The telegraph process X(t), t ≥ 0, (Goldstein, Q J Mech Appl Math 4:129-156, 1951) and the geometric telegraph process S(t) = s0 exp{μ -1/2σ2)t + σ X(t)}with μ a known real constant and σ > 0 a parameter are supposed to be observed at n + 1 equidistant time points t i = iΔ n ,i = 0,1,..., n. For both models λ, the underlying rate of the Poisson process, is a parameter to be estimated. In the geometric case, also σ > 0 has to be estimated. We propose different estimators of the parameters and we investigate their performance under the asymptotics, i.e. Δ n → 0, nΔ n = T < ∞ as n → ∞, with T > 0 fixed. The process X(t) in non markovian, non stationary and not ergodic thus we build a contrast function to derive an estimator. Given the complexity of the equations involved only estimators on the first model can be studied analytically. Therefore, we run an extensive Monte Carlo analysis to study the performance of the proposed estimators also for small sample size n. © 2007 Springer Science+Business Media B.V.
Parametric estimation for the standard and geometric telegraph process observed at discrete times / DE GREGORIO, Alessandro; Stefano Maria, Iacus. - In: STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES. - ISSN 1387-0874. - 11:3(2008), pp. 249-263. [10.1007/s11203-007-9017-9]
Parametric estimation for the standard and geometric telegraph process observed at discrete times
DE GREGORIO, ALESSANDRO;
2008
Abstract
The telegraph process X(t), t ≥ 0, (Goldstein, Q J Mech Appl Math 4:129-156, 1951) and the geometric telegraph process S(t) = s0 exp{μ -1/2σ2)t + σ X(t)}with μ a known real constant and σ > 0 a parameter are supposed to be observed at n + 1 equidistant time points t i = iΔ n ,i = 0,1,..., n. For both models λ, the underlying rate of the Poisson process, is a parameter to be estimated. In the geometric case, also σ > 0 has to be estimated. We propose different estimators of the parameters and we investigate their performance under the asymptotics, i.e. Δ n → 0, nΔ n = T < ∞ as n → ∞, with T > 0 fixed. The process X(t) in non markovian, non stationary and not ergodic thus we build a contrast function to derive an estimator. Given the complexity of the equations involved only estimators on the first model can be studied analytically. Therefore, we run an extensive Monte Carlo analysis to study the performance of the proposed estimators also for small sample size n. © 2007 Springer Science+Business Media B.V.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.