Autoregressive Stochastic Model Research Articles

Exact finite-dimensional filters for doubly stochastic auto-regressive processes

In this paper, we derive exact finite-dimensional recursive filters for a class of doubly stochastic auto-regressive (AR) models. We assume that the parameters of the doubly stochastic AR process vary according to a nonlinear polynomial function of a Gaussian state-space process. Apart from being of mathematical interest, these finite-dimensional filters have potential applications in time-series analysis and image-enhanced tracking of maneuvering targets.

GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study

We examine alternative generalized method of moments procedures for estimation of a stochastic autoregressive volatility model by Monte Carlo methods. We document the existence of a tradeoff between the number of moments, or information, included in estimation and the quality, or precision, of the objective function used for estimation. Furthermore, an approximation to the optimal weighting matrix is used to explore the impact of the weighting matrix for estimation, specification testing, and inference procedures. The results provide guidelines that help achieve desirable small-sample properties in settings characterized by strong conditional heteroscedasticity and correlation among the moments.

Data-dependent-systems and Fourier-transform methods for single-interferogram analysis

Results of wave-front phase detection obtained from a spatial method based on data-dependent-systems (DDS) methodology are compared with those obtained from the Fourier-transform method. DDS is a novel approach that extends and improves the way the stochastic autoregressive moving-average models are obtained and interpreted. The methodology is robust to noise influence and insensitive to the errors commonly associated with the Fourier transform. Both the Fourier-transform and the DDS methods use one interference pattern, and both offer means for filtering out disturbances such as noise and background variations. We present a brief review of the two methods to compare them theoretically, and then we describe their experimental implementation. The methods were applied to the same interferometric data sets, and the results are presented and compared to discuss relative advantages and disadvantages. In particular, it is shown that the DDS method preserves the detailed surface texture because a convolution of the component that represents the surface dynamic aspect with the component that corresponds to the independent and dynamic-free aspect is able to recover the original details. In contrast the Fourier-transform method smooths such details to an extent that depends on the subjective choice of filters.

Stochastic analysis and generation of synthetic sequences of daily global solar irradiation: Rabat site (Morocco)

A study of the stationary and sequential properties of daily global horizontal solar radiation is presented for Rabat (Morocco). The results from this analysis are essential for the analytic modelling of the long term performance of solar energy systems, and for the generation of synthetic daily solar radiation sequences. The only climatic information required is the monthly average of the clearness index. We show that the experimental data can be described by a linear auto-regressive stochastic model of first or second order, and that the probability density function PDF can be fitted by a simple, easy to calculate functional form. We also show that, by using this function, the clearness index sequences can be transformed into sequences with normal distribution but with the same auto-correlation properties. It becomes, then, easy to construct synthetic sequences of solar irradiation with the same statistical properties as the real data. These synthetic sequences are very useful for performance prediction of solar energy systems.

Discrete variable stochastic approximation procedures and recursive autoregressive model identification

Two stochastic approximation procedures are proposed for finding a point attaining the maximum of a regression function defined and observable only at points on a set of discrete variables. The asymptotic convergence property of the procedures is discussed using the theorem of almost supermartingales. The procedures are applied to the recursive identification of autoregressive time series models. The identification procedure consists of a recursive order estimation stage and a recursive autoregressive parameter updating stage, and gives the true autoregressive model or the best autoregressive approximation model.

Forecasting sales response for multiple time horizons and temporally aggregated data: A comparison of constant and stochastic coefficient models

Past research on time-varying sales-response models emphasized the application of different estimation techniques in examining variation in advertising effectiveness over time. This study focuses on comparing sales forecasts using constant and stochastic coefficients sales-response models. Selected constant and stochastic coefficient models are applied to six sets of bimonthly and one set of annual advertising and sales data to assess forecasting accuracy for time horizons of various lengths. Results show improved forecasting accuracy for a first-order autoregressive stochastic coefficient model, particularly in short-run forecasting applications.

Multivariate Weekly Streamflow Forecasting Model

In the operation of a reservoir system, it is of interest to know an estimate of the confidence interval of the future inflow volumes for each reservoir. In this paper, the one-step ahead forecasts of weekly inflows to each reservoir are obtained through the use of a multivariate autoregressive stochastic model (MAR) which, besides aerial dependency, represents the spatial inflow dependency otructure. The continuous incorporation of measurements favours a recursive estimation procedure for model's parameters. The stochastic model was formulated within the framework of the state-space representation where the state (MAR parameters) is modelled by a simple random walk process to allow for time dependency of parameters. The recursive algorithm employed is the extended Kalman Filter, in which the noise covariance is estimated at each step. The forecast error covariance matrix is used to built the confidence regions for inflows. A case study with a South Brazilian reservoir system for hydropower production is presented. The order of the MAR model was chosen based on performance indexes related to the forecast error obtained within the historical data. The comparison between the MAR model and the best univariate fit to each site series indicates that the multivariate scheme produces forecasts similar to the univariate ones, besides providing multivariate confidence regions for the future inflows.

Periodicity of Extinctions in the Geologic Past: Deterministic Versus Stochastic Explanations

The temporal spacing and the magnitude of major extinctions over the past 250 and 570 million years, based on the use of different metrics of extinction probability, are analyzed by comparing deterministic and stochastic explanations. The best-fitting time series model is a stochastic autoregressive model that displays a pseudoperiodic behavior with a cycle length of 31 million years for the past 250 million years, regardless of the metric of extinction probability. The periodicity lengthens and weakens when the analysis is extended to the entire Phanerozoic. The history of the probability of extinction for the entire Phanerozoic, based on time series analysis, does not support the reported bipartite distribution of Van Valen. Rather, the probability of extinction has decreased uniformly over Phanerozoic time whereas the inertia or stability of the biotic system after the Late Permian crisis has increased.

A study for improving precipitation occurrences modelling with a Markov chain

Daily precipitation occurrences and their monthly wet-days' sums of precipitation-measuring stations in Greece are modelled with a Markov chain. The order of the chain is taken to be seasonally varying in accordance with the precipitation station's meteorological conditions and geographical location. The modelling efficiency of the Markov chain is significantly improved when it is conjunctively used with a second-order autoregressive stochastic model fitted on the monthly wet-days' sums.

The Study on a Statistical Optimal Control of Ship's Motion (Part 1)

The author proposed the entirely new ship's autopilot system using a stochastic autoregressive model (AR autopilot) and corroborated that the system worked well in the actual sea test by a small training ship (about 310 g. ton). Many sea tests of the AR autopilot has been carried out by the same ship since the first trial.Emphasis of the tests was put on (1) the effects that the change of gains gives to the course keeping quality, (2) the robustness to the change of the disturbance, (3) the method to eliminate the offset from the desired course and so on.In this paper, the author analysed in detail the results gained at the above sea tests from the view points of the course keeping quality of the AR autopilot.

Non-linear stochastic models for seismic events with applications in event identification

A special class of pth-order autoregressive stochastic models is proposed for seismic records of explosions and earthquakes. These models are based on deterministic formulations proposed by Haskell, Von Seggern & Blandford and Aki. Statistical properties of the estimation procedure are derived and the model applied to seismic records of P waves. The method is shown to have applications in depth and reflection parameter estimation and in event discrimination.

Statistical Identification of Ship's Course Keeping Motion and Optimal Control

In the former paper, the authors proposed an entirely new autopilot system using a stochastic autoregressive model. According to the model fitting procedure, we could design flexibly an optimal controller under an appropriate evaluation function.In this paper, the experimental results that an on-line direct digital control using the model fitting procedure was applied to an actual ship are reported. For the sake of it, in chapter 2 and 3, the theory proposed in the former paper is outlined. In chapter 4, the hard and software developed for the realization of the on-line controlling of the ship are introduced. In subsequent chapters, the plan and the method of the actual sea tests are described and the results of the on-line direct digital controlling of the actual ship's course keeping motion are scrutinized.The new concept used in this paper for identification of system through the autoregressive model, the AIC (Akaike's Information Criterion) proposed by Dr. Akaike is discussed briefly in Appendix.

Stochastic modelling and forecast of the dosage area product

A case of pollution emission and monitoring in an area of northern Italy is considered in this paper. Specifically, air pollution is due to a point source of SO 2 (a power plant) while SO 2 ground concentration measurements are supplied by a network of 23 stations. The paper deals with the evaluation and stochastic modelling of an overall pollution index for the region of interest, namely the integral of the daily dosage over the region (dosage area product or DAP). The determination of the DAP from the point measurements is carried out by a simple least squares technique which gives a satisfactory interpolation of the recorded data. In particular, the family of curves used for interpolation is well suited to the distribution of the measurement network, in turn due to the conspicuous non-uniform distribution of the wind direction, a typical situation in the Po Valley area. The statistical characteristics of the DAP time series are analysed and a stationary autoregressive stochastic model is proposed in order to describe the fluctuations of the series. Moreover, a one step predictor, namely a recursive relationship allowing tomorrow's DAP to be forecast from data up to today, is determined. Finally, in order to improve the prediction, another stochastic model, which takes also gross meteorological information into account, is discussed.