On Some Characteristics of Liquidity Proxy Time Series. Evidence from the Polish Stock Market

  • Joanna OlbrysEmail author
  • Michal Mursztyn
Conference paper
Part of the Springer Proceedings in Business and Economics book series (SPBE)


The aim of this paper is to investigate major statistical properties of selected liquidity proxy time series based on high frequency (intraday) and low frequency (daily) data from the Warsaw Stock Exchange (WSE). We analyse daily time series of six liquidity estimates for the group of eighty-six WSE-traded companies, in the period from January 2005 to December 2016. These liquidity measures are: (1) percentage relative spread, (2) percentage realized spread, (3) percentage price impact, (4) percentage order ratio, (5) the modified daily turnover, and (6) the modified version of daily Amihud measure. We test distributional properties, linear and non-linear dependences, as well as stationarity of the analysed daily time series. Assessing statistical properties of time series of liquidity proxies is crucial for further research on econometric modelling of commonality in liquidity on the WSE.


Stock market Liquidity measure Time series Intraday data Daily data 



This study was supported by the grant “Comparative research on commonality in liquidity on the Central and Eastern European stock markets” from the National Science Centre in Poland, No. 2016/21/B/HS4/02004.


  1. Adkins, L. C. (2014). Using gretl for principles of econometrics (4th ed.), Version 1.041.Google Scholar
  2. Amihud, Y. (2002). Illiquidity and stock returns: Cross-section and time-series effects. Journal of financial markets, 5(1), 31–56.CrossRefGoogle Scholar
  3. Będowska-Sójka, B. (2017). Comparison of monthly stock liquidity measures for WSE-listed companies based on low-frequency data (in Polish). Problemy Zarzadzania-Managemnet Issues, 15(1), 178–192.CrossRefGoogle Scholar
  4. Bekaert, G., Harvey, C. R., & Lundblad, C. (2007). Liquidity and expected returns: Lessons from emerging markets. The Review of Financial Studies, 20(6), 1783–1831.CrossRefGoogle Scholar
  5. Campbell, J. Y., Lo, A. W., & MacKinlay, A. C. (1997). The econometrics of financial markets. New Jersey: Princeton University Press.Google Scholar
  6. Chakrabarty, B., Li, B., Nguyen, V., & Van Ness, R. A. (2007). Trade classification algorithms for electronic communications network trades. Journal of Banking & Finance, 31, 3806–3821.CrossRefGoogle Scholar
  7. Chan, K., & Fong, W.-M. (2000). Trade size, order imbalance, and the volatility-volume relation. Journal of Financial Economics, 57, 247–273.CrossRefGoogle Scholar
  8. Chordia, T., Roll, R., & Subrahmanyam, A. (2000). Commonality in liquidity. Journal of Financial Economics, 56, 3–28.CrossRefGoogle Scholar
  9. Chordia, T., Roll, R., & Subrahmanyam, A. (2002). Order imbalance, liquidity, and market returns. Journal of Financial Economics, 65, 111–130.CrossRefGoogle Scholar
  10. Cook, S., & Manning, N. (2004). Lag optimization and finite-sample size distortion of unit root tests. Economic Letters, 84(2), 267–274.CrossRefGoogle Scholar
  11. Doornik, J. A., & Hansen, H. (2008). An omnibus test for univariate and multivariate normality. Oxford Bulletin of Economics and Statistics, 70(Supp 1), 927–939.CrossRefGoogle Scholar
  12. Elliott, G., Rothenberg, T. J., & Stock, J. H. (1996). Efficient tests for an autoregressive unit root. Econometrica, 64(4), 813–836.CrossRefGoogle Scholar
  13. Fong, K. Y. L., Holden, C. W., & Trzcinka, C. (2017). What are the best liquidity proxies for global research? Review of Finance, 21, 1355–1401.CrossRefGoogle Scholar
  14. Foran, J., Hutchinson, M. C., & O’Sullivan, N. (2015). Liquidity commonality and pricing in UK. Research in International Business and Finance, 34, 281–293.CrossRefGoogle Scholar
  15. Glosten, L. R. (1987). Components of the bid-ask spread and the statistical properties of transaction prices. The Journal of Finance, 42(4), 1293–1307.CrossRefGoogle Scholar
  16. Goyenko, R. Y., Holden, C. W., & Trzcinka, C. A. (2009). Do liquidity measures measure liquidity? Journal of Financial Economics, 92, 153–181.CrossRefGoogle Scholar
  17. Huang, R. D., & Stoll, H. R. (1996). Dealer versus auction markets: A paired comparison of execution costs on NASDAQ and the NYSE. Journal of Financial Economics, 41, 313–357.CrossRefGoogle Scholar
  18. Kamara, A., Lou, X., & Sadka, R. (2008). The divergence of liquidity commonality in the cross-section of stocks. Journal of Financial Economics, 89(3), 444–466.CrossRefGoogle Scholar
  19. Karolyi, G. A., Lee, K.-H., & van Dijk, M. A. (2012). Understanding commonality in liquidity around the world. Journal of Financial Economics, 105(1), 82–112.CrossRefGoogle Scholar
  20. Kyle, A. S. (1985). Continuous auctions and insider trading. Econometrica, 53(6), 1315–1336.CrossRefGoogle Scholar
  21. Lee, C. M. C., & Ready, M. J. (1991). Inferring trade direction from intraday data. The Journal of Finance, 46(2), 733–746.CrossRefGoogle Scholar
  22. Lesmond, D. A. (2005). Liquidity of emerging markets. Journal of Financial Economics, 77(2), 411–452.CrossRefGoogle Scholar
  23. Lischewski, J., & Voronkova, S. (2012). Size, value and liquidity. Do they really matter on an emerging stock market? Emerging Markets Review, 13, 8–25.CrossRefGoogle Scholar
  24. Ljung, G., & Box, G. E. P. (1978). On a measure of lack of fit in time series models. Biometrika, 66, 67–72.Google Scholar
  25. McLeod, A. I., & Li, W. K. (1983). Diagnostic checking ARMA time series model using squared residual autocorrelations. Journal of Time Series Analysis, 4, 269–273.CrossRefGoogle Scholar
  26. Nowak, S., & Olbryś, J. (2015). Day-of-the-week effects in liquidity on the Warsaw Stock Exchange. Dynamic Econometric Models, 15, 49–69.CrossRefGoogle Scholar
  27. Nowak, S., & Olbryś, J. (2016). Direct evidence of non-trading on the Warsaw Stock Exchange. Research Papers of Wroclaw University of Economics. Wroclaw Conference in Finance: Contemporary Trends and Challenges 428, 184–194.Google Scholar
  28. Olbryś, J. (2014). Is illiquidity risk priced? The case of the Polish medium-size emerging stock market. Bank & Credit, 45(6), 513–536.Google Scholar
  29. Olbryś, J. (2018). Testing stability of correlations between liquidity proxies derived from intraday data on the Warsaw Stock Exchange. In K. Jajuga, H. Locarek-Junge, & L. Orlowski (Eds.), Contemporary trends and challenges in finance. Springer Proceedings in Business and Economics (pp. 67–79). Cham: Springer.Google Scholar
  30. Olbrys, J., & Mursztyn, M. (2018). Liquidity proxies based on intraday data: The case of the Polish order driven stock market. In N. Tsounis & A. Vlachvei (Eds.), Advances in Panel Data Analysis in Applied Economic Research. Springer Proceedings in Business and Economics (pp. 113–128). Cham: Springer.Google Scholar
  31. Olbryś, J., & Mursztyn, M. (2015). Comparison of selected trade classification algorithms on the Warsaw Stock Exchange. Advances Computer Science Research, 12, 37–52.Google Scholar
  32. Olbryś, J., & Mursztyn, M. (2017). Measurement of stock market liquidity supported by an algorithm inferring the initiator of a trade. Operations Research and Decisions, 27(4), 111–127.Google Scholar
  33. Stoll, H. S. (2000). Friction. The Journal of Finance, 55(4), 1479–1514.CrossRefGoogle Scholar
  34. Theissen, E. (2001). A test of the accuracy of the Lee/Ready trade classification algorithm. Journal of International Financial Markets, Institutions and Money, 11, 147–165.CrossRefGoogle Scholar
  35. Tsay, R. S. (2010). Analysis of financial time series. New York: Wiley.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Bialystok University of TechnologyBialystokPoland

Personalised recommendations