Time Series Analysis in Financial Econometrics

A Hands-On Guide with R and Python, following Tsay

Preface

This book is a hands-on introduction to time series analysis in financial econometrics. It follows the structure and spirit of Ruey Tsay’s Analysis of Financial Time Series (Tsay 2010), but with one deliberate difference: every concept is paired with runnable code in both R and Python and applied to live market data that you can re-download and reproduce on your own machine for any tickers you like.

The goal is not just to show you what the models say, but to let you rerun the entire pipeline yourself — swap in your own stocks or indices, and the analysis regenerates end to end.

What you will need

The executing engine for this book is R (via knitr). Python code is shown alongside every R block as copy-ready reference so you can work in whichever language you prefer — the two produce equivalent results, and where they differ (for example, different default optimizers in GARCH estimation) the text says so.

R packages

install.packages(c(
  "quantmod",   # download prices
  "xts", "zoo", # time-indexed data
  "PerformanceAnalytics",
  "tseries",    # unit-root / normality tests
  "urca",       # unit-root tests with explicit deterministic terms
  "forecast",   # ARIMA modelling and forecasting
  "rugarch",    # GARCH-family volatility models
  "FinTS"       # helper tests (e.g. ARCH-LM)
))

Python packages

pip install yfinance pandas numpy statsmodels arch matplotlib scipy

The dataset

Throughout the book we work with six daily series over roughly fifteen years, chosen so that they contrast with one another:

Series used throughout the book

Symbol in code	Instrument	Ticker	Role
AAPL	Apple Inc.	AAPL	individual stock
MSFT	Microsoft Corp.	MSFT	individual stock
AMZN	Amazon.com Inc.	AMZN	individual stock
SPX	S&P 500 index	^GSPC	broad US equity index
GLD	SPDR Gold Shares ETF	GLD	gold (primary)
GCF	COMEX gold futures	GC=F	gold (comparison)

Three individual mega-cap stocks, one broad equity index, and gold. Gold is included on purpose: it behaves differently from equities — most visibly, it lacks the strong “bad news raises volatility more than good news” leverage effect we will find in the stocks. That makes it a useful counter-example when we get to asymmetric volatility models.

We keep the analysis univariate: each series is modelled on its own. (The stocks are large constituents of the S&P 500, so a multivariate treatment would be dominated by one common factor — a topic we flag but do not pursue here.)

Estimation and forecast windows

The sample runs from 2011-07-01 to 2026-07-10. We split it once and use the same convention everywhere:

• Estimation window: data up to and including 2026-07-01 (3,771 trading days for the equity-calendar series). All models are fit here.
• Forecast holdout: the six trading days 2026-07-02 through 2026-07-10 (2026-07-03 is the observed Independence Day market closure). We never let the models see these; we compare forecasts against them.

A six-day holdout is generous enough to illustrate volatility forecasting and Value-at-Risk, but far too short to evaluate the accuracy of return forecasts — a point we return to, because it is itself one of the most important lessons in financial time series.

Reproducing the data

The CSV files live in the data/ folder next to this book, and students can download them directly. To rebuild them from scratch (or to fetch your own tickers), run the download once:

R

library(quantmod)
dir.create("data", showWarnings = FALSE)

tickers <- c(AAPL = "AAPL", MSFT = "MSFT", AMZN = "AMZN",
             SPX  = "^GSPC", GLD  = "GLD",  GCF = "GC=F")

for (nm in names(tickers)) {
  x  <- getSymbols(tickers[[nm]], src = "yahoo",
                   from = "2011-07-01", to = "2026-07-11",
                   auto.assign = FALSE)
  df <- data.frame(Date = index(x), coredata(x))
  colnames(df) <- c("Date","Open","High","Low","Close","Volume","Adjusted")
  write.csv(df, file.path("data", paste0(nm, ".csv")), row.names = FALSE)
}

Python

import yfinance as yf, os
os.makedirs("data", exist_ok=True)
tickers = {"AAPL":"AAPL","MSFT":"MSFT","AMZN":"AMZN",
           "SPX":"^GSPC","GLD":"GLD","GCF":"GC=F"}
for nm, sym in tickers.items():
    yf.download(sym, start="2011-07-01", end="2026-07-11",
                auto_adjust=False).to_csv(f"data/{nm}.csv")

Always use the Adjusted column

Every return we compute uses the adjusted close, which corrects for dividends and stock splits. Using the raw close would inject artificial jumps on ex-dividend and split dates and contaminate the return series. This is the first of many places where a small data-handling choice changes the statistics downstream — we make it explicit in 1  Asset Returns: Simple and Log.

Tsay, Ruey S. 2010. Analysis of Financial Time Series. 3rd ed. Hoboken, New Jersey: John Wiley & Sons.