We investigate the estimation of parameters in the random coefficient autoregressive model Xk = (φ+ bk)Xk−1 + ek, where (φ,ω 2, σ2) is the parameter of the process, Eb0 = ω2, Ee0 = σ 2. We consider a nonstationary RCA process satisfying E log |φ + b0| ≥ 0 and show that σ2 cannot be estimated by the quasi-maximum likelihood method. The asymptotic normality of the quasi-maximum likelihood estimat...

Maximum autoregressive processes like MARMA (Davis and Resnick, [5] 1989) or power MARMA (Ferreira and Canto e Castro, [12] 2008) have singular joint distributions, an unrealistic feature in most applications. To overcome this pitfall, absolute continuous versions were presented in Alpuim and Athayde [2] (1990) and Ferreira and Canto e Castro [14] (2010b), respectively. We consider an extended ...

( ) ( ) ( ) t t / L L e 1 1 e t + − = ρ and 1 Y L − + = t t β α , that is, we investigate the nonlinear least squares estimator. Starting with the simplest case 0 = β , we find that ( ) ( ) ( ) 1 e 1 e t + − = α α ρ / which is just a constant so the estimator that minimizes the error sum of squares must be ( ) ( ) ( ) ρ ρ α ˆ / ˆ ˆ − + = 1 1 ln where ρ̂ is the usual regression estimate of (the c...

A possibly non-stationary autoregressive process, of unknown finite order, with possibly infinite-variance innovations is studied. The Ordinary Least Squares autoregressive parameter estimates are shown to be consistent, and their rate of convergence, which depends on the index of stability, α, is established. We also establish consistency of lag-order selection criteria in the non-stationary c...

In this paper, we study a first order random coefficient autoregressive model with Laplace distribution as marginal. A random coefficient moving average model of order one with Laplace as marginal distribution is introduced and its properties are studied. By combining the two models, we develop a first order random coefficient autoregressive moving average model with Laplace marginal and discus...

Extreme value theories indicate that the range is an efficient estimator of local volatility on a financial asset return. This paper proposes a novel geometric process (GP) framework for range data that nests the well known Conditional Autoregressive Range (CARR) model. We extend the GP model of Lam (1988) to a Conditional Autoregressive Geometric Process Range (CARGPR) model that allows for fl...