Time Series

Time series analysis is a very interesting area of reserch in many current subjects and, obiously, it is also very interesting in computer security. This kind of series can be used, for example, to protect the corporate image, to obtain behavior patterns, etc..
Time series are defined as a set of observations uniformly ordered throughout the time. One of the many ways to categorize this type of series is according to the number of random varibles used to obtain of the model:
  • Univariate: The time series are described by means os a single random variable (e.g. The evolution of petrol price).
  • Multivariate: The time series are described by means of more than a random variable (e.g. The creation of carbon dioxide (CO2) according to carbon and oxygen concentration).
On the other hand, time series are formed by the following elements:
  • Trend: It is a component of the time series that reflects its direction in a long period.
  • Seasonal variables: It is a component of the series based on the oscillations that occur around the trend. This kind of variables are repetitive in a short-term periods over the time.
  • Other fluctuations: Components of the series which takes the residual values of which are not explained by either the trend or seasonal variations. This component may or may not have a random behavior.
Something which is really interesting in the time series analysis is the possibility of forecasting the future values. Time series analysis and forecasting can be performed by means of several algorithms including regression (the simplest), the Holt-Winters algorithm (forecasting of time series based on the decomposition of the series) or the Box-Jenkins methodology.

Other current techniques for time series analysis and forecastig are, for instance, wavelets, segmentation based on patterns to forecast chaotic time series, or the identification of anomalies in time series based on dimension fractals difference on the serie, for example, identifying anomalies in the time serie calculating it distribution over space (along with their microfluctuations), Minkowski-Bouligand dimension, and comparing it with the new data in the time serie, Procacci-Grassberger algorithm. This last technique, based mainly on the chaos theory, derived from physics, which is in continious evolution.

Aitor Corchero Rodríguez
S21sec labs

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