For the Fractionally Augmented Dickey Fuller test (illustrated in Table 1), a series is classified as either fractional or I(1) when over 85% of the results show consistency. In all fractional cases, d was non-stationary. FTSE 100 had 64% of the larger companies exhibited signs of fractionality, indicating an inefficient market. 32% proved to be weak form efficient, while 4% were indeterminate. Smaller companies proved 92% weak form efficient, with none proving fractional and 8% indeterminate.
Contrary to expected results for the relative size hypothesis, the larger companies prove, overall, to be inefficient when compared to smaller companies on the FTSE 100. The AIM results proved far less striated, yet still opposite by majority. 76% of the larger companies show weak form efficiency, with only 8% fractionality and 16% indeterminate. Smaller companies matched the FTSE less convincingly with 44% weak form efficient, 24% fractionality and 32% indeterminate.
AIM results overwhelmingly point larger companies as weak form efficient, although the majority of small companies did as well, on a much reduced scale. Table 2 illustrates the results from the Hamilton-Dahl and Bai-Perron tests for linearity. Given side-by-side for comparison, it should be noted that each variable had four tests applied for each method or model. These linearity tests proved inconclusive for the FTSE 100 in both large and small companies.
Regarding the AIM results, one can discern a relative trend in the larger companies, but again, the results are inconclusive over all. The increased probability of non-linearity amongst smaller companies together with the larger number of inconclusive fractionality results may find explanation in thin trading. In conclusion, the London Stock Exchange does not perform as expected concerning the weak form efficient market hypothesis as posed originally by Eugene Fama across the board. While some portions of the study indicate compliance, not all aspects indicate truth in the hypothesis.
The non-linear results of the one large and two smaller companies within the FTSE 100, indicate a more chaotic state for this particular trading entity. The same holds true for the four large and eight small companies on the AIM. The smaller companies on the FTSE 100 indicate weak form efficiency more so than the larger ones. The AIM results are exactly opposite. Larger companies proved weak form efficient, whereas smaller companies showed some signs, but not overwhelmingly so. More research into the specifics of the market styles and information dissemination is needed.