Time Series - Parameter Calibration

Introduction

Any statistical or machine learning model has some parameters which greatly influence how the data is modeled. For example, ARIMA has p, d, q values. These parameters are to be decided such that the error between actual values and modeled values is minimum. Parameter calibration is said to be the most crucial and time-consuming task of model fitting. Hence, it is very essential for us to choose optimal parameters.

Methods for Calibration of Parameters

There are various ways to calibrate parameters. This section talks about some of them in detail.

Hit-and-try

One common way of calibrating models is hand calibration, where you start by visualizing the time-series and intuitively try some parameter values and change them over and over until you achieve a good enough fit. It requires a good understanding of the model we are trying. For ARIMA model, hand calibration is done with the help of auto-correlation plot for ‘p’ parameter, partial auto-correlation plot for ‘q’ parameter and ADF-test to confirm the stationarity of time-series and setting ‘d’ parameter. We will discuss all these in detail in the coming chapters.

Grid Search

Another way of calibrating models is by grid search, which essentially means you try building a model for all possible combinations of parameters and select the one with minimum error. This is time-consuming and hence is useful when number of parameters to be calibrated and range of values they take are fewer as this involves multiple nested for loops.

Genetic Algorithm

Genetic algorithm works on the biological principle that a good solution will eventually evolve to the most ‘optimal’ solution. It uses biological operations of mutation, cross-over and selection to finally reach to an optimal solution.

For further knowledge you can read about other parameter optimization techniques like Bayesian optimization and Swarm optimization.