In analyzing the housing market, capturing the temporal change of the market structure is of importance. Shimizu et al. (2010) [1] showed that the hedonic price index works well to capture it. Pioneering work on the hedonic price index was done by Court (1939) [2], and Griliches (1961) [3] popularized it. In these works, time dummy variables play an important role to estimate the temporal change. To estimate the change of the time dummy coefficients, Shimizu et al. (2010) [4] proposed an overlapping-period hedonic model (OPHM), whose method smooths the coefficients with a rolling window, similar to the moving average method in time series analysis. However, this method is not available to forecast the dynamic change of prices and cannot consider cyclic systems, such as seasonal effects, to smooth coefficients. To overcome these limitations, modelling dynamic changes of coefficients is one of the possible methods.

Additionally, the works above mainly focused on the temporal the change of coefficient of the constant term. However, because other coefficients may also change temporally, we consider the change in all coefficients. The method was applied to a housing market by Guirguis et al.(2005) [5], but the authors did not focus on hedonic analysis. Therefore, in this study, we compare dynamic modelling with other hedonic methods to examine its features.

A hedonic linear regression model using time-varying coefficients is described as follows

y^ᶯt = β ^{T x,nt + E n,t}

We denote the price of the nth housing unit at time t as yn,t, and its housing attributes as xn,t. The hedonic coefficient at time t are described by Bt and change dynamically. En,t is independently and identically distributed Gaussian random noise.

Time dummy type models do not allow for the temporal change in coefficients except for the constant term. However, the model above allow all coefficients to change temporally. Therefore this is the extended version of time dummy models.

There are some possible methods to estimate Bt. The naïve method is to estimate Eq. (1) using the date for each time t. This method is called the “Separate Hedonic Model” in this paper. A similar method was applied in