No abstract

We consider the problem of the annual mean temperature prediction. The years taken into account and the corresponding annual mean temperatures are denoted by 0, . . . , n and t 0 , . . ., t n , respectively. We propose to predict the temperature t n+1 using the data t 0 , . . ., t n . For each 0 ≤ l ≤ n and each parametrization Θ (l) of the Euclidean space R l+1 we construct a list of weights for the data {t 0 , . . . , t l } based on the rows of Θ (l) which are correlated with the constant trend. Using these weights we define a list of predictors of t l+1 from the data t 0 , . . ., t l . We analyse how the parametrization affects the prediction, and provide three optimality criteria for the selection of weights and parametrization. We illustrate our results for the annual mean temperature of France and Morocco.

We study the problem of parameter estimation for a non-ergodic Gaussian Vasicektype model defined as dX t = (µ+θX t )dt+dG t , t ≥ 0 with unknown parameters θ > 0 and µ ∈ R, where G is a Gaussian process. We provide least square-type estimators θ T and µ T respectively for the drift parameters θ and µ based on continuous-time observations {X t , t ∈ [0, T ]} as T → ∞. Our aim is to derive some sufficient conditions on the driving Gaussian process G in order to ensure that θ T and µ T are strongly consistent, the limit distribution of θ T is a Cauchy-type distribution and µ T is asymptotically normal. We apply our result to fractional Vasicek, subfractional Vasicek and bifractional Vasicek processes. In addition, this work extends the result of [13] studied in the case where µ = 0.