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We will learn R in a problem-solving fashion, whereby new commands and syntax will be
introduced as needed. Fortunately, there are plenty of extremely useful tutorials for R availabile
on the internet and I will point them out as we go through the sequence of time series analysis
chapters.
7.4 Time Series Analysis Roadmap
We have previously discussed Bayesian statistics and how it will form the basis of many of our
time series and machine learning models. Eventually we will utilise Bayesian tools and machine
learning techniques in conjunction with the following time series methods in order to forecast
price level and direction, act as filters and determine "regime change", that is, determine when
our time series have changed their underlying statistical behaviour.
Our time series roadmap is as follows. Each of the topics below will form its own chapter.
Once we’ve examined these methods in depth, we will be in a position to create some sophisticated
modern models for examining financial data across different assets.
• Time Series Introduction - This chapter outlines the area of time series analysis, its
scope and how it can be applied to financial data.
• Serial Correlation - An absolutely fundamental aspect of modeling time series is the
concept of serial correlation. We will define it, visualise it and outline how it can be used
to fit time series models.
• Random Walks and White Noise - In this chapter we will look at two basic time
series models that will form the basis of the more complicated linear and conditional heteroskedastic
models of later chapters.
• ARMA Models - We will consider linear autoregressive, moving average and combined
autoregressive moving average models as our first attempt at predicting asset price movements.
• ARIMA and GARCH Models - We will extend the ARMA model to use differencing
and thus allowing them to be "integrated", leading to the ARIMA model. We will also
discuss non-stationary conditional heteroskedastic (volatility clustering) models.
• Cointegration - We have considered multivariate models in Successful Algorithmic Trading,
namely when we studied mean-reverting pairs of equities. In this chapter we will more
rigourously define cointegration and look at further tests for it.
• State-Space Models - State Space Modelling borrows from a long history of modern
control theory used in engineering. It allows us to model time series with rapidly varying
parameters, such as the β slope variable between two cointegrated assets in a linear regression.
In particular, we will consider the famous Kalman Filter and the Hidden Markov
Model. These will be two of the major uses of Bayesian analysis for time series in this
book.