||Presumably, real estate appreciation indices based on appraiser values do not reflect actual market value developments on real estate markets. Also the return volatilities of these indices do not reflect the actual risks on real estate markets. The reasons for this educated guess are that even in an efficient proceeding, errors in the real estate appraisal and index construction processes cannot completely be eliminated. So the question arises, whether there are possibilities to gain true market returns from appraiser based index returns. In the past, some researchers developed methods and recommended to apply them on index returns to obtain return series, which presumably fit better to true market returns. But since there are not exact information about the true market returns and types and extents of errors in the index returns, the construction of correction procedures for index returns seems to be arbitrary. It may be questioned, whether an approximation to actual market returns can be achieved at all by applications of correction procedures on index returns. Further it is of interest, whether estimated market returns series gained from applications of different correction procedures on reported index returns series match or deviate more or less from each other. These questions are the pivot of the present study. In fact, authors report very different results for their correction procedures – judged by the for investors relevant statistical characteristics of corrected returns series. Most researchers report for their correction procedures estimated market returns series that are more volatile than their underlying reported index returns series. But in the recent past Bond and Hwang (2007) found that the volatility of property returns is less than indicated by the UK IPD index returns. So there is a wide range of results for volatilities and statistical properties of real estate market returns. But since the results of different authors refer to different time segments, they are not directly comparable. So in the present study the correction procedures are applied on equal terms. They are revised and compared for identical time segments of an index. In a second step, a rolling window approach is applied on U.S. NPI and UK IPD index returns series to observe the magnitude of revisions by time in the statistical properties of unsmoothed return series. Further, it is suggested to modify the procedure of Bond and Hwang (2007) to fully meet the quality characteristics of the NPI index returns. Additionally to several kinds of errors already considered by the authors it is proposed to adjust the NPI index returns series also by the phenomena of stale appraisal and seasonality in appraisals. It is suggested that this potentially can be done by an incorporation of additional moving-average time lags in ARFIMA-models compared to the ARFIMA-models suggested, parameterized and estimated by Bond and Hwang (2007) for quarterly returns series. Alternatively, it is suggested that the phenomenon of “stale appraisal” inherent in NPI returns series can maybe be regarded by an application of an ARFIMA(1,d,1) on returns series in annual periodicity. Also the phenomenon of seasonality in appraisals is maybe captured by an autoregressive term of time lag four in quarterly returns series. In the present study, not only the result of Bond and Hwang (2007) is confirmed that the IPD index return volatility is upward biased by systematic errors. As opposed to Bond and Hwang (2007) it is also gained for NPI returns series that the volatility is upward biased.