# 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.