Applied aspects of time series models for predicting residential property prices in Bulgaria

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Accurate housing price forecasts play a critical role in balancing supply and demand in the residential real estate market, as well as in achieving the goals of various stakeholders – buyers, investors, construction contractors, public administration, real estate agencies, special investment purpose companies, etc. The present study aims to investigate the relationship between specific predictors and build a suitable model for forecasting housing prices in Bulgaria. In this regard, a study was conducted on transactions with residential real estate in the city of Sofia for the period from the first quarter of 2016 to the fourth quarter of 2021. The ARIMA model is used in the development to predict the values of the variables. Eight models are tested for the researched factors (24 in total). On this basis, the price per square meter of residential property was predicted, including estimated values from the ARIMA model for the parameters involved in the regression equation. The result showed that there is a strong relationship between the analyzed predictors and the studied variable – price per square meter of housing. The tested models are adequate and the statistical requirements for forecasting the prices of residential properties in Bulgaria are complied.

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    • Figure 1. Changes in the parameters under study from the first quarter of 2016 to the fourth quarter of 2021
    • Figure 2. Autocorrelation plot of the autocorrelation function “price per square meter” and autocorrelation plot of partial autocorrelation function “price per square meter”
    • Figure 3. Plot of the autocorrelation function of the ARIMA (1,1,1) model residuals “price per square meter” and Plot of the partial autocorrelation function of the ARIMA (1,1,1) model residuals “price per square meter”
    • Figure 4. Estimated price per square meter of real estate for three periods
    • Figure 5. Plot of the autocorrelation function – “income per person” and Plot of partial autocorrelation function – “income per person”
    • Figure 6. Autocorrelation plot of residuals from the ARIMA (2,1,0) model “income per person” and Partial autocorrelation plot of residuals from the ARIMA (2,1,0) model “income per person”
    • Figure 7. Estimated “income per person” for three periods
    • Figure 8. Plot of the autocorrelation function – “credit per person” and Plot of partial autocorrelation function – “credit per person”
    • Figure 9. Autocorrelation plot of residuals from the ARIMA (1,1,1) model “credit person” and Partial autocorrelation plot of residuals from the ARIMA (1,1,1) model “credit per person”
    • Figure 10. Estimated “credit per person” for three periods
    • Figure 11. Data on studied parameters and forecasts for three periods
    • Table 1. Data on price per square meter income per person and credit per person for the period January 1, 2016 – January 1, 2021
    • Table 2. Regression analysis results from quantitative assessment of the price per square meter
    • Table 3. ARIMA (1,1,1) model parameters – price per square meter
    • Table 4. Estimated values of “price per square meter”
    • Table 5. ARIMA (2,1,0) model parameters – “income per person”
    • Table 6. Estimated values of “income per person”
    • Table 7. ARIMA (1,1,1) model parameters – credit per person
    • Table 8. Estimated values of “credit per person”
    • Table 9. Estimated values of “price per square meter” calculated on the basis of regression equation and data from the ARIMA model
    • Data curation
      Svetoslav Iliychovski
    • Investigation
      Svetoslav Iliychovski
    • Resources
      Svetoslav Iliychovski, Teodora Filipova
    • Visualization
      Svetoslav Iliychovski
    • Writing – original draft
      Svetoslav Iliychovski, Mariana Petrova
    • Formal Analysis
      Teodora Filipova
    • Supervision
      Teodora Filipova
    • Writing – review & editing
      Teodora Filipova
    • Conceptualization
      Mariana Petrova
    • Methodology
      Mariana Petrova
    • Software
      Mariana Petrova
    • Validation
      Mariana Petrova