The focus of this chapter was on understanding the fundamental tools that are useful in studying time series. Time series analysis is a very large field, but in this brief synopsis, we explored the basic concepts that are essential to further study. We started off by looking at some properties of time series such as the autocorrelation function and saw how this, along with the partial autocorrelation function, can provide important clues about the underlying process involved.

Next, we introduced stationarity, which is a very useful property of some time series that in a nutshell says that the statistical behavior of the underlying process does not change over time. We introduced white noise as a stochastic process that forms the basis of many other processes. In particular, it appears in the random walk process, the moving average (MA) process, as well as the autoregressive process (AR). These, in turn, we saw can be combined to yield even more complex time series.

In order to handle the non-stationary case, we introduced the ARIMA process, which tries to render a time series stationary through differencing. We also touched upon ARCH processes, which explicitly model how the variance of a non-stationary time series varies. ARCH models can be combined with ARMA models. Through a number of real-world data sets, we saw our models in action and explored a procedure to select suitable parameters for them. In particular, we noted that we often focus first on finding the order of a time series before learning the parameters of a time series model of that order. Finally, we wrapped up our discussion with a brief glimpse of some other important approaches to modeling time series.

In the next chapter, we'll look at topic models as a type of predictive model that has become very popular with the abundance of text available online. We will see that we can use topic models as a special case where our output is a mixture of different classes. At the same time, we will see how topic models can be used as a form of dimensionality reduction on a large feature set.