APPROACHES TO MULTIVARIATE MODELING OF WATER RESOURCES TIME SERIES1

: Alternative approaches suggested for modeling multiseries of water resources systems are reviewed and compared. Most approaches fall within the general framework of multivariate ARMA models. Formal modeling procedures suggest a three-stage iterative process, namely: model identification, parameter estimation and diagnostic checks. Although a number of statistical tools are already available to follow such modeling process, in general, it is not an easy task, especially if high order vector ARMA models are used. However, simpler ARMA models such as the contemporaneous and the transfer-function models may be sufficient for most applications in water resources. Two examples of modeling bivariate and trivariate streamflow series are included. Alternative modeling procedures are used and compared by using data generation techniques. The results obtained suggest that low order models, as well as contemporaneous ARMA models, reproduce quite well the main statistical characteristics of the time series analyzed. It is assumed that the same conclusions apply for most water resources time series.

[1]  G. William Schwert,et al.  Tests for Predictive Relationships between Time Series Variables: A Monte Carlo Investigation , 1982 .

[2]  Larry D. Haugh,et al.  Causality in temporal systems: Characterization and a survey , 1977 .

[3]  R. Srikanthan,et al.  Sequential generation of monthly streamflows , 1978 .

[4]  J. Stedinger,et al.  Multisite ARMA(1,1) and Disaggregation Models for Annual Streamflow Generation , 1985 .

[5]  Ching-Chuong Lin,et al.  A simple test for normality against asymmetric alternatives , 1980 .

[6]  C. Granger.  Investigating Causal Relations by Econometric Models and Cross-Spectral Methods , 1969 .

[7]  J. Geweke,et al.  Measurement of Linear Dependence and Feedback between Multiple Time Series , 1982 .

[8]  Stochastic modelling of long-term persistence in streamflow sequences , 1974 .

[9]  Jery R. Stedinger,et al.  Disaggregation Procedures for Generating Serially Correlated Flow Vectors , 1984 .

[10]  Dennis P. Lettenmaier.  Parameter estimation for multivariate streamflow synthesis , 1980 .

[11]  Larry D. Haugh,et al.  Identification of Dynamic Regression (Distributed Lag) Models Connecting Two Time Series , 1977 .

[12]  J. M. Mejía,et al.  Disaggregation models in hydrology revisited , 1976 .

[13]  J. R. Wallis,et al.  Statistical Properties of Multivariate Fractional Noise Processes , 1971 .

[14]  S. Shapiro,et al.  An Analysis of Variance Test for Normality (Complete Samples) , 1965 .

[15]  G. C. Tiao,et al.  Modeling Multiple Time Series with Applications , 1981 .

[16]  Gwilym M. Jenkins,et al.  SOME ASPECTS OF MODELLING AND FORECASTING MULTIVARIATE TIME SERIES , 1981 .

[17]  Eric F. Wood,et al.  Model identification and parameter estimation for hydrologic input/output models , 1980 .

[18]  Johannes Ledolter,et al.  The analysis of multivariate time series applied to problems in hydrology , 1978 .

[19]  David H. Moreau,et al.  Weekly and monthly flows in synthetic hydrology , 1970 .

[20]  Eric F. Wood,et al.  Parameter estimation of multiple input‐output time series models: Application to rainfall‐runoff processes , 1982 .

[21]  Keith W. Hipel,et al.  Contemporaneous Autoregressive-Moving Average (carma) Modeling in Water Resources , 1985 .

[22]  Multilag multivariate autoregressive model for the generation of operational hydrology , 1972 .

[23]  Streamflow simulation: 3. The broken line process and operational hydrology , 1974 .

[24]  P. Newbold,et al.  Some Recent Developments in Time Series Analysis. III, Correspondent Paper , 1981 .

[25]  A. A. Harms,et al.  An extension to the Thomas‐Fiering Model for the sequential generation of streamflow , 1967 .

[26]  R. Valencia,et al.  Disaggregation processes in stochastic hydrology , 1973 .

[27]  A reconsideration of the Fiering two-station model , 1976 .

[28]  E. Hannan.  The Estimation of the Order of an ARMA Process , 1980 .

[29]  E. Wood,et al.  Identification of multivariate time series and multivariate input‐output models , 1982 .

[30]  David R. Maidment,et al.  Time patterns of water use in six Texas cities , 1984 .

[31]  N. C. Matalas,et al.  Synthetic hydrology based on regional statistical parameters , 1967 .

[32]  Kenneth F. Wallis,et al.  Multiple Time Series Modelling: Another Look at the Mink‐Muskrat Interaction , 1978 .

[33]  John L. Roberts.  Applications of Two Osculatory Formulas , 1937 .

[34]  N. Matalas.  Mathematical assessment of synthetic hydrology , 1967 .

[35]  E. J. Hannan,et al.  Vector linear time series models , 1976, Advances in Applied Probability.

[36]  A. V. Vecchia,et al.  Aggregation and Estimation for Low-Order Periodic ARMA Models , 1983 .

[37]  P. Tao,et al.  Multistation, multiyear synthesis of hydrologic time series by disaggregation , 1976 .

[38]  Comment upon multivariate synthetic hydrology , 1975 .

[39]  D. Krewski.  Jackknifing u-stastics ik finite populations , 1978 .

[40]  K. Wallis.  Multiple Time Series Analysis and the Final Form of Econometric Models , 1977 .

[41]  E. J. Hannan,et al.  Multivariate linear time series models , 1984, Advances in Applied Probability.

[42]  Ezio Todini.  The preservation of skewness in linear disaggregation schemes , 1980 .

[43]  H. Akaike.  A new look at the statistical model identification , 1974 .