Using ultra high frequency data in integrated variance estimation: gathering evidence on market microstructure noise

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2017
Kılıçkaya, İnci
In recent years, as a result of more readily available ultra high frequency data (UHFD), realized volatility (RV) measures became popular in the finance literature since in theory, sampling at İncreasingly higher frequency should lead to, in the limit, a consistent estimator of integrated return volatility (IV) for Ito-semimartingale asset prices. However, when observed prices are contaminated with an additive market microstructure noise (MMN), an asymptotic bias appears, and, therefore, it becomes necessary to mitigate the effect of MMN in estimation of IV. The success of the available methods in the literature to suppress the MMN effects must be considered only if the empirical evidence backs the assumptions underlying the methods developed for handling MMN. On this issue, we realize that empirical evidence on the MMN structure should be collected taking into account the dimensions of volatility estimation using high frequency data as these dimensions may impair the validity of the methods adopted to handle MMN in the first place. Accordingly, in this Thesis, first we provide a complete discussion of the dimensions of volatility estimation using UHFD. Next, we prove that the formal tests regarding the existence of MMN and the constant variance of MMN increments originally developed under calendar time sampling can also be used under transaction time sampling. Third, we propose a new approach to measure the liquidity of stocks in a high frequency setting. Finally, by using tick data from Borsa İstanbul National Equity Market for a period of 6 months, we show that (i) the data handling procedures as various combinations of cleaning and aggregation methods do not distort UHFD’s original traits, (ii) the return dynamics in transaction time are different from those in calendar time, (iii) the RV dynamics are affected by the sampling scheme and liquidity, (iv) the volatility signature plots point to the existence of MMN and suggest a positive relationship between the noise increment and the true price return, valid in all possible dimensions (sampling scheme, liquidity, data handling methods, and session-based or daily calculations), (v) the MMN exhibits statistically significant existence under both CTS and TTS for all stocks, however, the liquidity and the data handling methods matter under TTS in terms of rejection rates of the null hypothesis that the MMN statistically does not exist, (vi) the formal tests on the existence of MMN offer positive correlation between the noise and the efficient price, (vii) the liquidity and the sampling schemes are very influential on the rejection of the null hypothesis that the MMN increments have constant variance independent of the sampling frequency, in particular, under CTS, (assuming an i.i.d MMN with constant variance is proper for frequencies lower than 1 minute but under TTS, this assumption fails especially for liquid stocks), (viii) data handling has suppressive effects under TTS on the rejection percentages regarding the null hypothesis that the MMN increments have constant variance independent of sampling frequency.