# Financial Time Series

Analysis, Modelling and Applications

##### Location
Prague, NH Hotel Prague
N/A
N/A
English
##### Evaluation
N/A
Trends, Cyclical and Seasonal Variations
Linear Time Series Analysis
Forecasting Economic and Financial Variables
Using Autoregressive Models for Financial Forecasting
Testing and Correcting for Seasonality in Financial Time Series
Using ARCH Models to Predict Variance
Analyzing High-Frequency Data
Using Time Series Analysis in Financial Management
The purpose of this course are to give you a good understanding of financial time series, of the statistical tools used for analyzing these series, and of the practical applications of various econometric methods.

We start with a general introduction to time series analysis, and we explain how dynamic behavior of economic or financial variables (such as trends, cyclical variations, and seasonal variations) can be modelled and forecasted and how relationships between the time series of different financial variables and economic indicators can be detected.

We introduce and explain the concept of linear time series analysis. We describe linear models for handling serial dependencies and we discuss regression models with time series errors, seasonality, unit-root non-stationarity, and long-memory processes. We discuss the structure of an autoregressive model of order p, and we calculate one- and multiple-period ahead forecasts given the estimated coefficients, and we explain how autocorrelations of the residuals can be used to test whether the auto regressive model fits the time series. We describe the characteristics of random walk processes, and contrast them to covariance stationary processes. We also discuss how to test and correct for seasonality in a time-series model.

We then turn to the modelling of conditional heteroscedasticity. We introduce various econometric models (such as ARCH and GARCH), that describe the evolution of asset returns over time, and we demonstrate the use of these models to forecast volatility/variance over short and long horizons.

Further, we address the non-linearity in financial time series, introduce test statistics that can discriminate linear from non-linear series, and we present and discuss several non-linear models.

We explain how "high-frequency" financial data can be analysed and we show how serial correlations in e.g. stock returns can result from non-synchronous trading and "bid-ask" bounce. We also look at the dynamics of time duration between trades and at econometric models for analyzing transaction data.

We conclude with a complete practical case study of the use of time series analysis to improve portfolio management decision-making in a real-life investment setting.

# Program of the seminar: Financial Time Series

The seminar timetable follows Central European Time (CET).

## 09.15 - 12.00 General Introduction to Time Series Analysis

• Financial Time Series and their Characteristics
• Asset returns
• Dynamics of time series
• Trends, cyclical and seasonal variations and irregular variations
• Overview of Applications in Finance

## Linear Time Series Analysis

• Stationarity
• Random Walk Processes
• Correlation and Autocorrelation Functions
• White Noise and Linear Time Series
• Linear and Log-linear Trend Models
• Structure
• In-sample and out-of-sample forecasts
• Calculating predicted trend values given the estimated coefficients
• Small Exercises

## 13.00 - 16.30 Linear Time Series Analysis (Continued)

• Mean Reversion
• Autoregressive Models
• Moving Average Models
• ARMA Models
• Unit-Root Non-Stationarity
• Seasonal Models
• Testing and correcting for seasonality in a time-series model
• Examples: Seasonal adjustment of economic time series
• Regression Models with Time Series Errors
• Long-Memory Models
• Small Exercises

## 09.15 - 12.00 Conditional Heteroscedastic Models

• Volatility and Its Characteristics
• Analyzing Time Series for Nonstationarity
• Testing for Cointegration
• The ARCH Model
• The GARCH Model
• Random Coefficient Autoregressive Models
• Long-Memory Stochastic Model
• Examples of Applications
• Predicting variance with ARCH and GARCH models

## Non-Linear Models and their Applications

• Non-Linear Models
• Non-Linear Forecasting
• Example of Applications

## 13.00 - 16.30 High-Frequency Data Analysis

• Duration Models
• Non-Linear Duration Models
• Bivariate Models for Price Change and Duration

## Case Study: Using Time Series Analysis to Improve Portfolio Decisions

• Forecasting Stock and Commodity Prices