Long-Range Dependence in U.S. Home Price Volatility


The existence of GARCH effects in a financial price series means that the probability of large losses is much higher than standard mean-variance analysis suggests. Accordingly, several recent papers have investigated whether GARCH effects exist in the U.S. housing market, as changes in house prices can have far-ranging impacts on defaults, foreclosures, tax revenues and the values of mortgage-backed securities. Some research in finance indicates that the conditional variance of some assets exhibits far greater persistence, or even “long memory”, than is accounted for in standard GARCH models. If house prices do indeed have this very persistent volatility, properly estimating the conditional variance to allow for such persistence is crucial for optimal portfolio management. We examine a number of U.S. metropolitan areas, and find that, for those with significant GARCH effects, more than half indeed exhibit the very high persistence found in other assets such as equities. We also find that, for those markets exhibiting such persistent volatility, C-GARCH models typically do a better job in forecasting than standard GARCH models. Moreover, there is some tentative evidence that metro areas with the fastest appreciation may be most likely to have such long memory conditional variance. These findings should help in improving risk management, through, for instance the construction of better-specified value-at-risk models.

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I would like to thank Stan Longhofer for helpful conversations and the Barton School of Business at Wichita State University for financial support.

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Correspondence to William Miles.



Regional Classifications

OFHEO data: Northeast: Allentown, Baltimore, Bethesda, Boston, Bridgeport, Buffalo, Cambridge, Camden, Edison, Nassau, New York, Newark, Philadelphia, Pittsburgh, Providence, Rochester, Washington.

Southeast: Atlanta, Baton Rouge, Birmingham, Charlotte, Columbia, Deltona, Fort Lauderdale, Greensboro, Jacksonville, Little Rock, Louisville, Memphis, Miami, New Orleans, Orlando, Raleigh, Richmond, Tampa, West Palm Beach.

Midwest: Akron, Canton, Chicago, Cincinnati, Cleveland, Columbus, Dayton, Des Moines, Detroit, Flint, Fort Wayne, Gary, Indianapolis, Kansas City, Lake County, Lansing, Milwaukee, Minneapolis, Omaha, St. Louis, Warren, Wichita. Mountain: Denver, Fort Collins, Ogden, Salt Lake City.

Southwest: Albuquerque, Austin, Beaumont, Dallas, Fort Worth, Houston, Las Vegas, Oklahoma City, Phoenix, Reno, Tucson.

West Coast: Bakersfield, Bellingham, Fresno, Honolulu, Los Angeles, Modesto, Napa, Oakland, Oxnard, Portland, Riverside, Sacramento, Salinas, San Diego, San Francisco, San Jose, San Luis Obispo, Santa Ana, Santa Barbara, Santa Cruz, Santa Rosa, Seattle, Spokane, Stockton, Tacoma, Vallejo.

Case Shiller data: Northeast: Boston, New York, Washington.

Southeast: Atlanta, Charlotte, Miami, Tampa.

Midwest: Chicago, Cleveland, Detroit, Minneapolis.

Mountain: Denver.

Southwest: Dallas, Las Vegas, Phoenix.

West Coast: Los Angeles, Portland, San Diego, San Francisco, Seattle.

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Miles, W. Long-Range Dependence in U.S. Home Price Volatility. J Real Estate Finan Econ 42, 329–347 (2011). https://doi.org/10.1007/s11146-009-9204-0

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  • House prices
  • Long memory
  • Volatility