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.

# R

Blog posts for R programming.

# 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.

# Downloading S&P 500 Stock Data from Google/Quandl with R (Command Line Script)

**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.**

While most Americans have heard of the Dow Jones Industrial Average (DJIA), most people active in finance consider the S&P 500 stock index to be the better barometer of the overall American stock market. The 500 stocks included in the index are large-cap stocks seen as a leading indicator for the performance of stocks overall. Thus the S&P 500 and its component stocks are sometimes treated as “the market.”

# 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.

# Who Survives Riddler Nation?

## Introduction

Last week, I published an article on learning to fight in the Battle for Riddler Nation. Here’s a refresher of the rules:

In a distant, war-torn land, there are 10 castles. There are two warlords: you and your archenemy. Each castle has its own strategic value for a would-be conqueror. Specifically, the castles are worth 1, 2, 3, …, 9, and 10 victory points. You and your enemy each have 100 soldiers to distribute, any way you like, to fight at any of the 10 castles. Whoever sends more soldiers to a given castle conquers that castle and wins its victory points. If you each send the same number of troops, you split the points. You don’t know what distribution of forces your enemy has chosen until the battles begin. Whoever wins the most points wins the war.

# The End of the Honeymoon: Falling Out of Love with quantstrat

## Introduction

I spent good chunks of Friday, Saturday, and Sunday attempting to write another blog post on using R and the **quantstrat** package for backtesting, and all I have to show for my work is frustration. So I’ve started to fall out of love with **quantstrat** and am thinking of exploring Python backtesting libraries from now on.

Here’s my story…

# 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).