal

AbstractEstimating biodiversity and its variations through geologic time is a notoriously difficult task, due to several taphonomic and methodological effects that make the reconstructed signal potentially distinct from the unknown, original one. Through a simulation approach, we examine the effect of a major, surprisingly still understudied, source of potential disturbance: the effect of time discretization through biochronological construction, which generates spurious coexistences of taxa within discrete time intervals (i.e., biozones), and thus potentially makes continuous- and discrete-time biodiversity curves very different. Focusing on the taxonomic-richness dimension of biodiversity (including estimates of origination and extinction rates), our approach relies on generation of random continuous-time richness curves, which are then time-discretized to estimate the noise generated by this manipulation. A broad spectrum of data-set parameters (including average taxon longevity and biozone duration, total number of taxa, and simulated time interval) is evaluated through sensitivity analysis. We show that the deteriorating effect of time discretization on the richness signal depends highly on such parameters, most particularly on average biozone duration and taxonomic longevity because of their direct relationship with the number of false coexistences generated by time discretization. With several worst-case but realistic parameter combinations (e.g., when relatively short-lived taxa are analyzed in a long-ranging biozone framework), the original and time-discretized richness curves can ultimately show a very weak to zero correlation, making these two time series independent. Based on these simulation results, we propose a simple algorithm allowing the back-transformation of a discrete-time taxonomic-richness data set, as customarily constructed by paleontologists, into a continuous-time data set. We show that the reconstructed richness curve obtained this way fits the original signal much more closely, even when the parameter combination of the original data set is particularly adverse to an effective time-discretized reconstruction.

Gaussian Likelihood of Continuous-Time ARMAX Models When Data Are Stocks and Flows at Different Frequencies

1988 ◽  
Vol 4 (1) ◽  
pp. 108-124 ◽  
Author(s):  
Peter Zadrozny
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Likelihood Function ◽  
Moving Average ◽  
State Space Model ◽  
Likelihood Estimation ◽  
Time Data ◽  
Distributed Lag ◽  
Armax Model ◽  
Stocks And Flows

For purposes of maximum likelihood estimation, we show how to compute the Gaussian likelihood function when the data are generated by a higher-order continuous-time vector ARMAX model and are observed as stocks and flows at different frequencies. Continuous-time ARMAX models are analogous to discrete-time autoregressive moving-average models with distributed-lag exogenous variables. Stocks are variables observed at points in time and flows are variables observed as integrals over sampling intervals. We derive the implied state-space model of the discrete-time data and show how to use it to compute the Gaussian likelihood function with Kalman-filtering, prediction-error, decomposition of the data.

An IV-Scheme for Estimating Continuous-Time Stochastic Models from Discrete-Time Data

1994 ◽  
Vol 27 (8) ◽  
pp. 1561-1566 ◽  
Author(s):  
S. Bigi ◽  
T. Söderström ◽  
B. Carlsson
Keyword(s):  
Discrete Time ◽  
Stochastic Models ◽  
Continuous Time ◽  
Time Data

Least squares parameter estimation of continuous-time ARX models from discrete-time data

1997 ◽  
Vol 42 (5) ◽  
pp. 659-673 ◽  
Author(s):  
T. Soderstrom ◽  
H. Fan ◽  
B. Carlsson ◽  
S. Bigi
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Discrete Time ◽  
Continuous Time ◽  
Time Data
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