# The Econometrics of Time Series Data

• 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.