On the Computation of Optimal Designs for Certain time Series Models with Applications to Optimal Quantile Selection for Location or Scale Parameter Estimation

1982 ◽  
Vol 3 (2) ◽  
pp. 238-249 ◽  
Author(s):  
Randall L. Eubank ◽  
Patricia L. Smith ◽  
Philip W. Smith
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Scale Parameter ◽  
Optimal Designs ◽  
Time Series Models ◽  
Selection For

scholarly journals Breakdown coefficients and scaling properties of rain fields

1998 ◽  
Vol 5 (2) ◽  
pp. 93-104 ◽  
Author(s):  
D. Harris ◽  
M. Menabde ◽  
A. Seed ◽  
G. Austin
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Power Law ◽  
Scale Parameter ◽  
Probability Distributions ◽  
Scaling Analysis ◽  
Scaling Properties ◽  
Power Law Exponent ◽  
Scale Similarity ◽  
Parameter Estimation Techniques

Abstract. The theory of scale similarity and breakdown coefficients is applied here to intermittent rainfall data consisting of time series and spatial rain fields. The probability distributions (pdf) of the logarithm of the breakdown coefficients are the principal descriptor used. Rain fields are distinguished as being either multiscaling or multiaffine depending on whether the pdfs of breakdown coefficients are scale similar or scale dependent, respectively. Parameter  estimation techniques are developed which are applicable to both multiscaling and multiaffine fields. The scale parameter (width), σ, of the pdfs of the log-breakdown coefficients is a measure of the intermittency of a field. For multiaffine fields, this scale parameter is found to increase with scale in a power-law fashion consistent with a bounded-cascade picture of rainfall modelling. The resulting power-law exponent, H, is indicative of the smoothness of the field. Some details of breakdown coefficient analysis are addressed and a theoretical link between this analysis and moment scaling analysis is also presented. Breakdown coefficient properties of cascades are also investigated in the context of parameter estimation for modelling purposes.

Time series analysis and adaptive filtering in hydrology

1984 ◽  
Vol 16 (01) ◽  
pp. 17-18
Author(s):  
J. W. Delleur
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
River Flow ◽  
Time Series Models ◽  
Arma Models ◽  
Multivariate Models ◽  
Varying Coefficients ◽  
Daily Streamflow ◽  
Hydrologic Time Series ◽  
Selection Of

Most time series models in hydrology are used for river flow forecasting, for generation of synthetic data sequences or for the study of physical characteristics underlying the hydrological processes. The models are formulated as linear stochastic difference equations. Three phases are considered for the selection of a model based on a satisfactory representation of a given empirical time series: identification, estimation and validation. Several criteria have been proposed for the selection of the order of ARMA models. The Akaike information criterion (Ale) is popular among hydrologists, but the posterior probability criterion has the advantage of optimality and asymptotic consistency. There are numerous applications of AR or ARMA models to annual streamflow series which are stationary. Seasonal, monthly, weekly or daily streamflow series are cyclically stationary and generally exhibit periodicities in the mean and variance and possibly in the autocorrelation structure. Removal of the periodicity has been accomplished by fitting harmonic series or by subtracting the seasonal mean and dividing by the seasonal standard deviation, and a time series model is then fitted to the residual series. Alternatively, ARMA models with time-varying coefficients are also used. The multiplicative ARlMA model of Box and Jenkins is less frequent in hydrology because of the difficulty in the identification of the parameter structure. Multivariate models are used when river flows at different sites are considered. Parameter estimation in multivariate time series models can become cumbersome because of the dimensionality of the problem. Often the covariance matrix of the noise term is not known in advance and limited information estimates are used. Multivariate models have been used for annual and monthly series. Disaggregation models have been used to subdivide a yearly series into monthly or weekly series or to disaggregate a main river flow into tributary flows while maintaining certain space and time cross-correlations. The aggregation of monthly into yearly time series has been shown to improve the parameter estimation of the yearly series. Hydrologic time series occasionally exhibit changes in level due to natural or man-made causes such as forest fires, volcanic eruption, climatological change, urbanization etc. These situations can be treated making use of intervention analysis.

Time series analysis and adaptive filtering in hydrology

1984 ◽  
Vol 16 (1) ◽  
pp. 17-18
Author(s):  
J. W. Delleur
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
River Flow ◽  
Time Series Models ◽  
Arma Models ◽  
Multivariate Models ◽  
Varying Coefficients ◽  
Daily Streamflow ◽  
Hydrologic Time Series ◽  
Selection Of

Most time series models in hydrology are used for river flow forecasting, for generation of synthetic data sequences or for the study of physical characteristics underlying the hydrological processes. The models are formulated as linear stochastic difference equations. Three phases are considered for the selection of a model based on a satisfactory representation of a given empirical time series: identification, estimation and validation. Several criteria have been proposed for the selection of the order of ARMA models. The Akaike information criterion (Ale) is popular among hydrologists, but the posterior probability criterion has the advantage of optimality and asymptotic consistency. There are numerous applications of AR or ARMA models to annual streamflow series which are stationary. Seasonal, monthly, weekly or daily streamflow series are cyclically stationary and generally exhibit periodicities in the mean and variance and possibly in the autocorrelation structure. Removal of the periodicity has been accomplished by fitting harmonic series or by subtracting the seasonal mean and dividing by the seasonal standard deviation, and a time series model is then fitted to the residual series. Alternatively, ARMA models with time-varying coefficients are also used. The multiplicative ARlMA model of Box and Jenkins is less frequent in hydrology because of the difficulty in the identification of the parameter structure. Multivariate models are used when river flows at different sites are considered. Parameter estimation in multivariate time series models can become cumbersome because of the dimensionality of the problem. Often the covariance matrix of the noise term is not known in advance and limited information estimates are used. Multivariate models have been used for annual and monthly series. Disaggregation models have been used to subdivide a yearly series into monthly or weekly series or to disaggregate a main river flow into tributary flows while maintaining certain space and time cross-correlations. The aggregation of monthly into yearly time series has been shown to improve the parameter estimation of the yearly series. Hydrologic time series occasionally exhibit changes in level due to natural or man-made causes such as forest fires, volcanic eruption, climatological change, urbanization etc. These situations can be treated making use of intervention analysis.

scholarly journals A Simulation Comparison of Bootstrap Procedures in Periodically Correlated Time Series Models

2016 ◽  
Vol 12 (9) ◽  
pp. 6639-6643
Author(s):  
Lorena Margo ◽  
Eljona Milo
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Confidence Intervals ◽  
Periodic Structure ◽  
Programming Language ◽  
Dependent Data ◽  
Time Series Models ◽  
R Programming Language ◽  
R Programming

The presence of periodicity in data with periodic structure has become an important issue in parameter estimation. Several methods have been studied with intention estimating different parameters or constructing confidence intervals for the parameters. In this paper we investigate the performance of the bootstrap procedures designed for dependent data in the case of Periodically Correlated time series models. Several models with periodic structure are studied in this paper and we use R programming language to realize a simulation comparison of the performance of bootstrap procedures presented.

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