Overview

In this course, you will look at models and approaches that are designed to deal with challenges raised by time series data. The discussion covers the motivation for the use of particular models and the description of the characteristics of time series data, with a special attention raised to the potential memory. You will: – Discuss time series models, that refer to data that have been collected over a period on one or more variables for the same individual. – Explore both on stationary and non-stationary time series models, as well as the difference between the non-stationary data and the trend-stationary processes – Consider the problems that may occur with non-stationarity data. – Discover the applications of time series models that are of use when we want to model the GDP growth of an economy, and to test for the Purchasing Power Parity Hypothesis. – Explore the idea of forecasting using econometric models. – Discuss different criteria to decide how good your in-sample and out-of-sample forecasts are. – Explore the problem raised by data where the variance is non-constant, and models for volatility forecasting. – Estimate ARCH(p) and GARCH(p,q) models for volatility with real financial market data and present how to extend these models to the mean of the time series via Garch-in-mean. It is recommended that you have completed and understood the previous three courses in this Specialisation: The Classical Linear Regression Model, Hypothesis Testing in Econometrics and Topics in Applied Econometrics. By the end of this course, you will be able to: – Manipulate and plot the different types of data – Estimate and interpret the empirical autocorrelation function – Estimate and compare models for stationary series – Test for non-stationarity of time series data – Estimate and interpret cointegration equations – Perform in-sample and out-of-sample forecasting exercises – Estimate and compare models for changing volatility

Syllabus

Time Series Data

This week’s materials present a number of time series observations. We look at white noise, trend stationary and non-stationary time series. We explore both at real observation about the GDP and to financial markets observations, and to generated series of data. We introduce both the idea of autocorrelation function and that of partial autocorrelation function as tools to understand the degree of persistency in a series of data.

Stationary Time Series Models

This week we deal with stationary time series models. We present white noise, moving average, autoregression and autoregressive and moving average models. We describe the models and the different types of autocorrelation functions you have in each of these cases. We also discuss the problem of estimating the order of the autocorrelation and moving average models. We study the idea and the challenges raised by forecasting, and that’s raised by high persistency of the impact of shocks on the observed series.

Non-Stationary Time Series Models

This week we consider the problems raised by non-stationarity of time series observations. We define non-stationarity of time series data, and present the tests for non-stationarity, including the challenges raised by near non-stationarity, and that of potential correlation of the estimating model when testing for non-stationarity. We present a full example to show what are the consequences in cases where we adopt the classical linear regression model when observations are non-stationary. We introduce the idea of cointegration and present introductory models to test whether the variables are cointegrated.

Models for Changing Volatility

This week’s materials discuss some stylised facts present across financial market returns, independent of the period, the financial tool and the market we study, that are volatility clustering and aggregational gaussianity. We discuss why these models, being nonlinear in nature, cannot be estimated via the classical linear regression model, and discuss and estimate some examples of autoregressive conditional heteroscedastic models. We discuss advantages and shortcomings of these models; building on the latter, we present some generalisation of the approach to generalised conditional heteroscedastic models (GARCH), GARCH-in-meena, TGARCH amd IGRACH models.