一個健全有效的證券市場應該具有完全競爭市場的特性，而完全競爭市場之價格變動為一隨機性序列。因此，設定證券價格變動習性為隨機漫步之假定，乃在驗證此項隨機變動習性。隨機漫步假定之條件有二：(1)證券之價格變動為獨立序列；(2)證券之價格變動服從同一型態之機率分配。
國際上知名的證券市場均有很多專家學者從事其證券價格變動習性之研究，目的即在探討證券價格變動是否呈隨機性走勢。發表論著中以研究具有機率理論依據的隨機漫步假定為最多，其中又以研究證券價格變動為獨立性序列的文獻較為完備。至於尋求共同的機率分配型態，則由於證券價格變動分配的穩定性問題 ，未有明確的定論，而以主張證券價格變動為Stable Paretian分配的文獻較為具體
證券價格變動分配是否具穩定性，直接影響及證券價格變動是否服從同一型態之機率分配。因為如果證券價格變動分配不具穩定性，則其共同之機率分配型態將因而無法求得。然而穩定性問題雖然早經發現，但週詳地從事此項研究的文獻，封延至1978年才提出。本論文為求一貫性與完整性，對台灣證券市場價格變動習性之研究，除包含對隨機漫步假定之兩項條件，即價格變動為獨立性序列，且服從同一型態之機率分配，進行實證分析外，並在尋求共同機率分配之前，先行驗證其價格變動分配的穩定性
對台灣證券市場價格變動為獨立性序列之實證結果，指出除少數證券因營運狀況之起伏、或財務結構之變異，造成其價格連續上漲或連續下跌而導致價格變動略呈相依性外，就整體市場而言，其證券價格之變動，符合隨機漫步之獨立性假定。
對價格變動分配穩定性探討的結果，顯示台灣證券市場之價格變動序列具穩定性。惟在運用累積樣本標準差之趨勢驗證穩定性時，雖然發現明顯的收斂趨勢，但是否收斂至某一常數，則因受到樣本時隔的限制，而未有定論。
由於台灣證券市場之價格變動分配呈穩定性，故同一型態之機率分配應該存在，實證結果顯示台灣證券市場之價格變動分配，符合Stable Paretian分配的性質。惟該分配除包含常態分配與Cauchy分配兩特例外，並無固定的機率密度函數。故推定其母參數時，只能利用其性質，而所獲得之結果亦僅為近似值而已，不如一般運用機率密度函數推定之正確。
因此，就整體市場而言，台灣證券市場之證券價格變動，符合隨機漫步假定之兩項條件：(1)價格變動呈獨立性序列，(2)其共同分配型態為Stable Paretian分配，故台灣證券市場已可視同一個完全競爭市場。

A healthy and efficient stock exchange should possess the characteristics of a perfect competitivemarket, wherein price fluctuation patterns behave as a random sequence. To hypothesize that security price fluctuations follow the random walk pattern is to test the randomness character of the price fluctua-tion patterns. The hypothesis of random walk is based on two conditions: (l)the changes in security prices should be an independent sequence, and (2) they are identically distributed.
Most well established stock exchanges in the world have experts to analyze price fluctuation patterns. Their purpose is to investigate the randomness trend of stock price fluctuations. A large portion of the papers published thus for investigate the validity of random walk hypothesis based on the theory ofprobability. A majority of the papers which treatschanges in security prices as an independent, sequence are relatively complete. As to the question whether price changes are Identically distributed, no con- clusion has been reached because of the lack ofstationary properties in stock price fluctuation dis- tribution. However, most of the literature which support the stable paretian distribution assumption are to a certain extent complete.
Whether the change in security prices are identically distributed is directly affected by the statlonarity of the sequence of price changes. If there is no stationarity in price changes, no commondistribution can be found because of the non- existence of such distributions. Though the problem of stationarity was first brought up a number of years ago, detailed literature did not appear until 1978. For consistency and completeness, this paper will test the stationarity of the distribution of price changes before trying to find the common distribution while investigating and analyzing the two conditions of random walk hypothesis, that is the changes in security prices form an independentsequence and are identically distributed.
The results of an extensive research support the independence hypothesis with respect to the overall price fluctuations of the stock market with the exception of a few securities which appear to have steady price increasing or decreasing trends because of fluctuation in operations and/or changes in financial structure.
The results of this study show conclusive evi-dences that price changes are stationary in Taiwan stock market. We found obvious converging trend in testing the stationarity using the cumulative samplestandard deviation. However, we do not know whether it will converge to a constant because of the limi- tation ofsamnie time intervals.
Since the results support the stationarity, a common distribution should exist. In fact, the evidences show that the distribution of securityprice changes in Taiwan stock market is the stableparetian distribution.
The results of this paper support the two conditions of random walk hypothesis. Therefore, Taiwan stock market should approximately be a perfect competitive market.