This semester my studies all involve one key mathematical object: Gaussian processes. I’m taking a course on stochastic processes (which will talk about Wiener processes, a type of Gaussian process and arguably the most common) and mathematical finance, which involves stochastic differential equations (SDEs) used for derivative pricing, including in the Black-Scholes-Merton equation. Then I’m involved in a Gaussian process and stochastic calculus reading group. So these processes will take up a lot of my attention.

# finance

# Problems In Estimating GARCH Parameters in R

**UPDATE (11/2/17 3:00 PM MDT):** I got the following e-mail from Brian Peterson, a well-known R finance contributor, over R’s finance mailing list:

I would strongly suggest looking at

rugarchorrmgarch. The primary

maintainer of the RMetrics suite of packages, Diethelm Wuertz, was

killed in a car crash in 2016. That code is basically unmaintained.

*I will see if this solves the problem. Thanks Brian! I’m leaving this post up though as a warning to others to avoid fGarch in the future. This was news to me, books often refer to fGarch, so this could be a resource for those looking for working with GARCH models in R why not to use fGarch.*

**UPDATE (11/2/17 11:30 PM MDT):** I tried a quick experiment with **rugarch** and it appears to be plagued by this problem as well. Below is some quick code I ran. I may post a full study as soon as tomorrow.

library(rugarch) spec = ugarchspec(variance.model = list(garchOrder = c(1, 1)), mean.model = list(armaOrder = c(0, 0), include.mean = FALSE), fixed.pars = list(alpha1 = 0.2, beta1 = 0.2, omega = 0.2)) ugarchpath(spec = spec, n.sim = 1000, n.start = 1000) -> x srs = x@path$seriesSim spec1 = ugarchspec(variance.model = list(garchOrder = c(1, 1)), mean.model = list(armaOrder = c(0, 0), include.mean = FALSE)) ugarchfit(spec = spec1, data = srs) ugarchfit(spec = spec1, data = srs[1:100])

These days my research focuses on change point detection methods. These are statistical tests and procedures to detect a structural change in a sequence of data. An early example, from quality control, is detecting whether a machine became uncalibrated when producing a widget. There may be some measurement of interest, such as the diameter of a ball bearing, that we observe. The machine produces these widgets in sequence. Under the null hypothesis, the ball bearing’s mean diameter does not change, while under the alternative, at some unkown point in the manufacturing process the machine became uncalibrated and the mean diameter of the ball bearings changed. The test then decides between these two hypotheses.

# Stock Trading Analytics and Optimization in Python with PyFolio, R’s PerformanceAnalytics, and backtrader

**DISCLAIMER: Any losses incurred based on the content of this post are the responsibility of the trader, not me. I, the author, neither take responsibility for the conduct of others nor offer any guarantees. None of this should be considered as financial advice; the content of this article is only for educational/entertainment purposes.**

## Introduction

Having figured out how to perform walk-forward analysis in Python with **backtrader**, I want to have a look at evaluating a strategy’s performance. So far, I have cared about only one metric: the final value of the account at the end of a backtest relative. This should not be the only metric considered. Most people care not only about how much money was made but how much risk was taken on. People are risk-averse; one of finance’s leading principles is that higher risk should be compensated by higher returns. Thus many metrics exist that adjust returns for how much risk was taken on. Perhaps when optimizing only with respect to the final return of the strategy we end up choosing highly volatile strategies that lead to huge losses in out-of-sample data. Adjusting for risk may lead to better strategies being chosen.

# Order Type and Parameter Optimization in quantstrat

**DISCLAIMER: Any losses incurred based on the content of this post are the responsibility of the trader, not the author. The author takes no responsibility for the conduct of others nor offers any guarantees.**

## Introduction

You may have noticed I’ve been writing a lot about **quantstrat**, an R package for developing and backtesting trading strategies. The package strikes me as being so flexible, there’s still more to write about. So far I’ve introduced the package here and here, then recently discussed the important of accounting for transaction costs (and how to do so).

# An Introduction to Stock Market Data Analysis with R (Part 2)

*Around September of 2016 I wrote two articles on using Python for accessing, visualizing, and evaluating trading strategies (see part 1 and part 2). These have been my most popular posts, up until I published my article on learning programming languages (featuring my dad’s story as a programmer), and has been translated into both Russian (which used to be on backtest.ru at a link that now appears to no longer work) and Chinese (here and here). R has excellent packages for analyzing stock data, so I feel there should be a “translation” of the post for using R for stock data analysis.*

*This post is the second in a two-part series on stock data analysis using R, based on a lecture I gave on the subject for MATH 3900 (Data Science) at the University of Utah. (You can read the first post here.) In these posts, I discuss basics such as obtaining the data from Yahoo! Finance using pandas, visualizing stock data, moving averages, developing a moving-average crossover strategy, backtesting, and benchmarking. The final post will include practice problems. This post discusses moving average crossover strategies,backtesting, and benchmarking.*

**NOTE: The information in this post is of a general nature containing information and opinions from the author’s perspective. None of the content of this post should be considered financial advice. Furthermore, any code written here is provided without any form of guarantee. Individuals who choose to use it do so at their own risk.**

# An Introduction to Stock Market Data Analysis with R (Part 1)

*Around September of 2016 I wrote two articles on using Python for accessing, visualizing, and evaluating trading strategies (see part 1 and part 2). These have been my most popular posts, up until I published my article on learning programming languages (featuring my dad’s story as a programmer), and has been translated into both Russian (which used to be on backtest.ru at a link that now appears to no longer work) and Chinese (here and here). R has excellent packages for analyzing stock data, so I feel there should be a “translation” of the post for using R for stock data analysis.*

# Data or Die

In the 2016 election, few spectators realized Donald Trump’s data *advantage* until after he’d won.