Python libraries

There are a few popular libraries for classical time-series modeling in Python, but the most popular by far is statsmodels. The following chart compares the popularity of libraries in terms of the number of stars on GitHub:

Figure 5.3: Popularity of Python libraries for classical time-series forecasting

Statsmodels is clearly the most popular among these libraries. I've only chosen to include libraries that are actively maintained and that implement the algorithms directly rather than importing them from other libraries. The SkTime or Darts libraries, for example, offer traditional forecasting models, but they are not implemented there, but in statsmodels.

pmdarima (originally pyramid-arima) contains a parameter search to help fit the best ARIMA model to univariate time-series. Anticipy contains a number of models, such as exponential decay and step models. Arch implements tools for financial econometrics and functionality for Autoregressive Conditional Heteroscedasticity (ARCH).

While not as active as Scikit-Learn and only maintained by a couple of people, statsmodels is the go-to library for traditional statistics and econometrics approaches to time-series, with a much stronger emphasis on parameter estimation and statistical testing than machine learning.

Statsmodels

The statsmodels library can help to estimate statistical models and perform statistical tests. It's built on SciPy and NumPy and has lots of statistical functions and models.

The following table illustrates some of the modeling classes relevant to this chapter:

Class	Description
ar_model.AutoReg	Univariate Autoregression Model
arima.model.ARIMA	Autoregressive Integrated Moving Average (ARIMA) model
ExponentialSmoothing	Holt Winter's Exponential Smoothing
SimpleExpSmoothing	Simple Exponential Smoothing

Figure 5.4: A few models implemented in statsmodels

The ARIMA class also has functionality for SARIMA through a seasonal_order parameter, ARIMA, with seasonal components. By definition, ARIMA also supports MA, AR, and differencing (integration).

There are some other models, such as MarkovAutoregression, but we won't go through all of these – we will work through a selection.

Some other useful functions are listed here:

Function	Description
stattools.kpss	Kwiatkowski-Phillips-Schmidt-Shin test for stationarity
stattools.adfuller	Augmented Dickey-Fuller unit root test
stattools.ccf	The cross-correlation function
stattools.pacf	Partial autocorrelation estimate
stats.diagnostic.het_arch	Engle's Test for Autoregressive Conditional Heteroscedasticity (ARCH), also referred to as the ARCH-LM test
stattools.q_stat	Ljung-Box Q Statistic
tsa.seasonal.seasonal_decompose	Seasonal decomposition using moving averages
tsa.tsatools.detrend	Detrend a vector

Figure 5.5: Useful functions in statsmodels

As a convention, we import statsmodels like this:

import statsmodels.api as sm

These statsmodels algorithms are also available through SkTime, which makes them available through an interface similar to the Sklearn interface.

This should be enough for a brief overview. Let's get into the modeling itself!