Global Positioning System (GPS) stations located along coastal areas have the ability to measure tide gauge (TG) records by reflected signal reception from the sea water surface. In this study we used the GPS signal-to-noise ratio (SNR) data from the SEPT station (44.63 ⁰N, 124.05 ⁰W) located at South Beach, Oregon, USA, to estimate the TG records using only a few measurements. First, we derived the TG record from a GPS station (GPS-TG) and used traditional TG data from the National Water Level Observation Network (NWLON) sentinel station (Station ID: 9435380) located in Oregon for validation purposes because it was closest to the SEPT station. Our results show that the GPS-TG and NWLON-TG correlate well with the correlation coefficient (CC) of 0.942 and the root mean square (RMS) of their residuals was about 12.90 cm. The corresponding TG prediction by autoregressive moving average (ARMA-TG) and singular spectrum analysis (SSA-TG) models are evaluated for their effectiveness over the station. The comparative analysis demonstrates that the GPS-TG has improved correlation with ARMA-TG (CC of ~0.981 CC, RMS of ~4.80 cm), and SSA-TG (CC of ~0.998 CC, RMS of ~ 0.88 cm) compared to the NWLON-TG (CC of ~0.942 CC, RMS of ~12.90 cm) values. We believe the outcomes from this study contribute to a better understanding of the numerical modeling of TG records as well as other measurements based on reflectometry techniques.

This study considers the change-point test problem for time series based on the self-normalization ratio statistic test, which is constructed using residuals obtained from a support vector regression (SVR)-autoregressive moving average (ARMA) model. Under the null hypothesis, the series is a stationary process, and our test statistic converges to a non-degenerate distribution. Under the alternative hypothesis, there are change-points in the time series, and the self-normalization test statistic diverges to infinity. The simulations show that our proposed new test has better finite sample performance than other SVR-based tests in the literature. Finally, we illustrate its usefulness by analyzing two actual data sets.

Differences are introduced as outputs of linear systems called differencers, being considered two classes: shift and scale-invariant. Several types are presented, namely: nabla and delta, bilateral, tempered, bilinear, stretching, and shrinking. Both continuous and discrete-time are described. ARMA type systems based on differencers are introduced and exemplified. In passing, the incorrectness of the usual delta difference is shown.

In this paper we compare the effects of forecasting demand using individual (disaggregated) components versus first aggregating the components either fully or into several clusters. Demand streams are assumed to follow autoregressive moving average (ARMA) processes. Using individual demand streams will always lead to a superior forecast compared to any aggregates, however we show that if several aggregated clusters are formed in a structured manner then these subaggregated clusters will lead to a forecast with minimal increase in mean-squared forecast error. We show this result based on theoretical MSFE obtained directly from the models generating the clusters as well as estimated MSFE obtained directly from simulated demand observations. We suggest a pivot-algorithm, that we call Pivot Clustering, to create these clusters. We also provide theoretical results to investigate sub-aggregation, including for special cases such as, aggregating MA(1) streams and ARMA streams with similar or same parameters.

Conditional heteroskedastic financial time series are commonly modelled by (G)ARCH processes. ARCH(1) and GARCH were recently established in C[0,1] and L^2[0,1]. This article provides sufficient conditions for the existence of strictly stationary solutions, weak dependence and finite moments of (G)ARCH processes for any order in C[0,1] and L^p[0,1]. It deduces explicit asymptotic upper bounds of estimation errors for the shift term, the complete (G)ARCH operators and the projections of ARCH operators on finite-dimensional subspaces. The operator estimaton is based on Yule-Walker equations, and estimating the GARCH operators also involves a result estimating operators in invertible linear processes being valid beyond the scope of (G)ARCH. Moreover, our results regarding (G)ARCH can be transferred to functional AR(MA).

As one of the fastest-growing new energy sources, wind power technology has attracted widespread attention from all over the world. In order to improve the quality of wind power generation, wind speed prediction is an indispensable task. In this paper, an error correction based Variational Mode Decomposition and Broad Learning System (VMD-BLS) hybrid model is proposed for wind speed prediction. First, the wind speed is decomposed into multiple components by the VMD algorithm, and then an ARMA model is established for each component to find the optimal number of sequence divisions. Second, the BLS model is used to predict each component, and the prediction results are summed to obtain the wind speed forecast value. However, in some traditional methods, there is always time lag, which will reduce the forecast accuracy. To deal with this, a novel error correction technique is developed by utilizing BLS. Through verification experiment with actual data, it proves that the proposed method can reduce the phenomenon of prediction lag, and can achieve higher prediction accuracy than traditional approaches, which shows our method’s effectiveness in practice.