Forecasting share prices using Box-Jenkins methodology : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Statistics at Massey University

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Massey University
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Share Market efficiency has been extensively tested in financial and economics literature since the 1960's. Most of this research supports the weak and semi-strong efficient market hypothesis. However Umstead (1975) and (1977) found that aggregate quarterly share prices are inefficient enough so that application of Box-Jenkins Time Series techniques to publicly available information could have permitted an investor to earn an excess or ''above average" portfolio return. This study undertakes a similar statistical investigation of aggregate quarterly share prices in a New Zealand setting (using the Reserve Bank of New Zealand Index). The period covered by the study is March 1961 to December 1986 i.e. a total of 104 Quarterly observations. Initially, a univariate ARIMA model is built. Model parameters are estimated using only the first 76 observations (Mar 1961 - Dec 1979), and tested using the most recent 28 observations (Mar 1980 - Dec 1986). The model is evaluated (a) by computing a predicted R2, over the test period, (b) by observing the "hit rate" for correct and incorrect trading decisions, and (c) by constructing suitable trading rule tests i.e. simulating the results of three alternative portfolio strategies which could have been followed in the test period. The model is found to be successful at forecasting share price changes one quarter ahead, when compared with a naive forecast. The following conclusions are reached: (i) The sequence of aggregate quarterly share prices is not best described as a Random Walk but rather as a seasonal moving average ARIMA process. (ii) The sharemarket is efficient to the degree that significant trading benefits could not have been made over the test period utilising only publicly available information of previous prices (in the presence of 5 % round trip transaction costs and taxation). These conclusions appear to support Fama's definition of a weak-form efficient market.
Stocks, Prices, Mathematical models