Semi-Markov Toolbox

Markov and semi-Markov toolbox

The semi-Markov Toolbox allows to create Markov and semi-Markov models based on a real discrete, or previously discretized, phenomenon. The input of the toolbox is a discrete time series that must be given through a file .mat with only one variable: the discrete time series.
At the link (https://sites.google.com/site/flavioprattico/download) it is possible to download a .mat file, namely data.mat, with wind speed discretized data, in order to test the app.
The toolbox permits to chose the data and matrices saving or not and the kind of model (Markov, semi-Markov or both models) . At the end of the Monte Carlo simulation the histograms of the probability distribution functions are shown in simple plot in order to check the validity of the modeling. The output mat file with all the variables will collocate automatically in the folder where the data are loaded. In the mat file you will find the following variables (in case you have chosen "both models"):
ZReal_Data: it is the real discretized time series
ZMarkov: it is the synthetic time series generated through Markov model
ZSemi_Markov: it is the synthetic time series generated through the semi-Markov model
ZP_Markov: it is the Markov transition probability matrix
ZP_Semi_Markov: it is the semi-Markov transition probability matrices
ZG_Semi_Markov: it is the conditional cumulative distribution functions of the waiting time in each state
See the references below for more details on semi-Markov models and their application, especially reference [1].

[1] D’Amico, Guglielmo, Filippo Petroni, and Flavio Prattico. "First and second order semi-Markov chains for wind speed modeling." Physica A: Statistical Mechanics and its Applications 392.5 (2013): 1194-1201.

[2] D'Amico, Guglielmo, Filippo Petroni, and Flavio Prattico. "Reliability Measures of Second-Order Semi-Markov Chain Applied to Wind Energy Production." Journal of Renewable Energy 2013 (2012).

[3] D'Amico, Guglielmo, Filippo Petroni, and Flavio Prattico. "Wind speed modeled as an indexed semi‐Markov process." Environmetrics 24.6 (2013): 367-376.

[4] D’Amico, Guglielmo, Filippo Petroni, and Flavio Prattico. "Performance analysis of second order semi-markov chains: An application to wind energy production." Methodology and Computing in Applied Probability (2014): 1-14.

[5] D’Amico, Guglielmo, Filippo Petroni, and Flavio Prattico. "Wind speed and energy forecasting at different time scales: A nonparametric approach." Physica A: Statistical Mechanics and its Applications 406 (2014): 59-66.