Detecting and correcting for trends
In Chapter 5, Time Series Forecasting as Regression, we talked about forecasting being a difficult problem because it is intrinsically an extrapolation problem. Trends are one of the major contributors to forecasting being an extrapolation problem. If we have a time series that is trending upward, any model that attempts to forecast it needs to extrapolate beyond the range of values it has seen during training. ARIMA handles this using autoregression, whereas exponential smoothing handles it by modeling the trend explicitly. But standard regression may not be naturally suited to extrapolation. However, with suitable features, such as lags, it can start to do that. But if we can confidently estimate and extract a trend in the time series, we can simplify the problem we have to apply regression to by detrending the time series.
But before we move ahead, it is worth learning about two major types of trends.
