KZ
K. Zomerdijk
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This thesis concerns modeling residential real estate selling prices in a hedonic price model framework on a small spatial-temporal granularity. The research addresses the challenge of sparse spatial-temporal real estate data, i.e. many combinations of location and time with few or no transactions, by employing spatial dynamic factor models (SDFMs). Two types of SDFMs are employed: an SDFM with a 1D spatial structure based on the spatial random walk and an SDFM with a 2D spatial structure based on the Gaussian random field. To capture the information on the property characteristics, spatial dynamic factor models are combined with two different data-driven models, namely a neural network (NN) and an interpretable version of an NN, the local generalized linear model network (LGLMN). Both a Bayesian approach and an algorithmic approach are employed to estimate the models on both a PC and a high-performance computer (HPC). A simulation study is conducted to demonstrate the ability of an NN to capture linear and non-linear structures when combined with an SDFM and to show the ability of the LGLMN to replicate a linear structure. Furthermore, the models are evaluated on real transaction data from the municipality of Rotterdam. The findings demonstrate that the algorithmically estimated NN-adjusted SDFM based on the spatial random walk (NN-SRW-DFM) outperforms the other models in terms of accuracy with an out-of-sample MAPE of 0.128. Moreover, the results highlight a trade-off between accuracy, speed, and interpretability.
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This thesis concerns modeling residential real estate selling prices in a hedonic price model framework on a small spatial-temporal granularity. The research addresses the challenge of sparse spatial-temporal real estate data, i.e. many combinations of location and time with few or no transactions, by employing spatial dynamic factor models (SDFMs). Two types of SDFMs are employed: an SDFM with a 1D spatial structure based on the spatial random walk and an SDFM with a 2D spatial structure based on the Gaussian random field. To capture the information on the property characteristics, spatial dynamic factor models are combined with two different data-driven models, namely a neural network (NN) and an interpretable version of an NN, the local generalized linear model network (LGLMN). Both a Bayesian approach and an algorithmic approach are employed to estimate the models on both a PC and a high-performance computer (HPC). A simulation study is conducted to demonstrate the ability of an NN to capture linear and non-linear structures when combined with an SDFM and to show the ability of the LGLMN to replicate a linear structure. Furthermore, the models are evaluated on real transaction data from the municipality of Rotterdam. The findings demonstrate that the algorithmically estimated NN-adjusted SDFM based on the spatial random walk (NN-SRW-DFM) outperforms the other models in terms of accuracy with an out-of-sample MAPE of 0.128. Moreover, the results highlight a trade-off between accuracy, speed, and interpretability.
As an insurer you want identify the risks you take to prevent bankruptcy. The
theory of large deviations formalizes the study of such rare events. We will use the
theorem of Cramér, which is a main theorem in large deviation theory, to investigate
the rate at which the probability of large deviations of the sums of random variables
decay. Using Sanov’s theorem we will derive an expression for large deviations of
the empirical measure. Furthermore, we will use Gibbs’s principle to derive the
distribution of random variables conditional on a large deviation.
...
theory of large deviations formalizes the study of such rare events. We will use the
theorem of Cramér, which is a main theorem in large deviation theory, to investigate
the rate at which the probability of large deviations of the sums of random variables
decay. Using Sanov’s theorem we will derive an expression for large deviations of
the empirical measure. Furthermore, we will use Gibbs’s principle to derive the
distribution of random variables conditional on a large deviation.
...
As an insurer you want identify the risks you take to prevent bankruptcy. The
theory of large deviations formalizes the study of such rare events. We will use the
theorem of Cramér, which is a main theorem in large deviation theory, to investigate
the rate at which the probability of large deviations of the sums of random variables
decay. Using Sanov’s theorem we will derive an expression for large deviations of
the empirical measure. Furthermore, we will use Gibbs’s principle to derive the
distribution of random variables conditional on a large deviation.
theory of large deviations formalizes the study of such rare events. We will use the
theorem of Cramér, which is a main theorem in large deviation theory, to investigate
the rate at which the probability of large deviations of the sums of random variables
decay. Using Sanov’s theorem we will derive an expression for large deviations of
the empirical measure. Furthermore, we will use Gibbs’s principle to derive the
distribution of random variables conditional on a large deviation.