Time-series framework

In Aviv (2002a), we extend the model of Aviv (2001) by specifically considering questions related to VMI and CPFR, and by using an auto-correlated time series framework for the underlying demand process (we shall provide... 

The system identification step in the core-box modeling framework has two major sub-steps parameter estimation and model quality analysis. The parameter estimation step is usually solved as an optimization problem that minimizes a cost function that depends on the model s parameters. One choice of cost function is the sum of squares of the residuals, Si(t p) = yi(t) — yl(t p). However, one usually needs to put different weights, up (t), on the different samples, and additional information that is not part of the time-series is often added as extra terms k(p). These extra terms are large if the extra information is violated by the model, and small otherwise. A general least-squares cost function, Vp(p), is thus of the form... 

Since this monograph is devoted only to the conception of mathematical models, the inverse problem of estimation is not fully detailed. Nevertheless, estimating parameters of the models is crucial for verification and applications. Any parameter in a deterministic model can be sensibly estimated from time-series data only by embedding the model in a statistical framework. It is usually performed by assuming that instead of exact measurements on concentration, we have these values blurred by observation errors that are independent and normally distributed. The parameters in the deterministic formulation are estimated by nonlinear least-squares or maximum likelihood methods. 

An alternative SPM framework for autocorrelated data is developed by monitoring variations in time series model parameters that are updated at each new measurement instant. Parameter change detection with recursive weighted least squares was used to detect changes in the parameters and the order of a time series model that describes stock prices in financial markets [263]. Here, the recursive least squares is extended with adaptive forgetting. 

It can be concluded that ETD is a beneficial extension of static classification methods when online response to changes is required and the measurement devices exhibit a delayed behaviour. The DWT provides a useful framework for characterizing changes of a time series locally and on multiple time scales and could therefore beneficially be used for ETD. 

Chronology 1) A data series or framework referenced with respect to time (i.e., a time series). For lake sediment records, often the chronology describes the sediment depth-age relationship. 2) Time scale, which may be obtained through radiometric dating (e.g., C, U/Th) or counting of annual layers. 

More comprehensive analysis of traffic safety measures should be done. The key variables should be traffic fatalities, the traffic fatality rates and the analysis should be based on a general individual net benefit type of framework. Econometric and statistical time series models should be emphasized so as to facilitate bottom line analysis of fatality rates. Bottom line analysis is essential to a better understanding of determinants of traffic safety and taking some of the mystery out of mystery plunges. Bottom-line evaluation is essential to overall evaluation of traffic safety policy. Bottom line evaluation provides additional information on interactions within the traffic safety system. These interactions are difficult to incorporate precisely in anal is of polity measures evaluated one at a time. 

These are the most basic equations needed in order to utilize U-Th series radionuclides as time-dependent tracers. In turn, they can provide an apparent age of a process or a geochronological framework. 

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