Lessons

Date	Recording	Title	Professor's notes	Description
02 21	Recording	Introduction Stochastic processes (SP)	1.1_MIDA_Introduction 1.2_MIDA_Stochastic_Processes	A general introduction to the course content and to stochastic processes.
02 22	Recording	Weak description of SP Stationary stochastic processes (SSP) White noise (WN) Moving average processes (MA)	1.2_MIDA_Stochastic_Processes 1.3_MIDA_Model_Classes	How to characterize a stochastic process using a weak description: - Mean function - Covariance function Definition of stationary stochastic processes and white noise. Definition of moving average (MA) processes and discussion about stationarity of MA.
02 23	Recording	MA stationary? Covariance properties for SSP MA(inf) processes MA(inf) stationary?	1.3_MIDA_Model_Classes	Demostration of the stationary of MA processes. Definition of some important properties of covariance function for SSP. Definition of moving average processes of infinite order MA(inf) and discussion about their stationarity.
02 28	Recording	Auto Regressive AR ARMA Steady state solutions Shift Operator Operational representation of ARMA Transfer function	1.3_MIDA_Model_Classes	Definition of AR and ARMA processes with the steady-state solution of both. Steady state solution of AR(1). A steady state solution is an MA(inf) process. Defining shift operators and their properties. Defining the operatorial representation of ARMA as well the steady state solution in this representation: the transfer function.
03 01	Recording	Transfer function composition (series/parallel) Switch shift operator powers Zeros and poles Assintotically stable Minimum fase When ARMA is well-defined?	1.3_MIDA_Model_Classes	Defined the different ways to compose transfer function and output processes: sereis and parallel. How to switch the powers of the shift operator from positive to negative and viceversa. Defined what zeros and poles of a transfer function are. When a transfer function is assintoticallt stable or a minimum fase. Discussion about when an ARMA process is well definded using the associated transfer function (with idea of proof).
03 02	Recording	Solutions different from steady-state Computing ARMA weak (wide-sense) characterization	1.3_MIDA_Model_Classes	Discussion about non steady-state solutions of the ARMA recursive equation, highlighting how they converge to the steady-state solution exponentially fast. Computing the weak (wide-sense) characterization of AR/ARMA processes which means computing the mean and the covariance using the recursive equation and the transfer function. We started from AR(1) and then discussed a general ARMA process.
03 08	Recording	Non zero mean ARMA Gain theorem Unbiased processes ARMAX Frequency domain Properties of spectrum Spectrum of digital filter output	1.3_MIDA_Model_Classes 1.4_MIDA_Frequency_Domain_Analysis
03 09	Recording	Spectrum antitrasformation Relation between covariance and spectrum Wiener-Kinchin theorem Spectrum of ARMA 4 sources of uniqueness of ARMA	1.4_MIDA_Frequency_Domain_Analysis
03 10	Recording	4th source of uniqueness of ARMA Canonical representation of ARMA Introduction to linear optimal prediction Mean square error	1.4_MIDA_Frequency_Domain_Analysis 1.5_MIDA_Prediction
03 15	Recording	Optimal linear predictor from noise Long k-step division Optimal linear predictor from output
03 16	Recording	Reconstructing WN from output values Predictors from finite sequence of values Optimal prediction of non-sero mean ARMA
03 22	Recording	ARMAX predictors Model identification introduction Black box and grey box model identification PEM identification
03 23	Recording	PEM identification cost function PEM cost function computation Least square identification