The FOU(p) processes can be considered as an alternative to ARMA (or ARFIMA) processes to model time series. Also, there is no substantial loss when we model a time series using FOU(p) processes with the same lambda, than using differents values of lambda. In this work we propose a new method to estimate the unique value of lambda in a FOU(p) process. Under certain conditions, we will prove consistency and asymptotic normality. We will show that this new method is more easy and fast to compute. By simulations, we show that the new procedure work well and is more efficient than the general method. Also, we include an application to real data, and we show that the new method work well too and outperforms the family of ARMA(p, q).
翻译:FOU(p) 进程可以被视为ARMA(或ARFIMA) 模拟时间序列进程的替代物。 另外,如果我们用同一种羊羔的数值,用FOU(p) 程序模拟一个时间序列,就不会有重大损失。 在这项工作中,我们提出了一个新的方法来估计FOU(p) 进程中羊羔的独特价值。 在某些条件下, 我们将证明一致性和无症状的正常性。 我们将显示这一新的方法比较容易和快速地进行计算。 通过模拟, 我们显示新程序运作良好, 并且比一般方法效率更高。 此外, 我们还包括了对真实数据的应用程序, 我们显示新方法也运作良好, 并且超越了ARMA(p, q) 的家族 。