Often, data follows seasonal or cyclical trends. This is true not only for natural phenomena such as tides, weather, and wildlife populations, but also for human activities such as website hits and purchasing habits. Some trends are hourly, such as the times of day when people send an email (that is, mostly working hours), and others are monthly, such as the months when people buy the most ice cream, and then there's everything in between (per minute, per day of the week, per year, and so on). With seasonal data, if we just fit a linear trend to the data, we will miss most of the ups and downs that reflect the seasonal aspects. Instead, what we'll see is only the general long-term trend. Yet, sometimes we want to be able to forecast the next month's sales or the next week's website traffic. In order to do this, we will need a more refined model.
We will look at two approaches: autoregressive integrated moving average (ARIMA) and DLMs. In each case, we'll use a...