# COMPG001 - Financial Data and Statistics

**Note:** Whilst every effort is made to keep the syllabus and assessment records correct, the precise details must be checked with the lecturer(s).

Code | COMPG001 |
---|---|

Year | MSc |

Prerequisites | Students must be familiar with basic probability and statistics concepts. They must also have some familiarity with mathematical analysis. |

Term | 2 |

Taught By | Tomaso Aste (100%) |

Aims | The course is aimed at introducing to financial data analytics. The course is primarily focused on the observation of financial market dynamics of both individual assets and collective group of assets and the individuation of regularities, patterns and laws from a statistical perspective. Instruments to analyse, characterize, validate, parameterize and model complex financial datasets will be introduced. Practical issues on data analysis and statistics of high frequency and low frequency financial data will be covered. |

Learning Outcomes | Students will become able to analyse main statistical features of complex financial datasets. On successful completion of the course, a student should have a good understanding on: 1) the empirical probability distributions of financial returns; 2) how to characterize, parameterize and validate these distributions; 3) the quantification inter-dependency/causality structure between financial assets; 4) how to use the outcome of data-analytics to develop better tools for forecasting, valuation and risk management. Further information and material available to students on the course Moodle page. |

# Content

**Empirical investigation of financial market-data**Essential practical familiarization with financial data. Typical challenges with real financial data. Basics on data acquisition, manipulation, filtering, graphical representation and plotting.

**Statistical properties single financial asset**Statistical distribution of returns. Moments of the distribution. Non-Normal distributions and fat-tails. Large fluctuations and tail risk. Stable distributions. Generalized extreme value distribution. Estimation methods to characterize the tails of the distributions. Calibration and validation. Applications to measures of risk.

**Scaling laws**Random walks. Stochastic processes with non-defined variance. Fractal and multi-fractal nature of financial signals. Scaling laws. Persistence, anti-persistence and autocorrelation in financial signals. Hurst exponent, definition and characterization of multiscaling signals.

**Statistical properties of groups of financial assets**Marginal probabilities, joint probability, and conditional probability. Measures of dependency: linear and non-linear correlations. Lagged correlations and causality. Information theoretic perspective: mutual information, transfer entrophy. Spurious correlations. Correlation filtering through networks. Calibration, validation and application issues.

# Method of Instruction

3 hours of lectures per week.

# Assessment

The course has the following assessment components:

- Coursework (50%)
- Written examination (2.5 hours, 50%)

To pass this course, students must:

- Obtain an overall pass mark of 50% for all sections combined.

# Resources

**Recommended texts**Casella G. & Berger R. L.,

*Statistical Inference*, Brooks/Coles, 2002.

Bouchaud, J.- P. & Potters, M.,

*Theory of Financial Risk and Derivative Pricing: from Statistical Physics to Risk Management*, Cambridge University Press, 2003.

Lehmann, E. L. & Romano, J. P.,

*Testing Statistical Hypotheses*, Springer, 2006.

**Further reading**Coles, S.,

*An Introduction to Statistical Modeling of Extreme Values*, Springer, 2001.

Gumbel, E. J.,

*Statistics of Extremes*, Echo Point Books & Media, 2013.

Further books and other resources will be indicated during the course.