# Alternative Investment markets Essay

The Gil-Alana (2006) description of time series behaviour of stock market indexes by a fractional representation serves as the foundation for this study of weak form efficiency in the London Stock Exchange. Such a possibility could be due to long-memory or nonlinearities and has serious consequences for the efficient market hypothesis in stock markets. This study utilises the time-series of individual share prices for one hundred companies from the London Main (FTSE) and Alternative Investment (AIM) markets.

A simple Fraction Augmented Dickey-Fuller (FADF) test explores long-memory utilising a range of consistent estimates of the fractional differencing parameter d. Application of random field-based tests and traditional tests for structural breaks, examine the possibility for non-linearity. ? Weak form efficiency posits that the current share price fully reflects the information implicit in the share price history of a company.

This implies that the share price time series, say {Pit}T/t=0 for share i, does not exhibit serial correlation or “memory”. Recent literature puts forward the case for a generic random walk type model, albeit one with less stringent assumptions than those imposed in earlier literature on market efficiency. Traditionally the analysis has been whether {Pit}T/t=0 is I(1) or I(0). In the I(0) case, Pit is

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covariance stationary and displays the property of short-memory. In the I(1) case, Pit is non-stationary and non-mean reverting.

Fractional integration relaxes the assumption that the differencing parameter d is an integer. Therefore, a time-series process with 0 < d < 1 is defined as a long-memory process. If 0 < d < 0. 5 the series Pit is covariance stationary, but the autocorrelation function is more persistent with a longer decay period, than when d = 0. If 0. 5 ? d < 1, Pit is not covariance stationary, but it is mean reverting, with a persistent, slowly decaying autocorrelation function.

Thus, if Pit is I(d) with o < d < 1 it exhibits memory and is then not consistent with weak form efficiency. While studies focusing on the non-stationary nature of time series have dominated the literature, increasing attention is focusing on the issue of whether series that appear integrated of order < 0 are actually non-linear stationary series. Al-Loughani and Chappell suggests this non-linearity may be the cause of negative results with regards to many tests and variables.

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