Weather modelling using a multivariate latent Gaussian model

We propose a vector auto-regressive moving average process as a model for daily weather data. For the rainfall variable a monotonic transformation is applied to achieve marginal normality, thus, defining a latent variable, with zero rainfall data corresponding to censored values below a threshold. Methodology is presented for model identification, estimation and validation, illustrated using data from Mylnefield, Scotland. The new model, a vector second-order auto-regressive first-order moving average (VARMA(2,1)) process, fits the data better, and produces more realistic simulated series than, existing models of Richardson [Water Resources Res. 17 (1981) 182] and Peiris and McNicol [Agric. Forest Meteorol. 79 (1996) 219].