Category Archives: Research

Automatic ARMA/GARCH selection in parallel

In the original ARMA/GARCH post I outlined the implementation of the garchSearch function. There have been a few requests for the code so … here it is. Quite easy to use too:

library(quantmod)
source("garchAuto.R")

spy = getSymbols("SPY", auto.assign=FALSE)
rets = ROC(Cl(spy), na.pad=FALSE)
fit = garchAuto(rets, cores=8, trace=TRUE)

After the last code line above, fit contains the best (according to the AIC statistic) model, which is the return value of garchFit. The function has reasonable defaults, but also provides controls over various aspects of the model selection – check the code.

The function is called garchAuto, following the naming convention of the fGarch package. In fact, I am trying to get it into the fGarch package, but haven’t heard back yet. There are reasons why I don’t feel too optimistic about this happening, hence, my decision to publish it here.

Last, if you wonder why I abandoned the original garchSearch name, the reason is that a similar function from the forecast package is called auto.arima (“auto”, not “search”).

Trading with SVMs: Performance

To get a feeling of SVM performance in trading, I run different setups on the S&P 500 historical data from … the 50s. The main motif behind using this decade was to decide what parameters to vary and what to keep steady prior to running the most important tests. Treat it as an “in-sample” test to avoid (further;)) over-fitting. First the performance chart:

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Trading with Support Vector Machines (SVM)

Finally all the stars have aligned and I can confidently devote some time for back-testing of new trading systems, and Support Vector Machines (SVM) are the new “toy” which is going to keep me busy for a while.

SVMs are a well-known tool from the area of supervised Machine Learning, and they are used both for classification and regression. For more details refer to the literature.

It seems to me that the most intuitive application for trading is regression, so let’s start by building an SVM regression model.

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Back-testing Rules

Nowadays there are many trading strategies shared online with reproducible, decent, results. Have you asked yourself, if the strategies are so profitable, why the author bother even sharing them, when the path to riches is clear – just implement the strategy and use it?

There are people, of course, who are fascinated and challenged by the market mechanics and for them coming up with a theoretical result how to beat the market is all that they are looking for. A quick “fix” it is, but that’s not the entire story.

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A Greedy ARMA/GARCH Model Selection

An idea that I have been toying for a while, has been to study the effect of a domain-specific optimization strategy in the ARMA+GARCH models. If you recall from this long tutorial, the implemented approach cycles through all models within a the specified ranges for the parameters and chooses the best model based on the AIC statistic. One idea which I have studied recently is to try to improve the model selection by using a different criteria to determine the “best” model, namely to use a domain-specific strategy.

Here is where greed enters the picture: Since our domain is finance, and they claim greed is good. What if we choose the model which has best performance in-sample?

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Trading at the Close – the Mechanics

When investing strategies are back tested, the prevailing approach is to use daily closing prices both for the signal and for the entry point. This is all well in theory, but implementing such a system in practice is far from straightforward. The most obvious problem is that the close remains unknown until the end of the day, thus, we don’t know what our action needs to be at the close before the close is in place, but that’s the end of the trading day. A form of the chicken and egg problem.

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ARMA Models for Trading

In this tutorial I am going to share my R&D and trading experience using the well-known from statistics Autoregressive Moving Average Model (ARMA). There is a lot written about these models, however, I strongly recommend Introductory Time Series with R, which I find is a perfect combination between light theoretical background and practical implementations in R. Another good reading is the online e-book Forecasting: principles and practice written by Rob Hyndman, an expert in statistical forecasting and the author of the excellent forecast R package.

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