Let's turn to how you choose your ARIMA parameters when designing a trading model. When you run a ARIMA models you have six key decisions to make, choose the Data: d, p, and q, type of ARIMA model, estimation method and finally choose the best model overall. First, you must decide how much data to use. Through experience I've often found that this is the most difficult step in the entire process. When you use financial data you're likely to have too much data rather than too little data. You may collect trade data at a daily frequency, may even find trade data at intraday frequencies, like every hour or every minute, and you may even find data that is based on quotes, that is bid prices, bid sizes, ask prices, ask sizes. Remember that all of these have associated observation times. Second, you must decide which value of d to use, when d is zero you use the data as is, when d is one you take the first differences. For example, suppose you work with equity prices, if you decide to work with prices then d is equal to zero, if you work with log returns then you effectively choose d to be equal to one. Once you have the form of the data, the analysis takes different paths. Suppose instead you work with bond yields, if you decide to work with yields then d is equal to zero, if you work with yield changes then you effectively choose d to be one. The general term for prices or yields is levels, the general term for returns or yield changes is differences. If you use levels you will get one set of results, if you use differences you will get a different set of results. Neither model may be incorrect, however, you may be more justified in using one model than the other. Third, you must select the values of p and q. Recall that p is the number of AR lags and Q is the number of MA lags. These values have to be integers but remember you can also choose them to be zero. Fourth, you choose the type of ARIMA model. When you dig deeper you will find that there are several varieties. Most likely you are running this on software, you will find a number of ARIMA models, some do fractional estimation, some adds seasonality. Fifth, you choose the method of estimation. Unlike the parameters in the linear regression models, the parameters in ARIMA models are more difficult to estimate. The method of estimation is key, you might use maximum likelihood, quasi maximum likelihood, generalized method of moments, non-parametric methods and estimation, and even estimation by simulation. Often you may think the software does this for you, but you really have to identify what the software uses as default. If you don't explicitly choose an estimation method, the software will do so, but that is still a choice you make. Based on your choices you now have a set of estimated parameters coefficients. You're six choices determine these values. You may certainly run more than one model, and so choose among candidate models based on some model criteria. Once you have selected the best model, then refer to the values the software has provided. These values will be your tools for making predictions. All of your decision-making leads you to a set of weights. If you had a positive value for p, then you get values for the weighting of the lagged observations. These are the coefficients of the AR terms. If you had a positive value for q, you get the weightings of the lagged unobserved or error terms. So the sixth and final choice you make is easy to state, you choose the values of the parameters.