Miscalleneous

Here we regroup all additional useful functions that do not necessarily deserve a section of their own.

rate_evolution — Function

rate_evolution(series)

The rate of evolution is a way to test the stationarity of a categorical time-series. If the rate evolves more or less linearly, then the time-series can reasonably be considered stationary. It is most informative to plot the rate of evolution of each categories on the same graph for a direct visual inspection.

Parameters:

  • series (Array{any,1}): 1-D Array of categorical time-series.

Returns: RATE, Array containing, for each category, an array representing it's rate of evolution.

LaggedBivariateProbability — Function

LaggedBivariateProbability(serie, Lags::Array{Int64,1}, Category1, Category2)

Returns the lagged bivariate probability of two given categories, Pij. Given i and j two categories, and l a lag (or array of lags), Pij is the probability to have the category j at time t + l, if we have i at time t.

Parameters:

  • serie (Array{any,1}): 1-D Array of categorical time-series.
  • category1
  • category2

Returns: pij, Array containing, for each value in lags, the lagged bivariate probability.

varcov — Function

varcov(ts::Array{Float64,2})

Computes the covariance-variance matrix of a given multivariate time-series. This can also be used for a univariate time-series but the input should still be 2-D.

Parameters:

Returns: cov_matrix the correpsonding covariance matrix.

power_spectrum — Function

power_spectrum(x::Array{Float64,1}, window::Int, step::Int)

Computes an estimation of the power-spectrum of the input time-series x.

Parameters:

  • x (Array{Float,1}): 1-D Array of real-valued time-series.
  • window (Int): Integer specifying the size of the window for averaging Must be shorter than length(x). Recommended value is 1/10th of length(x).
  • step (Int): Parameters controlling the overlap between the windows. Shouldn't be biggger than div(window,2).

Returns: pxx, the estimated power-spectrum.