Search Results (10)

Multivariate space–time datasets are often collected at discrete, regularly monitored time intervals and are typically treated as components of time series in environmental science and other applied fields. To effectively characterize such data in geostatistical frameworks, valid and practical covariance models are essential. In this work, we propose several classes of multivariate spatio-temporal covariance matrix functions to model underlying stochastic processes whose discrete temporal margins correspond to well-known autoregressive and moving average (ARMA) models. We derive sufficient and/or necessary conditions under which these functions yield valid covariance matrices. By leveraging established methodologies from time series analysis and spatial statistics, the proposed models are straightforward to identify and fit in practice. Finally, we demonstrate the utility of these multivariate covariance functions through an application to Kansas weather data, using co-kriging for prediction and comparing the results to those obtained from traditional spatio-temporal models. Full article

This research focuses on the study of stochastic processes with irregularly spaced time intervals, which is present in a wide range of fields such as climatology, astronomy, medicine, and economics. Some studies have proposed irregular autoregressive (iAR) and moving average (iMA) models separately, and moving average autoregressive processes (iARMA) for positive autoregressions. The objective of this work is to generalize the iARMA model to include negative correlations. A first-order moving average autoregressive model for irregular discrete time series is presented, being an ergodic and strictly stationary Gaussian process. Parameter estimation is performed by Maximum Likelihood, and its performances are evaluated for finite samples through Monte Carlo simulations. The estimation of the autocorrelation function (ACF) is performed using the DCF (Discrete Correlation Function) estimator, evaluating its performance by varying the sample size and average time interval. The model was implemented on real data from two different contexts; the first one consists of the two-week measurement of star flares of the Orion Nebula in the development of the COUP and the second pertains to the measurement of sunspot cycles from 1860 to 1990 and their relationship to temperature variation in the northern hemisphere. Full article

In this paper, a hybrid of a Wavelet Decomposition–Generalised Auto-Regressive Conditional Heteroscedasticity–Extreme Value Theory (WD-ARMA-GARCH-EVT) model is applied to estimate the Value at Risk (VaR) of BitCoin (BTC/USD) and the South African Rand (ZAR/USD). The aim is to measure and compare the riskiness of the two currencies. New and improved estimation techniques for VaR have been suggested in the last decade in the aftermath of the global financial crisis of 2008. This paper aims to provide an improved alternative to the already existing statistical tools in estimating a currency VaR empirically. Maximal Overlap Discrete Wavelet Transform (MODWT) and two mother wavelet filters on the returns series are considered in this paper, viz., the Haar and Daubechies (d4). The findings show that BitCoin/USD is riskier than ZAR/USD since it has a higher VaR per unit invested in each currency. At the 99% significance level, BitCoin/USD has average values of VaR of 2.71% and 4.98% for the WD-ARMA-GARCH-GPD and WD-ARMA-GARCH-GEVD models, respectively; and this is slightly higher than the respective 2.69% and 3.59% for the ZAR/USD. The average BitCoin/USD returns of 0.001990 are higher than ZAR/USD returns of −0.000125. These findings are consistent with the mean-variance portfolio theory, which suggests a higher yield for riskier assets. Based on the p-values of the Kupiec likelihood ratio test, the hybrid model adequacy is largely accepted, as p-values are greater than 0.05, except for the WD-ARMA-GARCH-GEVD models at a 99% significance level for both currencies. The findings are helpful to financial risk practitioners and forex traders in formulating their diversification and hedging strategies and ascertaining the risk-adjusted capital requirement to be set aside as a cushion in the event of the occurrence of an actual loss. Full article

The equivalence of continuous-/discrete-time autoregressive-moving average (ARMA) systems is considered in this paper. For the integer-order cases, the interrelations between systems defined by continuous-time (CT) differential and discrete-time (DT) difference equations are found, leading to formulae relating partial fractions of the continuous and discrete transfer functions. Simple transformations are presented to allow interconversions between both systems, recovering formulae obtained with the impulse invariant method. These transformations are also used to formulate a covariance equivalence. The spectral correspondence implied by the bilinear (Tustin) transformation is used to study the equivalence between the two types of systems. The general fractional CT/DT ARMA systems are also studied by considering two DT differential fractional autoregressive-moving average (FARMA) systems based on the nabla/delta and bilinear derivatives. The interrelations CT/DT are also considered, paying special attention to the systems defined by the bilinear derivatives. Full article

Rockslides along a stepped failure surface have characteristics of stepped deformation characteristic and it is difficult to predict the failure time. In this study, the deformation characteristics and disaster prediction model of the Fengning granite rockslide were analyzed based on field surveys and monitoring data. To evaluate the stability, the shear strength parameters of the sliding surface were determined based on the back-propagation neural network and three-dimensional discrete element numerical method. Through the correlation analysis of deformation monitoring results with rainfall and blasting, it is shown that the landslide was triggered by excavation, rainfall, and blasting vibrations. The landslide displacement prediction model was established by using long short-term memory neural network (LSTM) based on the monitoring data, and the prediction results are compared with those using the BP model, SVM model and ARMA model. Results show that the LSTM model has strong advantages and good reliability for the stepped landslide deformation with short-term influence, and the predicted LSTM values were very consistent with the measured values, with a correlation coefficient of 0.977. Combined with the distribution characteristics of joints, the damage influence scope of the landslide was simulated by three-dimensional discrete element, which provides decision-making basis for disaster warning after slope instability. The method proposed in this paper can provide references for early warning and treatment of geological disasters. Full article

For the modeling of categorical time series, both nominal or ordinal time series, an extension of the basic discrete autoregressive moving-average (ARMA) models is proposed. It uses an observation-driven regime-switching mechanism, leading to the family of RS-DARMA models. After having discussed the stochastic properties of RS-DARMA models in general, we focus on the particular case of the first-order RS-DAR model. This RS-DAR $\left(1\right)$ model constitutes a parsimoniously parameterized type of Markov chain, which has an easy-to-interpret data-generating mechanism and may also handle negative forms of serial dependence. Approaches for model fitting are elaborated on, and they are illustrated by two real-data examples: the modeling of a nominal sequence from biology, and of an ordinal time series regarding cloudiness. For future research, one might use the RS-DAR $\left(1\right)$ model for constructing parsimonious advanced models, and one might adapt techniques for smoother regime transitions. Full article

The serial dependence of categorical data is commonly described using Markovian models. Such models are very flexible, but they can suffer from a huge number of parameters if the state space or the model order becomes large. To address the problem of a large number of model parameters, the class of (new) discrete autoregressive moving-average (NDARMA) models has been proposed as a parsimonious alternative to Markov models. However, NDARMA models do not allow any negative model parameters, which might be a severe drawback in practical applications. In particular, this model class cannot capture any negative serial correlation. For the special case of binary data, we propose an extension of the NDARMA model class that allows for negative model parameters, and, hence, autocorrelations leading to the considerably larger and more flexible model class of generalized binary ARMA (gbARMA) processes. We provide stationary conditions, give the stationary solution, and derive stochastic properties of gbARMA processes. For the purely autoregressive case, classical Yule–Walker equations hold that facilitate parameter estimation of gbAR models. Yule–Walker type equations are also derived for gbARMA processes. Full article

Forecasting electricity demand through time series is a tool used by transmission system operators to establish future operating conditions. The accuracy of these forecasts is essential for the precise development of activity. However, the accuracy of the forecasts is enormously subject to the calendar effect. The multiple seasonal Holt–Winters models are widely used due to the great precision and simplicity that they offer. Usually, these models relate this calendar effect to external variables that contribute to modification of their forecasts a posteriori. In this work, a new point of view is presented, where the calendar effect constitutes a built-in part of the Holt–Winters model. In particular, the proposed model incorporates discrete-interval moving seasonalities. Moreover, a clear example of the application of this methodology to situations that are difficult to treat, such as the days of Easter, is presented. The results show that the proposed model performs well, outperforming the regular Holt–Winters model and other methods such as artificial neural networks and Exponential Smoothing State Space Model with Box-Cox Transformation, ARMA Errors, Trend and Seasonal Components (TBATS) methods. Full article

Rainfall prediction is a fundamental process in providing inputs for climate impact studies and hydrological process assessments. Rainfall events are, however, a complicated phenomenon and continues to be a challenge in forecasting. This paper introduces novel hybrid models for monthly rainfall prediction in which we combined two pre-processing methods (Seasonal Decomposition and Discrete Wavelet Transform) and two feed-forward neural networks (Artificial Neural Network and Seasonal Artificial Neural Network). In detail, observed monthly rainfall time series at the Ca Mau hydrological station in Vietnam were decomposed by using the two pre-processing data methods applied to five sub-signals at four levels by wavelet analysis, and three sub-sets by seasonal decomposition. After that, the processed data were used to feed the feed-forward Neural Network (ANN) and Seasonal Artificial Neural Network (SANN) rainfall prediction models. For model evaluations, the anticipated models were compared with the traditional Genetic Algorithm and Simulated Annealing algorithm (GA-SA) supported by Autoregressive Moving Average (ARMA) and Autoregressive Integrated Moving Average (ARIMA). Results showed both the wavelet transform and seasonal decomposition methods combined with the SANN model could satisfactorily simulate non-stationary and non-linear time series-related problems such as rainfall prediction, but wavelet transform along with SANN provided the most accurately predicted monthly rainfall. Full article

To address the static voltage stability issue and suppress the voltage fluctuation caused by the increasing integration of wind farms and solar photovoltaic (PV) power plants, a two-tier reactive power and voltage control strategy based on ARMA power forecasting models for wind and solar plants is proposed in this paper. Firstly, ARMA models are established to forecast the output of wind farms and solar PV plants. Secondly, the discrete equipment is pre-regulated based on the single-step prediction information from ARMA forecasting models according to the optimization result. Thirdly, a multi-objective optimization model is presented and solved by particle swarm optimization (PSO) according to the measured data and the proposed static voltage stability index. Finally, the IEEE14 bus system including a wind farm and solar PV plant is utilized to test the effectiveness of the proposed strategy. The results show that the proposed strategy can suppress voltage fluctuation and improve the static voltage stability under the condition of high penetration of renewables including wind and solar power. Full article