Signal processing is a field of engineering and applied mathematics that analyzes analog and digital signals, corresponding to variables that vary with time. One of the categories of signal processing techniques is time series analysis. A time series is an ordered list of data points starting with the oldest measurements first. The data points are usually equidistant, for instance, consistent with daily or annual sampling. In time series analysis, the order of the values is important. It's common to try to derive a relation between a value and another data point or combination of data points a fixed number of periods in the past, in the same time series.
The time series examples in this chapter use annual sunspot cycles data. This data is provided by the statsmodels package (an open source Python project). The examples use NumPy/SciPy, pandas, and also statsmodels.
We will cover the following topics in this chapter:
- Moving averages
- Window functions
- Cointegration
- Autocorrelation
- Autoregressive models
- ARMA models
- Generating periodic signals
- Fourier analysis
- Spectral analysis
- Filtering
To install statsmodels, execute the following command:
$ pip install statsmodels $ pip freeze|grep stat statsmodels==0.6.0
Open the pkg_check.py file provided in the code bundle, and change the code to list the statsmodels subpackages to get the following result:
statmodels version 0.6.0.dev-3303360 statsmodels.base statsmodels.compatnp statsmodels.datasets statsmodels.discrete statsmodels.distributions statsmodels.emplike statsmodels.formula statsmodels.genmod statsmodels.graphics statsmodels.interface statsmodels.iolib statsmodels.miscmodels statsmodels.nonparametric DESCRIPTION For an overview of this module, see docs/source/nonparametric.rst PACKAGE CONTENTS _kernel_base _smoothers_lowess api bandwidths statsmodels.regression statsmodels.resampling statsmodels.robust statsmodels.sandbox statsmodels.stats statsmodels.tests statsmodels.tools statsmodels.tsa