Time Series Analysis
These lectures are centred on a particular kind of data: time series.
Time series definition
Formally we define a time series as a realisation of a random process.
Roughly speaking, a random process is a family of stochastic variables over some probability space $\left(\Omega, \mathcal{F}, p\right)$.
\[\mathcal{X} := \left\{x_i(\omega) \ \vert \ i\in \mathcal{T} \right\}\, .\]Hence, a time series can be represented as a sequence of values
\[y(t_i) = y_i \qquad \text{at times} \qquad t_i \, ,\]and we might also have at each time step some auxiliary features
\[X(t_i) = X_i \, ,\]which we think are related with the values of $y_i$.
Practical time series analysis
We are going to illustrate some pandas methods to treat time indexed data and to extract useful information out of them.
Time series decomposition
A very important skill is to separate the time phenomena into their basic components to split the analysis and to weight contributions.
Time series forecast
We give some examples of models to forecast the future behaviour of time indexed data.