\( \newcommand{\bm}[1]{\boldsymbol{#1}} \newcommand{\textm}[1]{\textsf{#1}} \def\T{{\mkern-2mu\raise-1mu\mathsf{T}}} \newcommand{\R}{\mathbb{R}} % real numbers \newcommand{\E}{{\rm I\kern-.2em E}} \newcommand{\w}{\bm{w}} % bold w \newcommand{\bmu}{\bm{\mu}} % bold mu \newcommand{\bSigma}{\bm{\Sigma}} % bold mu \newcommand{\bigO}{O} %\mathcal{O} \renewcommand{\d}[1]{\operatorname{d}\!{#1}} \)

Chapter 4 Financial Data: Time Series Modeling

“It is very hard to predict, especially the future.”

— Niels Bohr

The efficient-market hypothesis states that the price of a security already contains all the publicly available information about the future (Fama, 1970). From that, it makes sense to model a sequence of prices as a random walk (Malkiel, 1973) or, equivalently, to model returns as a sequence of independent and identically distributed (i.i.d.) random variables as explored in Chapter 3. This is a widely adopted model by practitioners and academics.

Nevertheless, another line of thought precisely supports the opposite view in favor of inefficient and irrational markets (Shiller, 1981) under the so-called behavioral finance (Shiller, 2003). Indeed, it is undeniable that financial data exhibit some temporal structure that could be potentially modeled and exploited (Lo and Mackinlay, 2002). One of the most noticeable structural aspects is the volatility clustering (overviewed in Chapter 2). This chapter examines the temporal structure in financial time series in the form of mean models and variance (or volatility) models with emphasis on the Kalman filter.

This material will be published by Cambridge University Press as Portfolio Optimization: Theory and Application by Daniel P. Palomar. This pre-publication version is free to view and download for personal use only; not for re-distribution, re-sale, or use in derivative works. © Daniel P. Palomar 2024.

References

Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. The Journal of Finance, 25(2), 383–417.

Lo, A. W., and Mackinlay, A. C. (2002). A non-random walk down Wall Street. Princeton, NJ: Princeton University Press.

Malkiel, B. G. (1973). A random walk down Wall Street. New York: W. W. Norton.

Shiller, R. J. (1981). Do stock prices move too much to be justified by subsequent changes in dividends? American Economic Review, 71(3), 421–436.

Shiller, R. J. (2003). From efficient markets theory to behavioral finance. Journal of Economic Perspectives, 17(1), 83–104.