# 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.category1category2

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:

ts(Array{Float,2}): 2-D input array of multivariate time-series.

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.