As the number of risk factors increases, the ability of the VAR 18 3.3 Formulation of risk factors model to explain the variation in multiple areas decreases due to the limitations of the model, specif- ically, the inability to perform Cholesky decomposition when the number of risk factors becomes too large. [...] With the absence of a stationary component in the expression of the stochastic difference equation, the analysis of volatility becomes the focus of the next, after the series of residuals is detrended, which is regarded as a series of new observations in each area at the most granular scale. [...] Furthermore, the superior performance of the hierarchical model with empirical copulas compared to both the MinT(Shrink) model indicates that the inclusion of copulas in the model helps to capture the dependence structure of the data more accurately, resulting in improved forecasting accuracy. [...] One possible explanation for the observed pattern is that the capture of the stochastic term with the use of volatility analysis alleviates the bias in the distribution of the original simulated average house price index at the country level. [...] In year N , the proportion of the marginal effect of the annual change in a particular factor to the marginal effect of the annual change in the log of the national house price is calculated in order to determine the impact of that factor on changes in house prices coefficientf (Ωji) ∑ × fPt (Ωj) t∈Year N coefficient (Ω ) ∑ × 100%, (36)l0 ji × l0,t t∈Year N which is considered the effect of the fa.
- Pages
- 51
- Published in
- Australia
