Continuous Time Series Models Research Articles

Groundwater system response at sites with different agricultural land uses: case of the Guarani Aquifer outcrop area, Brotas/SP-Brazil

ABSTRACTA system identification approach can be incorporated in groundwater time series analysis, revealing information concerning the local hydrogeological situation. The aim of this work was to analyse water table fluctuations in an outcrop area of the Guarani Aquifer System (GAS) in Brotas/SP, Brazil, using data from a groundwater monitoring network. The water table dynamic was modelled using continuous time series models that reference the hydrogeological system upon which they operate. The model’s climatological inputs of precipitation and evapotranspiration generate impulse response (IR) functions with parameters that can be related to the physical conditions concerning the hydrological processes involved. The interpretation of the model parameters from two sets of monitoring wells selected at different land-use sites is presented, exemplifying the effect of different water table depths and the distance to the nearest drainage location. Systematic trends of water table depths were also identified from model parameters at specific periods and related to plant development, crop harvest and land-use changes.EDITOR D. KoutsoyiannisASSOCIATE EDITOR L. Ruiz

Continuous Time Series Models for Modeling Daily Electricity Prices

This paper aims to provide a unified frame for discussing, summarizing and organizing the main advances in electricity price modeling using the continuous time series modeling approach. This work is organized in three topics: how have been extracted the deterministic patterns present in the daily prices; how have been modeled the stochastic component using mean-reversion models; and how have been modeled the stochastic components using regime-switching models. The review leads to the conclusion that there is no agreement on which are the better approaches, and the analized papers do not discuss how the selected techniques for extracting the deterministic components affect the results of the modeling of the stochastic component. These are important question that must be answered in future research.

A Two-stage Estimation Approach of Continuous-time Series Models with Jumps

In modern financial economics continuous time-series diffusion models are more convenient to deal with than discrete time models when they are used to depict important economic variables such as stock prices, exchange rates and interest rates. A two-stage estimation approach is proposed to deal with the continuous-time models with jumps, in which the initial settings are quite resilient. This paper presents an example: first, the realized volatility theory is applied to the jumps and diffusion parameters of the model; then it uses forward Kolmogorov equation of actual price distribution at steady state to estimate the drift parameters. The model relies little on initial settings and optimization algorithms. The empirical results show that the estimations are stable and reliable. Hence the model is easier to extend to the estimation of complex set continuous time series.

Computer synthesis of three-dimensional surfaces

A new technique for the synthesis of three-dimensional surfaces has been developed. The method is based on the application of the discrete and continuous two-dimensional Fourier transformations associated with the theory of discrete and continuous time series models. This new technique facilitates the synthesis of three-dimensional surfaces with predetermined properties in any number of desired directions.

Continuous Time Series Models for Unequally Spaced Data Applied to Modeling Atomic Clocks

State space representations and Kalman filters used to calculate likelihoods have increased the ease and flexibility of fitting time series models to data. When data are unequally spaced with no underlying basic sampling interval, continuous time series models are more natural than discrete time series models. State space representations still provide the flexibility needed to include a large class of models. This paper gives a survey of state space methods for continuous time processes, discusses extensions to multivariate data at unequally spaced time points with missing data within the observation vector, and gives an example of estimating time and model parameters from an ensemble of atomic clocks.

An instrumental variable method for model order identification

The paper describes a simple instrumental variable method for identifying the structure of a wide class of time-series models. The method is aimed at providing a parametrically efficient (parsimonious) model structure which will lead to a combination of low residual error variance, i.e. a good explanation of the data, and low parametric estimation error variance (as measured by some norm associated with the covariance matrix of the estimation errors). It can be applied to single input-single output and multivariable systems using either discrete or continuous-time series models. It can also function as a recursive (on-line) test for reduction in model order.

Characterization of the formation of base sheet paper using spectral moments determined from time-series models

The fibre distribution in a sheet of paper, referred to as the formation, is largely the result of turbulence, a stochastic process. Continuous time-series models developed from discrete light-transmission profiles are used to characterize formation. The models are used to obtain explicit expressions for the spectral moments of the profiles. From the moments, estimates of two characteristic lengths of the fibre distribution can be obtained and are interpreted as the average and largest flock size. These lengths are used to develop an index for evaluating the formation of four samples of base sheet paper. The results of this characterization agree with other methods, but this technique has the advantage of providing a physical interpretation of the index.

Evaluation of coated abrasive grain geometry and wear via continuous time series models

The coated abrasive profiles are characterized using the second order continuous autoregressive model. Based on a two sided moving average representation of this model, expressions are derived to calculate the geometry (apex angle, base width and orientation) of an average grain. Experimental results and analysis for six new and one worn coated abrasive are presented; and the capability of the grain geometry parameters to quantize wear is discussed.