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The Diploma Project Economic and Mathematical Modelling of Real Estate Costs Depending on Certain Factors Економіко-математичне моделювання вартості житла в залежності від певних чинників Done by: Dmytro Zvieriev Scientific Supervisor: Sergiy Borysovych Vakarchuk

Introduction The purpose of the research is ◦ to define efficiency of modern methods; ◦ to offer an alternative model – ARMAX; ◦ to show advantages of using the ARMAX model in real estate forecasting. The subject of the research is ◦ secondary real estate market in Dnipropetrovsk; ◦ average cost of real estate.

A number of tasks There a lot of existing forecasting methods • Is the alternative model effective? • What about a real example instead of mathematical interpretations? Inputs Question • How many factors are to be included? • What about data redundancy?

Structure of Modern Methods • Least squares • Exponential smoothing • Likelihood modelling • Correlation analysis • Regression analysis • Auto regressive (AR) • Auto regressive moving average (ARMA) • Moving average (MA) Forecasting methods

Structure of Modern Methods • Least squares • Exponential smoothing • Likelihood modelling • Correlation analysis • Regression analysis • Auto regressive (AR) • Auto regressive moving average (ARMA) • Moving average (MA) Forecasting methods

An alternative offer - ARMAX – Auto Regressive Moving Average model with e. Xogenous inputs The blue line means predicted values, the red one means squared error.

The keystone to success is an effective approach from the beginning Input data analysis A large amount of inputs Partial Cross Correlation values estimation ◦ Two-Stage Least Squares usage ◦ Correlation matrix analysis

Summary ARMAX model statistics Indicator Value R 2 0. 941913 Standard error 5. 368632 Durbin-Watson statistics 2. 312138 The sum of the rest squares 201. 7555

Summary An example of the ARMAX model efficiency* Predicted value, Real value, Absolute error, UAH** UAH 11. 2010 277366. 40 277760. 00 393. 60 0. 14 12. 2010 270278. 40 271040. 00 761. 60 0. 28 01. 2011 271868. 80 271680. 00 188. 80 0. 07 02. 2011 269465. 60 - - - Data Error, % * - under the condition of real estate cost forecasting of 40 m 2 ** - 1 USD = 8 UAH

EFFECTIVE FORECASING = ARMAX QUALITATIVE FORECASTING = ARMAX Data Predicted value Real value Absolute error Error, % 10. 2007 -02. 2011 variable 41. 23* 3. 44* 11. 2010 866. 77 868. 00 1. 23 0. 14 12. 2010 844. 62 847. 00 2. 38 0. 28 01. 2011 849. 59 849. 00 0. 59 0. 07 02. 2011 842. 08 - - - * - an average value on all sample of the predicted value

Future prospect Minimisation of losses for investors Effective business for realtors, consulting companies, governmental organisations, etc. Replacement of the existing forecasting methods Addition of new information and specification of the existing one ◦ Reduce error value

EFFECTIVE FORECASING = ARMAX QUALITATIVE FORECASTING = ARMAX