The CUSUM statistic of change point under NA sequences

In this paper, we investigate the CUSUM statistic of change point under the negatively associated (NA) sequences. By establishing the consistency estimators for mean and covariance functions respectively, the limit distribution of the CUSUM statistic is proved to be a standard Brownian bridge, which extends the results obtained under the case of an independent normal sample and the moving average processes. Finally, the finite sample properties of the CUSUM statistic are given to show the efficiency of the method by simulation studies and an application on a real data analysis.

SPHARMA approximations for stationary functional time series on the sphere

In this paper, we focus on isotropic and stationary sphere-cross-time random fields. We first introduce the class of spherical functional autoregressive-moving average processes (SPHARMA), which extend in a natural way the spherical functional autoregressions (SPHAR) recently studied in Caponera and Marinucci (Ann Stat 49(1):346–369, 2021) and Caponera et al. (Stoch Process Appl 137:167–199, 2021); more importantly, we then show that SPHAR and SPHARMA processes of sufficiently large order can be exploited to approximate every isotropic and stationary sphere-cross-time random field, thus generalizing to this infinite-dimensional framework some classical results on real-valued stationary processes. Further characterizations in terms of functional spectral representation theorems and Wold-like decompositions are also established.

Seasonal and Annual Probabilistic Forecasting of Water Levels in Large Lakes (Case Study of the Ladoga Lake)

The production functions of water-dependent sectors of the economy can include the water level in the lake as a natural resource. This characteristic must be able to reliably predict for the effective functioning of sectors of the economy. In the article the main attention is paid to the methods of forecasting based on the extrapolation of natural variations of the large lakes water level. As an example, is considered. In this paper, it is assumed that the level varies accordingly to a stochastic multi-cycle process with principal energy-containing zones in frequency bands associated with seasonal and multi-annual variations. Hence, the multi-year monthly and yearly averaged time series are represented by the ARIMA (auto-regression integrated moving average) processes. Forecasts are generated by using of the seasonal ARIMA-models, which take into account not only the seasonal but also the evolution non-stationarity. To compare the forecasts and the actual values, the relative errors are computed. It is shown that implementation of the models mainly allows receiving good and excellent forecasts. Subject Classification Numbers: UDC 556.555.2.06(4)

Complete moment convergence of moving average processes for m-WOD sequence

In this paper, the complete moment convergence for the partial sum of moving average processes $\{X_{n}=\sum_{i=-\infty }^{\infty }a_{i}Y_{i+n},n\geq 1\}$ { X n = ∑ i = − ∞ ∞ a i Y i + n , n ≥ 1 } is established under some mild conditions, where $\{Y_{i},-\infty < i<\infty \}$ { Y i , − ∞ < i < ∞ } is a sequence of m-widely orthant dependent (m-WOD, for short) random variables which is stochastically dominated by a random variable Y, and $\{a_{i},-\infty < i<\infty \}$ { a i , − ∞ < i < ∞ } is an absolutely summable sequence of real numbers. These conclusions promote and improve the corresponding results from m-extended negatively dependent (m-END, for short) sequences to m-WOD sequences.