Introduction to Statistical Modeling Statistical Signal Processing Predictive Modeling

1. Possess and understand knowledge that provides foundations for the development and / or application of this knowledge, often, in a research context. 2. Apply the acquired knowledge to solve problems in new or unfamiliar environments within multidisciplinary contexts related to their area of study. 3. Integrate knowledge and face the complexity of formulating judgments based on information that, being incomplete or limited, should include reflections on the social and ethical responsibilities linked to the application of their knowledge and judgments. 4. Possess learning skills that allow them to continue studying in a way that will be self-directed or autonomous. 1. Apply the theoretical foundations of the techniques for the collection, storage, treatment and presentation of information as a basis for the development and adaptation of these techniques to specific problems. 2. Identify the most appropriate data analysis techniques for each problem and apply them for the analysis, design and resolution of these problems. 3. Obtain practical and efficient solutions for problems of treatment of data sets, both individually and as a team. 4. Synthesize the conclusions obtained from these analyzes and present them clearly and convincingly, both in writing and orally. 5. Be able to generate new ideas (creativity) and anticipate new situations, in the contexts of data analysis and decision making. 6. Use skills for teamwork and to relate to others autonomously. Specific Competences: 1. Use the basic results of statistical inference and regression as a basis for prediction methods. 2. Identify and select the appropriate software tools for the treatment of time series. 3. Use advanced statistical procedures for the treatment of time series in areas such as modeling, inference and prediction. 4. Design systems for the processing of time series, from the initial collection and filtering of them, their statistical analysis, to the presentation of the final results.

K3: To know fundamental contents in their area of study starting from the basis of general secondary education and reaching a level proper of advanced textbooks, including also some aspects of the forefront of their field of study. K5: Ability to understand and relate fundamental concepts of probability and statistics and be able to represent and manipulate data to extract meaningful information from them K10: To know and manage the fundamentals of analog and digital signal processing in the time and frequency domains, including sampling, filtering and transforms, with applications to signal processing in the field of Data Science and Engineering. S1: To plan and organize team work making the right decisions based on available information and gathering data in digital environments. S3: Ability to solve technological, computer, mathematical and statistical problems that may arise in data engineering and science, applying knowledge of mathematics, probability and statistics, programming, databases, and languages, grammars and automata. S4: Ability to solve mathematically formulated problems applied to various subjects, using numerical algorithms and computational techniques, and applying knowledge of: algebra; geometry; differential and integral calculus; numerical methods; numerical algorithms; statistics and optimization S5: Ability to correctly identify predictive problems corresponding to certain objectives and data, based on knowledge of algorithms, modeling, prediction and filtering, and to use the basic results of regression analysis as the basis for prediction methods C2: To develop those learning skills necessary to undertake further studies with a high degree of autonomy.

1. Introduction to time series 1.1 Examples of univariate time series 1.2 Examples of multivariate time series 1.3 Software for time series analysis 2. Time series decomposition. 2.1 Time series components. 2.2 Classical decomposition. 2.3 ARIMA decomposition. 2.4 STL decomposition. 2.5 Forecasting with decomposition. 2.7 Exponential smoothing techniques. 3. ARIMA models. 3.1 Stationarity and differencing. 3.2 Backshift notation 3.3 Autoregressive models. 3.4 Moving average models. 3.5 Non-seasonal ARIMA models. 3.6 Estimation and order selection. 3.7 Seasonal ARIMA models. 3.7 Forecasting with ARIMA models. 4. Advanced forecasting methods. 4.1 Dynamic regression models. 4.2 Vector autoregressions. 4.3 Dynamic factorial models. 4.4 Forecasting hierarchical or grouped time series. 5. Conditional heteroscedastic models. 5.1 GARCH models. 5.2 Statistical properties. 5.3 Estimating parameters and volatilities.

Theoretical classes with support material on the web. Practical classes of resolution of problems, with additional problems in the web and its solutions. Practical computer classes in computer rooms. Realization of a prediction project under the supervision of professors. For the realization of the project it will be required that the student uses statistical / econometric software for the construction of models and its application to predict. Oral presentations of the progress in the projects will be made with debates among the students and a final defense of the project.