Random Walk and Price Trends: The Live Cattle Futures Market

Abstract

A NOTABLE and provocative development in the recent literature has been the application of the theory of random walks to the analysis of price behavior in the stock and commodity futures markets. The basic hypothesis of the random walk theory is that a particular price series behaves as a simple stochastic process. Successive price changes are independent random variables, implying that the past history of a series generates no information that would be useful in predicting future price changes.Several authors have tested this independence hypothesis, but with mixed results. Many of the studies on stock market prices are contained in a book edited by Cootner [5], and some show evidence that stock prices behave as a random walk,' while others reject the theory.2 Similar recent testing on commodity futures prices has added to the controversy. Tied to this assortment of results has been a variety of analytical techniques, each with its own justification, ranging from sophisticated statistical tools, such as spectral analysis, to mechanical trading rules which attempt to generate speculative profits.Among the studies on commodity futures prices, Larson [13], using autocorrelograms, found evidence to support Working's [17] theory of anticipatory prices which implies that prices move randomly. Stevenson and Bear [16], who used an assortment of statistical tools and mechanical trading rules, concluded that corn and soybean futures prices move in a systematic rather than a random fashion. This tended to agree with earlier work done by Houthakker [11] who applied a stop-loss scheme to corn trading. On the other hand, Cargill and Rausser [3], utilizing spectral analysis on various futures contracts for 1967, including corn, concluded that "a simple stochastic process appears consistent with commodity markets price behavior."A major shortcoming of the entire analysis and a possible reason for the lack of wide acceptance for any single result is the failure to subject identical data to both statistical and mechanical filter tests. The consequence has been varying results, depending upon data and tests used. Only Stevenson and Bear have attempted to apply alternative statistical tools and mechanical trading rules to similar data. However, as will be noted later, one may quarrel with their choice of statistical tools-namely, serial correlation and runs analysis. It is the purpose of this paper to rectify this void in the literature by applying both a sophisticated statistical tool and mechanical filter tests to similar data. Spectral analysis along with several mechanical filters will be employed to test whether the live cattle futures prices move in a random or a systematic fashion.

Uso de análise espectral e regras de filtragem em operações com contratos futuros de soja no Brasil

“…Irwin e Uhrig (1984), ao aplicarem sistemas operacionais (trading systems) com base em indicadores de análi-se técnica, em séries de preços futuros agropecuários no período de 1960 a 1983, registraram lucratividade. Park e Irwin (2004 Nesse sentido, observa-se que Leuthold (1972) usou a análise espectral em conjunto com regras de filtragem nos mercados futuros de commodities agropecuárias, rejeitando a ocorrência de passeio aleatório e da HEM nos preços futuros de boi gordo. Identificou a possibilidade de arbitragem e padrões de lucratividade em operações com contratos futuros da commodity.…”

“…Para o teste, aplicou-se a análise espectral, por ser um instrumental estatístico robusto, indicando a aleatoriedade da série temporal, ao construir intervalos de confiança para os valores estimados, conforme Rausser e Cargill (1970) e Leuthold (1972).…”

“…A janela de lags de Parzen é geralmente utilizada em procedimentos de estimação. Os pesos são da forma (KOOPMANS, 1995;LEUTHOLD, 1972):…”

“…Adicionalmente, a rejeição da hipótese de passeio aleatório rejeita a hipótese de eficiência semiforte de mercado dos preços futuros de soja da BM&F-Bovespa (RAUSSER; CARGILL, 1970;LEUTHOLD, 1972;PRAETZ, 1979;GOSS, 1983).…”

“…A combinação de regras de filtragem com a análise espectral pode resultar em estratégias operacionais factíveis e lucrativas. Como ilustração, alguns autores avaliaram a HEM aplicando aná-lise espectral e regras de filtro em mercados futuros de commodities, obtendo resultados financeiros positivos nas operações simuladas (LEUTHOLD, 1972;MURPHY, 1987).…”