CHAPTER 3
THE FRAMEWORKS
3.1 Theoretical Framework
Studies conducted in the past have contributed principles related to the estimation of the Hurst Exponent. The theories present in this research provide the foundation for estimating the Hurst exponent.
3.1.1. Brownian Motion theory
This theory was first coined by Robert Brown. It was primarily referred as the random motion observed under microscope of pollen immersed in water. In addition to that, Albert Einstein mentioned that this theory was caused by the random bombardment of (heat excited) water molecules on the pollen. Hence, it is just the molecular nature of matter. (Rodriguez, A.). Brownian motion was explained by assuming that the immersed particle was continuously batter by molecules found in the medium surrounding the particle. This concept was then transformed to an abstracted process that has been used in modeling the stock market and quantum mechanics (Dunbar, 2016). In other financial application, Louis Bachelier’s doctoral dissertation talks about the random and volatile movement of stock-market prices; he than proposed that the prices of a stock follows Brownian Motion (Shafer & Vovk, 2001). Bachelier stated that stock price change over nonoverlapping time intervals are independent and Gaussian with the variance of each price change being proportional to length of time involved (Shafer & Vovk, 2001). 3.1.2. Persistent Time Series A type of time series wherein an increase in values will most likely be followed by an increase in the short term and a decrease in values will most likely be followed by another decrease in the short term (Mansukhani, 2012). 3.1.3, Anti - Persistent Time Series In an anti-persistent time series, also known as a mean-reverting series, an increase will most likely be followed by a decrease or vice-versa (i.e., values will tend to revert to a mean). This means that future values have a tendency to return to a long-term mean (Mansukhani, 2012). 3.1.4. Efficient Market Hypothesis This theory refers to the informational efficiency of the market, the prices of the assets are reflected by all available information. …show more content…
Moreover, investors and traders will not be able to earn excess profits. Simply, this theory states that investors cannot beat the market (Jonathan Clarke, Tomas Jandik, Gershon Mandelker).
According to Malkiel (1992), The Efficient Market Hypothesis (EMH) is described in three different forms:
The weak form of the Efficient Market Hypothesis (EMH) claims that prices fully reflect all available past information in the historical sequence of prices. Consequently, investors cannot apply a strategy that may yield abnormal profits based on the analysis of past price movements (also known as technical analysis). This form of market efficiency is associated to the Random Walk Hypothesis.
The semi-strong form of the Efficient Market Hypothesis (EMH) claims that the prices do not only reflect past information but all publicly available information. Thus, if markets are efficient in this context, the analysis of balance sheets, income statements, or any other available public information (also known as fundamental analysis) will not produce an abnormal amount of profit. The strong form of the Efficient Market Hypothesis (EMH) claims that all available information known to anyone participating in the market about a company is reflected in market prices. Therefore, these individuals who have significant and sensitive information about the company cannot capitalize on their knowledge to obtain abnormal amounts of profit or a superior position in the market. 3.1.5 Hurst Exponent At times, investors do not react when there is no established trend because they wait for the confirmation of the information that is new. A biased random walk behavior is indeed led by an absorption of information that is uneven. The Hurst Exponent was made because of the existence of such biased random walk behavior (Peters, 1996). Even if the series is not distributed normally, the Hurst exponent could find a random series from a non-random series. Peters (1996) also mentioned that the Hurst Exponent has been a big application to many time series such as economic and capital market analysis. Since it is robust with few assumptions, the applicability is broad for analysis on time series. The values of the Hurst exponent range between 0 and 1 so based on the Hurst exponent value H, a
THE FRAMEWORKS
3.1 Theoretical Framework
Studies conducted in the past have contributed principles related to the estimation of the Hurst Exponent. The theories present in this research provide the foundation for estimating the Hurst exponent.
3.1.1. Brownian Motion theory
This theory was first coined by Robert Brown. It was primarily referred as the random motion observed under microscope of pollen immersed in water. In addition to that, Albert Einstein mentioned that this theory was caused by the random bombardment of (heat excited) water molecules on the pollen. Hence, it is just the molecular nature of matter. (Rodriguez, A.). Brownian motion was explained by assuming that the immersed particle was continuously batter by molecules found in the medium surrounding the particle. This concept was then transformed to an abstracted process that has been used in modeling the stock market and quantum mechanics (Dunbar, 2016). In other financial application, Louis Bachelier’s doctoral dissertation talks about the random and volatile movement of stock-market prices; he than proposed that the prices of a stock follows Brownian Motion (Shafer & Vovk, 2001). Bachelier stated that stock price change over nonoverlapping time intervals are independent and Gaussian with the variance of each price change being proportional to length of time involved (Shafer & Vovk, 2001). 3.1.2. Persistent Time Series A type of time series wherein an increase in values will most likely be followed by an increase in the short term and a decrease in values will most likely be followed by another decrease in the short term (Mansukhani, 2012). 3.1.3, Anti - Persistent Time Series In an anti-persistent time series, also known as a mean-reverting series, an increase will most likely be followed by a decrease or vice-versa (i.e., values will tend to revert to a mean). This means that future values have a tendency to return to a long-term mean (Mansukhani, 2012). 3.1.4. Efficient Market Hypothesis This theory refers to the informational efficiency of the market, the prices of the assets are reflected by all available information. …show more content…
Moreover, investors and traders will not be able to earn excess profits. Simply, this theory states that investors cannot beat the market (Jonathan Clarke, Tomas Jandik, Gershon Mandelker).
According to Malkiel (1992), The Efficient Market Hypothesis (EMH) is described in three different forms:
The weak form of the Efficient Market Hypothesis (EMH) claims that prices fully reflect all available past information in the historical sequence of prices. Consequently, investors cannot apply a strategy that may yield abnormal profits based on the analysis of past price movements (also known as technical analysis). This form of market efficiency is associated to the Random Walk Hypothesis.
The semi-strong form of the Efficient Market Hypothesis (EMH) claims that the prices do not only reflect past information but all publicly available information. Thus, if markets are efficient in this context, the analysis of balance sheets, income statements, or any other available public information (also known as fundamental analysis) will not produce an abnormal amount of profit. The strong form of the Efficient Market Hypothesis (EMH) claims that all available information known to anyone participating in the market about a company is reflected in market prices. Therefore, these individuals who have significant and sensitive information about the company cannot capitalize on their knowledge to obtain abnormal amounts of profit or a superior position in the market. 3.1.5 Hurst Exponent At times, investors do not react when there is no established trend because they wait for the confirmation of the information that is new. A biased random walk behavior is indeed led by an absorption of information that is uneven. The Hurst Exponent was made because of the existence of such biased random walk behavior (Peters, 1996). Even if the series is not distributed normally, the Hurst exponent could find a random series from a non-random series. Peters (1996) also mentioned that the Hurst Exponent has been a big application to many time series such as economic and capital market analysis. Since it is robust with few assumptions, the applicability is broad for analysis on time series. The values of the Hurst exponent range between 0 and 1 so based on the Hurst exponent value H, a