## Model Components |
## SeasonalA seasonal component of a time series can be introduced when a time series reacts differently for each month, quarter, week, or even day of the week. This seasonal variation can be defined as repetitive and predictable movement around a trend line that changes based on the seasonal frequency. Thus, the seasonal component of a time series has a fixed or known length. A seasonal frequency is generally defined by the periodicity of the dataset or how frequently the observations are spaced in time. The seasonal frequency is defined as a model input and incorporated into each forecasting model as necessary.
Determining seasonality involves comparing the expected values for a given period (i.e. month, quarter, weekday) to the grand mean. We want to know, for any given time period, how far above or below the grand mean can the forecast be expected to land. Hence, the formula for a seasonal factor in the ith period is:where
Di is the average value for the ith period (i.e. monthly, weekly, quarterly, etc.) and D is the grand mean. So, this gives us an indication of the magnitude of the seasonal factor in a given month, week, quarter, etc. For example, a seasonal factor of 1.25 in a given month tells us that the expected value for that month is 25% above the grand mean. A factor of .8 for a given week tells us that the expected value for that week is 20% below the grand average. |