Estimation of Parameters and Updating Procedures
In Chapter 3 we discussed and developed a number of decision and forecasting models. Further in Chapter 4 we discussed how one can apply these models using real life and also synthetic (simulated) data. While realizing the limitations of the data used to apply these models, we discussed and developed an SDSS in Real Estate using GIS in Chapter 5. The purpose of this Chapter is to discuss the methods and techniques for updating the values of the parameters involved in the models from time to time using the data collected in SDSS. This is important since the real life is not static and ever changing and ...view middle of the document...
5 the parameters µ and σ with regard to a particular property are to be estimated and re-estimated as time passes.
• For Box-Jenkin model described in Chapter 3 and Chapter 4 parameters α, β, γ with regard to a particular property are to be estimated and re-estimated as time passes.
• The risk parameter r in the equation (9) in Chapter 3 involves judgment of the decision maker and this is required to be estimated and re-estimated as time passes.
For other models described in Chapter 3 are also to be studied once the appropriate data are available. Furthermore, for qualitative factors, as mentioned in Chapter 5, survey data need to be collected from time to time. This is required to ensure the robustness of decision making, especially for screening a possible set of properties to be considered for investment and developing a feasible set of properties on which hybrid forecasting model to be applied.
6.2. Methods of Estimating Quantitative Parameters
For Itô model described in section 3.5 the parameters µ and σ with regard to a particular property are to be estimated by using respectively the formulae (14) in Chapter 4 and the standard formula for estimating standard deviation. The estimation of the parameter δ, which represents the opportunity cost of developing the property, involves expert judgments in relation to µ. All these three parameters should be estimated from time to time using past time series data for each property.
Method for estimation of the parameters α, β, γ that are involved in Equation (14) in Chapter 4 is described in Section 3.5.4.
The risk parameter r in equation (9) in Chapter 3 involves judgment of the decision maker. It should be estimated from time to time by using methods described in Gupta et al (1974). However, a simple approach would be to try various values of r and draw the graph of U(y) as given in equation (9) in Chapter 3 and ask which graph is acceptable to the decision maker. Accept the value of r corresponding to whichever graph is selected by the decision maker.
For other parameters involved in all other models considered in Chapter 3 general regression methods may be used from time to time as Data Base gets updated.
The main method that has been applied in this research is the method of mathematical modeling for which the solutions have been found by using mathematical programming algorithms. For smaller problems EXCEL SOLVER is adequate to solve such problems. For larger problems, commercial package like LINDO is required to find solutions to such problems. Even for estimating the parameters of a forecasting model, one can conveniently use EXCEL SOLVER, as has been done in this research, by minimizing the sum of squares of forecasting errors over the period/domain of the actual data set.
6.3. Methods of Estimating Qualitative Parameters:
The basic objective of qualitative parameters is to ensure robustness of decision making. This may be achieved by developing a SDSS...