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      FIGURE 4-9: A comparison of patterns exhibited by time series.

If you’re including seasonality in your model, incorporate it in the quarterly, monthly, or even biannual period — wherever it’s appropriate. Time series may show nonstationary processes — unpredictable cyclical behavior that isn’t related to seasonality and that results from economic or industry-wide conditions instead. Because they’re not predictable, nonstationary processes can’t be forecasted. You must transform nonstationary data to stationary data before moving forward with an evaluation.

      Take a look at the solid lines shown earlier, in Figure 4-9. These represent the mathematical models used to forecast points in the time series. The mathematical models shown represent good, precise forecasts because they’re a close fit to the actual data. The actual data contains some random error, thus making it impossible to forecast perfectly.

      Modeling univariate time series data

      Similar to how multivariate analysis is the analysis of relationships between multiple variables, univariate analysis is the quantitative analysis of only one variable at a time. When you model univariate time series, you’re modeling time series changes that represent changes in a single variable over time.

Autoregressive moving average (ARMA) is a class of forecasting methods that you can use to predict future values from current and historical data. As its name implies, the family of ARMA models combines autoregression techniques (analyses that assume that previous observations are good predictors of future values and perform an autoregression analysis to forecast for those future values) and moving average techniques — models that measure the level of the constant time series and then update the forecast model if any changes are detected. If you’re looking for a simple model or a model that will work for only a small dataset, the ARMA model isn’t a good fit for your needs. An alternative in this case might be to just stick with simple linear regression. In Figure 4-10, you can see that the model forecast data and the actual data are a close fit.