Another way to model time series is to think of the stock return hovering around in moving average. As an analogy, imagine that you’re walking at night while holding a lantern, a moth flies around the lantern, moving a bit randomly, but still following the general path of your lantern. In this analogy, the lantern represents the average position. The moth’s smaller movements relative to the lantern are the residuals. The moth’s movement relative to the ground is a combination of the lantern’s movement and the moth’s relative movements. In the moving average model, often called an MA model, we started with the average Mu. To get the value at time T, we add a linear combination of residuals from the previous time periods. In financial time series, the residuals represent the new unpredictable information that cannot be captured by the past data points. The residuals are the difference between the model’s past predictions with the actual values that occurred. Moving average models are defined as MAQ where Q is the lag. To decide the best value for Q in an MAQ model, you can draw an autocorrelation plot. Correlation between two variables is a measure of how much one variable moves when the other variable moves. Correlation ranges between negative one and one. Autocorrelation is a measure of how much the current value moves in relation to one of its previous values. For example, let’s say we noticed that the current stock return is usually positive when its previous value is positive, and vice versa. Then, we can say that the stock has a positive autocorrelation with it’s T minus 1 value. Note how an autocorrelation plot is different from performing a multiple regression. Correlation measures the pairwise relationship between exactly two periods at a time. Multiple regression measures how a set of independent variables collectively influence the value of the dependent variable. When we view an autocorrelation plot, we want to use the lag that contains highly positive or highly negative correlations. When we reach some time periods with little correlation, we can choose the lag to ignore those values and any other time periods further back in time.