Economics/ 8. Mathematical methods in economics

Post-graduate student, Orlovska N.

Taras Shevchenko National University of Kyiv, Ukraine

The Persistence of Poland Stock Market Fluctuations

Crisis increasing in the market is accompanied not only by its chaotic dynamics, but also the increasing nervousness of the participants – nonpersistent behavior, or, on the contrary, the formation of "gregarious" tendencies - persistent behavior. It becomes apparent in macroeconomic trends’ behavior and increasing of volatility, macroeconomic disbalance. The market reaction can be instant or slowed with risk accumulation. It depends on the rate of disparity. This allows finding the crisis beforehand. Permanent deviation of fluctuations from norm lets us know about decreasing of macroeconomic stability and crisis existing, that can be used as crisis indicator [1, с.147].

The aim of the research is identification and forecasting financial time series in case of WIG 20 using of R/S-analysis. It has been calculated since 1994 in Poland, and comprises 20 of the largest and most liquid companies listed on the Warsaw Stock Exchange.  It constitutes more than half of the market capitalization. Participants in this index are adjusted every quarter and revised on an annual basis (every January). There are three main sectors under the WIG20 index: services account for nearly 23% of the index, industry nearly 34% and financial accounts for 43.2%. Under these sectors there are subsectors like telecoms, fuel industry or banking respectively.

The significance of the WIG20 index, especially in western countries, is increasing due to the fact that Poland is the largest post-communist country in the region. Also, the Warsaw Stock Exchange has proven to be more “international” by listing shares of foreign companies from the Czech Republic or Ukraine, making the WSE more attractive to foreign capital, and bringing as well the attention of the international investment community [4].

Let’s start with the graph of the returns dynamics of this time series during the period of 2008-2012.

Fig. 1. Dynamics of WIG20 returns during 2008-2010

Source: http://stooq.pl/q/d/?s=wig20&i=d&d1=20111110&d2=20120601&l=4

Fig. 2. Dynamics of WIG20 returns during 2010-2012

Source: http://stooq.pl/q/d/?s=wig20&i=d&d1=20111110&d2=20120601&l=4

At first, the set of logarithmic returns is generating , where - value of WIG20 at moment t, Δt - time gap. As we analyze daily data, the time gap is equal to one day. We get a new sequence , which will be divided to subsequences of length n. [3, c.25-26]

From and we obtain the value of Hurts exponent, which is equal to slope ratio.

Fig. 3. R/S analysis

Source: authorial calculation

Hurst exponent is H = 0.6159, which more than 0.5. It means that series is not a "white noise" and can’t be the random walk. So we can conclude about long memory processes: every observation contains the information about previous events, "remember" them.

The time series is persistent, i.e. deviations tend to keep the same sign, and it characterized by the "black noise", or noise with fractional dimension processes. Data sets like this are referred to as fractional Brownian motion.

The fractal dimension provides an indication of how rough a surface is. As equation shows, the fractal dimension is directly related to the Hurst exponent for a statistically self-similar data set. In our case the D = 1.3841 is between 1 and 1.5, the time series is somewhere between a straight line and Gaussian random walk. The importance of the fractal dimension of a time series lies in the fact that it recognizes that a process can be somewhere between deterministic and random.

Thus, the result of the R/S - analysis is persistent values, which correspond to the processes of "black noise". Fractional noise is closely related to relaxation processes (a form of dynamic equilibrium, i.e. the time it takes the system to reach a new equilibrium after the violation prior to some action of external forces). [2, p. 166-168]

The evaluated data set is fractal with a positive correlation in changes of yield of index WIG20, a tendency for the emergence of trends and crises are revealed, the market is inefficient and prone to the emergence of the crisis. The value of H close to 0.5, indicating the relative efficiency (efficiency in weak form) using an index to assess the current situation in the market, but does not reject the possibility of trends and possible short-term local management, reflecting the echo of the financial crisis.

Stocks in Poland had a positive performance during the last month. The WIG, a major stock market index based in Poland, rallied 239 points or 0.59 percent during the last 30 days. Historically, from 1991 until 2012, the WIG averaged 24767.6 reaching an all time high of 67568.5 in July of 2007 and a record low of 635.3 in June of 1992 [5]. The index dynamics during first six months of 2012 is similar to the behavior during the first half of 2010. It confirms our conclusions as to the Hurst exponent. Thus, if the is no unpredictable shocks, it can be expected the significant growing.

References

1. Mansurov A. Forecasting of currency crisis by fractal analysis/ A. Mansurov // Probl. of forecasting, №1, 2008. – P.145-158.

2. Peters E. The fractal analysis of financial markets: using of theory of chaos in investment and economics/ E. Peters // - M.: Internet-trading, 2004. – 304p.

3. Soloviov V. Modelling of complicated economic systems: school appliances/ V.Soloviov, V.Soloviova, N.Haradzhian// - Kryvyi Rig: NMetAU, 2010. – 119p.

4. HighSky Brockers [Online] https://www.highsky.com/markets/markets-overview/stock-markets/wig-20.

5. Trading Economics [Online] http://www.tradingeconomics.com/ poland/stock-market