In the last chapter, we focused on linear models tailored to cross-sectional data where the input data belongs to the same time period as the output they aim to explain or predict. In this chapter, we will focus on time series data where observations differ by period, which also creates a natural ordering. Our goal will be to identify historical patterns in data and leverage these patterns to predict how the time series will behave in the future.
We already encountered panel data with both a cross-sectional and a time series dimension in the last chapter and learned how the Fama-Macbeth regression estimates the value of taking certain factor risks over time and across assets. However, the relationship between returns across time is typically fairly low, so this procedure could largely ignore the time dimension. The models in this chapter focus on time series models where past values contain predictive signals about future developments. Time series models can also predict features that are then used in cross-sectional models.
More specifically, in this chapter, we focus on models that extract signals from previously observed data to predict future values for the same time series. The time dimension of trading makes the application of time series models to market, fundamental, and alternative data very popular. Time series data will become even more prevalent as an ever broader array of connected devices collects regular measurements that may contain predictive signals. Key applications include the prediction of asset returns, correlations or covariances, or volatility.
We focus on linear time series models in this chapter as a baseline for non-linear models like recurrent or convolutional neural networks that we apply to time series data in part 4 of this book. We being by introducing tools to diagnose time series characteristics, including stationarity, and extract features that capture potential patterns. Then we introduce univariate and multivariate time series models and apply them to forecast macro data and volatility patterns. We conclude with the concept of cointegration and how to apply it to develop a pairs trading strategy.
In particular, we will cover the following topics:
- How to use time series analysis to diagnose diagnostic statistics that inform the modeling process
- How to estimate and diagnose autoregressive and moving-average time series models
- How to build Autoregressive Conditional Heteroskedasticity (ARCH) models to predict volatility
- How to build vector autoregressive models
- How to use cointegration for a pairs trading strategy