# STATISTICAL SCIENCES FOR FINANCE | TIME SERIES ANALYSIS

## STATISTICAL SCIENCES FOR FINANCE TIME SERIES ANALYSIS

 0222400034 DEPARTMENT OF ECONOMICS AND STATISTICS EQF7 STATISTICAL SCIENCES FOR FINANCE 2022/2023

 OBBLIGATORIO YEAR OF COURSE 1 YEAR OF DIDACTIC SYSTEM 2014 AUTUMN SEMESTER
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY SECS-S/01 10 60 LESSONS COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS
 CIRA PERNA T
ExamDate
TIME SERIES ANALYSIS 04/04/2023 - 09:30
TIME SERIES ANALYSIS 04/04/2023 - 09:30
Objectives
KNOWLEDGE AND ABILITY OF COMPREHENSION
THIS COURSE ATTEMPTS TO GIVE AN INTRODUCTORY ACCOUNT OF TIME SERIES MODELS AND THEIR APPLICATION TO MODELLING AND PREDICTION OF DATA COLLECTED SEQUENTIALLY IN TIME. THE AIM IS TO PROVIDE SPECIFIC TECHNIQUES FOR DATA ANALYSIS AND AT THE SAME TIME TO PROVIDE SOME UNDERSTANDING OF THE THEORETICAL BASIS FOR THE INTRODUCED TECHNIQUES AND MODELS. TOPICS COVERED WILL INCLUDE UNIVARIATE STATIONARY AND NON-STATIONARY MODELS, ARMA/ARIMA MODELS, MODEL IDENTIFICATION AND ESTIMATION. DETAILED IMPLEMENTATION OF THE MODELS WITHIN DATA EXAMPLES USING THE R STATISTICAL SOFTWARE WILL BE CONSIDERED.
THE AIM OF THIS COURSE IS: TO INTRODUCE THE STUDENTS TO THE MAIN DEVELOPMENTS IN TIME SERIES ANALYSIS; TO LEARN THEORETICAL, APPLIED AND COMPUTATIONAL METHODS FOR TIME SERIES ANALYSIS AND FORECASTING; TO GAIN EXPERIENCE IN MODEL BUILDING.
THE STATISTICAL TOOLS INTRODUCED IN THE COURSE WILL BE PRESENTED HIGHLIGHTING SOME IMPORTANT THEORETICAL RESULTS AND THEIR POSSIBLE IMPLEMENTATION IN EMPIRICAL CONTEXTS. THE STUDENT WILL BE PROVIDED WITH TOOLS ON HOW TO SELECT AND USE THE APPROPRIATE STATISTICAL TOOLS FOR THE ANALYSIS OF TIME SERIES, AS WELL AS ON HOW TO INTERPRET AND COMMENT ON THE RESULTS.

ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING
STATISTICAL TOOLS INTRODUCED IN THE COURSE WILL BE PRESENTED WITH THE PURPOSE TO HIGHLIGHT SOME IMPORTANT THEORETICAL RESULTS AND THEIR POSSIBLE IMPLEMENTATION IN EMPIRICAL CONTEXTS
THE STUDENT WILL BE GIVEN EVIDENCE OF HOW TO SELECT AND USE THE APPROPRIATE STATISTICAL TOOLS AS WELL AS HOW TO INTERPRET AND COMMENT THE RESULTS OF THE ANALYZES PERFORMED

Prerequisites
STATISTICS
Contents
THE COURSE IS 60 HOURS (10 CFU) FOR THE MASTER DEGREE IN STATISTICAL SCIENCES FOR FINANCE,

CHARACTERISTICS OF TIME SERIES. (5H)
THE NATURE OF TIME SERIES DATA. TIME SERIES STATISTICAL MODELS. MEASURES OF DEPENDENCE: AUTOCORRELATION AND CROSS-CORRELATION. STATIONARY TIME SERIES. ESTIMATION OF CORRELATION.

TIME SERIES DECOMPOSITION. (10H)
THE COMPONENTS OF A TIME SERIES. CLASSICAL DECOMPOSITION. STL DECOMPOSITION. BOX-COX TRANSFORMATION

STOCHASTIC PROCESSES. (15H)
THE BACKWARD AND FORWARD OPERATORS. WEAK AND STRONG STATIONARITY. GAUSSIAN STOCHASTIC PROCESSES. LINEAR STOCHASTIC PROCESSES. WOLD’S DECOMPOSITION. ERGODICITY. INVERTIBILITY

AUTOREGRESSIVE INTEGRATED MOVING AVERAGE (ARIMA) MODELS (20H)
INTRODUCTION, LINEAR MODELS FOR STATIONARY TIME SERIES. STATIONARITY, STATIONARY TIME SERIES,
GENESIS OF ARMA MODELS. FINITE ORDER MOVING AVERAGE (MA) MODELS. THE FIRST-ORDER MOVING AVERAGE MODEL, MA(L ). THE SECOND-ORDER MOVING AVERAGE MODEL, MA(2). FINITE ORDER AUTOREGRESSIVE MODELS. FIRST -ORDER AUTOREGRESSIVE MODEL, AR(L ). SECOND-ORDER AUTOREGRESSIVE MODEL, AR(2). GENERAL AUTOREGRESSIVE MODEL, AR(P). AUTOCORRELATION FUNCTION AND PARTIAL AUTOCORRELATION FUNCTION. MIXED AUTOREGRESSIVE-MOVING AVERAGE (ARMA). MODELS. NONSTATIONARY MODELS. INTEGRATED ARMA MODELS. TIME SERIES MODEL BUILDING. MODEL IDENTIFICATION. PARAMETER ESTIMATION. DIAGNOSTIC CHECKING. EXAMPLES OF BUILDING ARIMA MODELS. SEASONAL PROCESSES. FORECASTING ARIMA PROCESSES

ADDITIONAL TIME DOMAIN TOPICS. (10H + 3H FOR THE STUDENTS OF DATA SCIENCE AND INNOVATION MANAGEMENT)
INTRODUCTION. LONG MEMORY ARMA AND FRACTIONAL DIFFERENCING .UNIT ROOT TESTING. GARCH MODELS. THRESHOLD MODELS. A REVIEW OF NON-PARAMETRIC METHODS IN TIME SERIES ANALYSIS.

Teaching Methods
LECTURES (40H) AND PRACTICAL EXERCISES (20H + 3H FOR THE STUDENTS OF DATA SCIENCE AND INNOVATION MANAGEMENT)
Verification of learning
PROJECT WORK WITH DISCUSSION AND ORAL EXAMINATION
THIS COURSE HAS MANDATORY PROJECT WORK AS AN ESSENTIAL LEARNING ACTIVITY: STUDENTS ARE ASKED TO FIND AND ANALYSE THEIR OWN REAL TIME SERIES USING R PACKAGE THE PROJECT WORK IS DONE IN GROUPS OF 1-3 STUDENTS AND IS EVALUATED ON THE BASIS OF A WRITTEN REPORT. ACTIVE PARTICIPATION IN THE GROUP WORK IS REQUIRED THROUGHOUT THE PROJECT WORK TO PASS.THE INDIVIDUAL DISCUSSION OF THE PROJECT WORK IS AN ELEMENT OF EVALUATION. EACH STUDENT IS GRADED INDIVIDUALLY ON THE BASIS OF THE DISCUSSION OF THE PROJECT.
THE SECOND TEST CONSISTS OF AN ORAL EXAMINATION (MANDATORY) ON THE TOPICS OF THE COURSE. STUDENTS WILL BE EVALUATED BY USING A SCALE OF 30.
Texts
SHUMWAY R.H. AND STOFFER D.S. TIME SERIES ANALYSIS AND ITS APPLICATIONS, WITH R EXAMPLES (THIRD EDITION), SPRINGER, 2011