Machine Learning and Big Data with kdb+/q

CHAPTER 14Time Series Econometrics

kdb+/q is a very powerful language to store, manage and analyse large data sets. Time series are data sets containing a set of values of observation at discrete points in time. Time series are present in nearly all fields of applications that rely on a form of data that measures how things evolve. One of the main objectives of time series analysis is the forecast of future realisations of a random phenomenon. One typical example of time series analysis in finance is the forecast of the evolution of a financial asset based on its historical returns, sometimes with the help of exogenous variables such as macroeconomic factors or intrinsic values of the underlying instrument.

This chapter presents the main forecasting techniques in time series analysis and shows how they can be implemented in q. The chapter is divided into two parts. The first part introduces the autoregressive and moving average processes, stationarity and Granger causality tests and vector autoregressive models. The second part presents a possible implementation of the processes in q.

14.1 AUTOREGRESSIVE AND MOVING AVERAGE PROCESSES

14.1.1 Introduction

A time series is a sequential set of data constructed chronologically over consecutive times t=0,1,2,... denoted . Time series can be discrete, where data are usually sampled at equally spaced time intervals, or continuous. ...