摘要:

ABSTRACTResults involving correlation properties and parameter estimation for autoregressive‐moving average models with periodic parameters are presented. A multivariate representation of the PARMA model is used to derive parameter space restrictions and difference equations for the periodic autocorrelations. Close approximation to the likelihood function for Gaussian PARMA processes results in efficient maximum‐likelihood estimation procedures. Terms in the Fourier expansion of the parameters are sequentially included, and a selection criterion is given for determining the optimal number of harmonics to be included. Application of the techniques is demonstrated through analysis of a monthly streamflow time ser

ISSN:1093-474X    

DOI:10.1111/j.1752-1688.1985.tb00167.x

出版商:Blackwell Publishing Ltd    

年代:1985

数据来源: WILEY

摘要:

ABSTRACTRecent developments with respect to transfer function‐noise models are reviewed and used to model and forecast quarter‐monthly (i.e., near‐weekly) natural inflows to the Lac St‐Jean reservoir in the Province of Quebec, Canada. The covariate series are rainfall and snowmelt, the latter being a novel derivation from daily rainfall, snowfall and temperature series. It is clearly demonstrated using the residual variance and the Akaike information criterion that modeling is improved as one starts with a deseasonalized ARMA model of the inflow series and successively adds transfer functions for the rainfall and snowmelt series. It is further demonstrated that the transfer function‐noise model is better than a periodic autoregressive model of the inflow series. A split‐sample experiment is used to compare one‐step‐ahead forecasts from this transfer function‐noise model with forecasts from other stochastic models as well as with forecasts from a so‐called conceptual hydrological model (i.e., a model which attempts to mathematically simulate the physical processes involved in the hydrological cycle). It is concluded that the transfer function‐noise model is the preferred model for forecasting the quarter‐monthly La

ISSN:1093-474X    

DOI:10.1111/j.1752-1688.1985.tb00168.x

出版商:Blackwell Publishing Ltd    

年代:1985

数据来源: WILEY

摘要:

ABSTRACTFourier inference is a collection of analytic techniques and philosophic attitudes, for the analysis of data, wherein essential use is made of empirical Fourier transforms. This paper sets down some basic results concerning the finite Fourier transforms of stationary process data and then, to illustrate the approach, uses those results to develop procedures for: 1) estimating cloud and storm motion, 2) passive sonar and 3) fitting finite parameter models to nonGaussian time series via bispectral fitting. This last procedure is illustrated by an analysis of a stretch of Mississippi River runoff data. Examples 1), 2) refer to data having the form Y(xj, yj, t) for j = 1, …, J and t = 0, …, T‐l say, and view that data as part of a realization of a spatial‐temporal process. Such data has become common in geophysics generally and in hydrology particularly. The goal of this paper is to present some new statistical procedures pertinent to problems in the water sciences, equally it is to illustrate the genesis of those procedures and how their properties may be appro

ISSN:1093-474X    

DOI:10.1111/j.1752-1688.1985.tb00169.x

出版商:Blackwell Publishing Ltd    

年代:1985

数据来源: WILEY

摘要:

ABSTRACTStochastic models fitted to hydrologic data of different time scales are interrelated because the higher time scale data (aggregated data) are derived from those of lower time scale. Relationships between the statistical properties and parameters of models of aggregated data and of original data are examined in this paper. It is also shown that the aggregated data can be more accurately predicted by using a valid model of the original data than by using a valid model of the aggregated data. This property is particularly important in forecasting annual values because only a few annual values are usually available and the resulting forecasts are relatively inaccurate if models based only on annual data are used. The relationships and forecasting equations are developed for general aggregation time and can be used for hourly and daily, daily and monthly or monthly and yearly data. The method is illustrated by using monthly and yearly streamflow data. The results indicate that various statistical characteristics and parameters of the model of annual data can be accurately estimated by using the monthly data and forecasts of annual data by using monthly models have smaller one step ahead mean square error than those obtained by using annual data models.

ISSN:1093-474X    

DOI:10.1111/j.1752-1688.1985.tb00170.x

出版商:Blackwell Publishing Ltd    

年代:1985

数据来源: WILEY

摘要:

ABSTRACTA method is presented to assist policy makers in determining the combination of number of sampling stations and number of years of sampling necessary to state with a given probability that a step reduction in atmospheric deposition rates of a given magnitude has occurred at a pre‐specified time. This pre‐specified time would typically be the time at which a sulfate emission control program took effect, and the given magnitude of reduction is some percentage change in deposition rate one might expect to occur as a result of the emission control. In order to determine this probability of detection, a stochastic model of sulfate deposition rates is developed, based on New York State bulk collection network data. The model considers the effect of variation in precipitation, seasonal variations, serial correlation, and site‐to‐site (cross) correlation. A nonparametric statistical test which is well suited to detection of step changes in such multi‐site data sets is developed. It is related to the Mann‐Whitney Rank‐Sum test. The test is used in Monte Carlo simulations along with the stochastic model to derive statistical power functions. These power functions describe the probability of detecting (α=0.05) a step trend in deposition rate as a function of the size of the step‐trend, record length before and after the step‐trend, and the number of stations sampled. The results show that, for an area the size of New York State, very little power is gained by increasing the number of stations beyond about eight. The results allow policy makers to determine the tradeoff between the cost of monitoring and time required to detect a step‐trend of a given magnitude with

ISSN:1093-474X    

DOI:10.1111/j.1752-1688.1985.tb00171.x

出版商:Blackwell Publishing Ltd    

年代:1985

数据来源: WILEY

摘要:

ABSTRACTTo accommodate possible parameter changes in time series at times which are not specified in advance, we propose an adaptive procedure for estimating parameters and for forecasting. The mechanism for activating the adaptive procedure is a successively updated change‐detection statistic. The statistic has small expected value when no change is present and has large value when change takes place ‐ the larger the change, the larger the statistic. The statistic defines discounting factors which determine how much of the past will be used both for estimating parameters and for forecasting. The change‐detection statistic is designed to effect major changes to parameter estimates and to forecasts in a discrete fashion only, as opposed to certain other adaptive procedures that react continuously to perceived fluctuations in data, and so indicate change even when parameters remain fixed. The procedure is illustrated using exponential smoothing and Holt's linear exponential smoothing and is applied to a hydrological s

ISSN:1093-474X    

DOI:10.1111/j.1752-1688.1985.tb00172.x

出版商:Blackwell Publishing Ltd    

年代:1985

数据来源: WILEY

摘要:

ABSTRACTMuch attention has been invested in the model choice problem for peak annual flows, in the context of flood frequency analysis. The authors would sidestep this dilemma through non‐parametric density estimation methodology, but recognize that the standard nonparametric estimators preclude the use of prior information and related data, and furthermore have virtually no tail at all. Here we offer a remedy for these inadequacies by introducing an estimator which mixes parametric and nonparametric density estimates. We prove that our mixture rule is consistent. By this procedure, we do allow incorporation of prior information, experience, and regional data information, but nevertheless provide a safeguard against incorrect model choic

ISSN:1093-474X    

DOI:10.1111/j.1752-1688.1985.tb00173.x

出版商:Blackwell Publishing Ltd    

年代:1985

数据来源: WILEY

摘要:

ABSTRACTBayesian Processor of Forecasts (BPF) combines a prior distribution, which describes the natural uncertainty about the realization of a hydrologic process, with a likelihood function, which describes the uncertainty in categorical forecasts of that process, and outputs a posterior distribution of the process, conditional upon the forecasts. The posterior distribution provides a means of incorporating uncertain forecasts into optimal decision models. We present fundamentals of building BPF for time series. They include a general formulation, stochastic independence assumptions and their interpretation, computationally tractable models for forecasts of an independent process and a first‐order Markov process, and parametric representations for normal‐linear processes. An example is shown of an application to the annual time series of seasonal snowmelt runoff volume foreca

ISSN:1093-474X    

DOI:10.1111/j.1752-1688.1985.tb00174.x

出版商:Blackwell Publishing Ltd    

年代:1985

数据来源: WILEY

摘要:

ABSTRACTAn important class of models, frequently used in hydrology for the forecasting of hydrologic variables one or more time periods ahead, or for the generation of synthetic data sequences, is the class of autoregressive(AR) models. As the AR models belong to the family of linear stochastic difference equations, they have both a deterministic and a stochastic component. The stochastic component is often assumed to have a Gaussian distribution. It is well known that hydrologic observations (e.g., stream flows) are heavily affected by noise. To account explicitly for the observation noise, the linear stochastic difference equation is expressed in state variable form and an observation model is introduced. The discrete Kalman filter algorithm can then be used to obtain estimates of the state variable vector. Typically, in hydrologic systems, model parameters, system noise statistics and measurement noise statistics are unknown, and have to be estimated. In this study an adaptive algorithm is discussed which estimates these quantities simultaneously with the state variables. The performance of the algorithm is evaluated by using simulated data.

ISSN:1093-474X    

DOI:10.1111/j.1752-1688.1985.tb00175.x

出版商:Blackwell Publishing Ltd    

年代:1985

数据来源: WILEY

摘要:

ABSTRACTResults are reported from an application of the state space formulation and the Kalman filter to real‐time forecasting of daily river flows. It is shown that the application of filtering techniques improves the overall forecasting performance of the model. As is true for most hydrologic systems, the model is not completely known. Therefore, the procedures pertaining to on‐line parameter and noise statistics estimation, as presented in the first paper, are implemented. The example in this paper shows that these techniques also perform satisfactorily when applied to a real‐world situ

ISSN:1093-474X    

DOI:10.1111/j.1752-1688.1985.tb00176.x

出版商:Blackwell Publishing Ltd    

年代:1985

数据来源: WILEY