Market Forecasting Model: ARIMA by Albert E. Parish Jr., Ph.D.
Numerous statistical and time series techniques have been adapted for use in modeling futures prices series by using the microcomputer. One such model is the AutoRegressive Integrated Moving-Average (ARIMA) method. Let us demonstrate the use of the model in trading by applying it to the Chicago Board of Trade (CBOT) wheat contract.
Some background in time series analysis is necessary before we can discuss the specifics of ARIMA modeling. If Pt represents the closing price, let Pt be the CBOT wheat contract on day t. On any given day, the closing price is a random variable, so it can take on one of a range of values, each with a certain probability of occurrence. For the wheat contract, this range of values is defined by adding and subtracting the daily price limit of 20 cents to the previous day's closing price. The variable Pt is determined by a distribution that assigns a probability of occurrence to each possible value on day t- A set of T days of observations is a portion of a probability distribution of a long sequence of observation extending far into the future and the past. Observations are made on different days are usually dependent on one other, and it is this statistical dependence that time series analysis studies. I used 1,054 days for the wheat contract from July 3, 1983, through July 30,1987.