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.