This study analyzed the interrelationship and lead-lag relationship between price changes by housing type with the TVP-VARX model and Wavelet Phase Difference. As a result of the empirical analysis, the price of all housing types has a strong tendency to decrease after 2020 due to rising interest rates. The interrelationship between price changes by housing type is time-varying, and the impact of increase in apartment price on the price of detached and row houses increases over time. On the other hand, the impact of increase in detached house prices on prices of other housing types increases and then decreases sharply after August 2020. The impact of increase in row house price on prices of other types of housing generally remains constant, but temporarily increases around August 2020. At this time, in the interrelationship between prices by housing type, the impact of increase in apartment price on the price of other housing types is the largest on average. Next, it is confirmed that the impact of increase in the price of detached and row houses has a large impact on other housing types. The lead-lag relationship between price changes by housing type, which is detached → row → apartment, clearly has made after 2019. However, the interrelationship, influence, and lead-lag relationship between price changes by housing type by region are different. Accordingly, this study suggests that it is necessary to discriminately select housing types and policies to be supplied for price stabilization in the housing market according to the time and region.