Price Dynamics in Public and Private Commercial Real Estate Markets

For example, in Structural Time Series Models, the long-term trend is usually treated as polynomial of time variable and is estimated with moving average method or exponential smoothing method. The cycle component is usually estimated with Fourier transform, requiring the cyclical pattern to be stable with a fixed period.

It should also be pointed out that commercial real estate market experienced a major crash in late 1980s and early 1990s. This crash followed a major episode of overbuilding of commercial space in 1980s. The overbuilding was partly encouraged by the Economics Recovery Tax Act of 1981 that lowered capital gains tax rate and accelerated cost recovery system that significantly shortened the period over which commercial real estate can be depreciated. The Tax Reform Act of 1986 eliminated the accelerated cost recovery provision of 1981 Act and made it impossible for taxpayers to offset ordinary income with tax losses from commercial real estate investments, and thus contributed to the market crash and slowdown in construction in late 1980s and early 1990s. Following the savings-and-loan crisis, banks essentially stopped making construction loans and commercial real estate mortgages. This offered an opportunity for the creation of conduit financing whereby investment banks, led by Bear Stearns and Lehman Brothers, started originating commercial mortgages and packaging them for sale to investors as mortgage-backed securities. This led to a recovery in commercial real estate market. Then on February 1994, the Fed unexpectedly started the most aggressive tightening in Fed history, as a result of which the real estate market suffered significantly.

By decomposing the original series into a time dependent sum of different frequency components, wavelet technology is also likely to improve the quality of forecasting. However, incorporating wavelets increases the model complexity due to more approximation steps, as well as more error sources. Schlüter and Deuschle (2010) discuss this trade-off by comparing the forecasting quality of wavelet-based method and other traditional methods (i.e., Census X-12, ARMA, ARIMA). They find that wavelet-based forecasting generally performs better than classical techniques, especially when a strong long-term pattern dominates short-term oscillations. However, for time series with a minor trend and a strong random component, wavelets generate only little improvements.

The formula takes into consideration any capital improvements and/or any partial sales that occurred during the quarter,

See Dewandaru et al. (2015, 2016).

Since the original time series is not a normal distribution, Monte Carlo method is used here to establish significance levels and confidence intervals for the wavelet power spectrum.

The cone shaped curve in the figure is known as the Cone of Influence. Because one is dealing with finite-length time series, errors will occur at the beginning and end of the wavelet power spectrum. One solution to these edge effects is to pad the end of the time series with zeroes before doing the wavelet transform and then remove them afterward. The region in which the transform suffers from these edge effects is called the cone of influence. A more detailed explanation can be found in Aguiar-Conraria and Soares (2010).

The intervals are defined in terms of the results from Trend and Cycles Decomposition. We find that, the short and long cycle of public and private commercial market is ranging from 6.5 to 17.5 years, which is 26 to 70 quarters accordingly.

We focus on the direction, rather than the magnitude, of the lead-lag relationship. As a result, we do not differentiate among different values in the (0,90) or (−90,0) intervals.

Examples of studies on price diffusion process in residential markets include Dolde and Tirtiroglu (2003), DeFusco et al. (2015) and Cohen and Zabel (2017).

We are grateful to David Ling and Andy Naranjo for sharing their data and calculations with us.

The WILSHIRE Real Estate Securities Index (WILSHIRE) is a market capitalization weighted index of publicly traded real estate securities including REITs, real estate operating companies (REOCs), and public partnerships.

A simpler version of the derivations here can be found in Appendix C that uses Haar Wavelet, considered to be the simplest possible wavelet.

In orthogonal wavelet analysis, the number of convolutions at each scale is proportional to the width of the wavelet basis at that scale. It is gives the most compact representation of the signal as it produces a wavelet spectrum that contains discrete “blocks” of wavelet power.

Smoothing is needed because without it coherency would be identically one at all times and scales. Smoothing can be achieved by a convolution (see Cazelles et al. 2007)

Cycle 1 exhibits the reconstructed signal excluding low-pass component (LFA7) and high-pass component in layer 1 (LFD1) and layer 2 (LFD2). Cycle 2 exhibits the reconstructed signal excluding low-pass component (LFA5), high-pass component in layer 1 (LFD1) and high-pass component in layer 2 (LFD2). Cycle 3 exhibits the reconstructed signal excluding low-pass component (LFA5), high-pass component in layer 1 (LFD1), high-pass component in layer 2 (LFD2) and high-pass component in layer 3 (LFD3). Cycle 4 exhibits the reconstructed signal excluding low-pass component (LFA5), high-pass component in layer 1 (LFD1), high-pass component in layer 2 (LFD2), high-pass component in layer 3 (LFD3) and high-pass component in layer 4 (LFD4).