A notable Gamma‐Lindley first‐order autoregressive process: An application to hydrological data

Abstract

AbstractA new Gamma‐Lindley (GaL) first‐order autoregressive process (AR) is introduced, called GaL‐AR(1). The distribution for the GaL‐AR(1) innovation process and some of its structural properties are derived, such as the Laplace transform for its bivariate distribution, the conditional variance and expected value, and the spectral and autocorrelation functions. We propose two different estimation procedures whose asymptotic properties are studied by Monte Carlo experiments. An application to actual data from hydrology is performed. Results point out that our process outperforms other six non‐Gaussian AR(1) models that are well defined in the time series literature.