Accumulative prediction error and the selection of time series models

2006 ◽  
Vol 50 (2) ◽  
pp. 149-166 ◽  
Author(s):  
Eric-Jan Wagenmakers ◽  
Peter Grünwald ◽  
Mark Steyvers
Keyword(s):  
Time Series ◽  
Prediction Error ◽  
Time Series Models ◽  
Selection Of

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 Adaptation Parameters of Time Series Models for Forecasting

2021 ◽  
Vol 2096 (1) ◽  
pp. 012050
Author(s):  
S I Klevtsov ◽  
A V Maksimov
Keyword(s):  
Time Series ◽  
Second Order ◽  
Point Of View ◽  
Prediction Intervals ◽  
Time Series Models ◽  
Technical Parameters ◽  
Polynomial Models ◽  
Over Time ◽  
Selection Of

Abstract Prospects for using time series to predict changes in technical parameters in real time are considered. The task is to assess the trend dynamics of the parameter. Adaptive polynomial models of the first and second order, based on the method of multiple exponential smoothing, were selected for forecasting. The models have been modified to adapt to the peculiarities of the computing process in the microcontroller. The initial data, the acceleration values in three axes, were obtained using a three-axis accelerometer installed on the vehicle. Comparison of the forecasting results showed that the second-order adaptive polynomial model is generally more preferable from the point of view of the reduced error. Both models can be used to estimate the change in a parameter for an arbitrary number of prediction intervals. The efficiency of using the models for the forecasting problem largely depends on the determination of the adaptation parameters, such as the smoothing constant and the initial estimates of the coefficients of the time series model. The paper considers the features of the behavior of the models and defines the rules for the selection of adaptation parameters depending on the nature of the change in the technical parameter over time.

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