The Estimation of Parameters in Systems of Stochastic Differential Equations

Phillips, A. W.

doi:10.1093/biomet/46.1-2.67

Cited by 83 publications

(21 citation statements)

References 0 publications

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“…The fact that (7) and (8) Similar results were earlier established for the special case that coe¢ cients and sampling intervals are constant over time, early references being Bartlett (1946), Walker (1950), Phillips (1959. Then if the initial conditions are at 1, and, say, Y (t) is covariance stationary, (5) and (8) to spatial and spatio-temporal data.…”

Section: X(t)supporting

confidence: 61%

On Discrete Sampling of Time-Varying Continuous-Time Systems

Robinson

2009

Econom. Theory

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We consider a multivariate continuous time process, generated by a system of linear stochastic differential equations, driven by white noise and involving coefficients that possibly vary over time. The process is observable only at discrete, but not necessarily equally-spaced, time points (though equal spacing significantly simplifies matters). Such settings represent partial extensions of ones studied extensively by A.R. Bergstrom. A model for the observed time series is deduced. Initially we focus on a first-order model, but higher-order ones are discussed in case of equally-spaced observations. Some discussion of issues of statistical inference is included.

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Section: X(t)supporting

confidence: 61%

On Discrete Sampling of Time-Varying Continuous-Time Systems

Robinson

2009

Econom. Theory

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“…Others (e.g., GNP or investment) are better approximated as integrals over some fixed period of cal-endar time, such as a month or quarter; that is, they are flows. The estimation of continuous-time autoregressions using equally spaced data on stock variables and (to a lesser extent) flows has received considerable theoretical attention (see Bergstrom 1976Bergstrom , 1983Phadke and Wu 1974;A. W. Phillips 1959;P.…”

Section: Estimationmentioning

confidence: 99%

Estimating Continuous-Time Processes Subject to Time Deformation

Stock

1988

Journal of the American Statistical Association

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A class of time series models is presented in which variables evolve on a data-based rather than calendar time scale. The discrete calendar-time model thus obtained exhibits time-varying parameters and conditional heteroscedasticity. Using a procedure based on the Kalman filter, univariate models are estimated for postwar U.S. real gross national product (GNP) and short-and long-term interest rates. The results indicate significant time scale nonlinearities.

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“…Using results in Phillips (1958) it can be shown that the spectral density of fQ(t), t real} generated by (5.7), is given by:…”

Section: Q(t) (T) -mentioning

confidence: 99%

The Permanent Income Hypothesis Revisited

Christiano¹,

Eichenbaum²,

Marshall³

1987

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This paper investigates whether there are simple versions of the permanent income hypothesis which are consistent with the aggregate U.S. consumption and output data.Our analysis is conducted within the confines of a simple dynamic general equilibrium model of aggregate real output, investment, hours of work and consumption.We study the quantitative importance of two perturbations to the version of our model which predicts that observed consumption follows a random walk: (i) changing the production technology specification which rationalizes the random walk result, and (ii) replacing the assumption that agents' decision intervals coincide with the data sampling interval with the assumption that agents make decisions on a continuous time basis. We find substantially less evidence against the continuous time models than against their discrete time counterparts. In fact neither of the two continuous time models can be rejected at conventional significance levels.The continuous time models outperform their discrete time counterparts primarily because they explicitly account for the fact that the data used to test the models are time averaged measures of the underlying unobserved point-in-time variables.The net result is that they are better able to accommodate the degree of serial correlation present in the first difference of observed per capita U.S. consumption.

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The Estimation of Parameters in Systems of Stochastic Differential Equations

Cited by 83 publications

References 0 publications

On Discrete Sampling of Time-Varying Continuous-Time Systems

On Discrete Sampling of Time-Varying Continuous-Time Systems

Estimating Continuous-Time Processes Subject to Time Deformation

The Permanent Income Hypothesis Revisited

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