# Matlab Code

Be aware that, since 2015, I no longer use Matlab and all code available here is not being actively maintained.

## MS_Regress - Markov Regime Switching Models

The package and its description are available in Github.

## ACD Models

This package includes functions and scripts for the estimation and simulation of ACD (autoregressive conditional duration) models.

The zip file includes:

• Scripts and functions for Estimation of an ACD(q,p) model with exponential or weibull distribution
• Scripts and functions for Simulation of an ACD(q,p) model with exponential or weibull distribution
• Scripts for cool plots/movies of weibull, burr and generalized gamma distributions.
• Scripts and functions for visualizing the log likelihood space of the model (the figure showed above)

Required Products: Statistics, Optimization

This Matlab code provides a simple function that access google trends for a given string and location, parses the data and return dates, frequency of data and google’s search volume to the user.

Fell free to use it or provide suggestions on how to improve it.

INSTRUCTIONS

2. Manually open one chrome brownser and leave it open during the whole process

5. Run the example script

## Random Portfolios

Considering some input arguments, this function performs n simulations with random trades in a price matrix, saving 3 performance indicators (annualized return, annualized standard deviation and annualized sharpe) at each simulation

For example, suppose that you’re a trader and have earned 15% of annualized logarithm return over 248 trading days (1 year) where you traded, in average, for long positions only, 5 stocks for each day and for 50 days. This function will check if a monkey with no skill whatsoever can, in average, replicate your return after transaction costs (defined by the user). If such mamel can do it, maybe you should review your approach at trading.

From the academic point of view, this is called as the bootstrap method for assessing performance. The present code is a variant of such.

The use of random seeds for portfolio performance is not new. The first paper to use it, as I recall is Cumby and Modest (1987). More recently, a more formal approach at the method was given in Burns (2006).

For a practical application of the codes published here, please check the papers of Perlin (2007a) and Perlin (2007b).

## Nearest Neighbor Algorithm

This is the algorithm involved on the use of the non-linear forecast of a time series based on the nearest neighbour method.

The basic idea of the NN algorithm is that the time series copies it’s own past behavior, and such fact can be used for forecasting purposes. On the zip file there are two functions: one is the univariate version of NN (nn.m) and the other is the multivariate approach, also called simultaneous NN (snn.m).

The routines of the file were build according to the work of Rodriguez, Rivero and Artilles (2001).

This function performs the classical pairs trading framework in a given set of prices

From Wikipedia, the free encyclopedia: “The pairs trade was developed in the late 1980s by quantitative analysts and pioneered by Gerald Bamberger while at Morgan Stanley. With the help of others at Morgan Stanley at the time, including Nunzio Tartaglia, Bamberger found that certain securities, often competitors in the same sector, were correlated in their day-to-day price movements. When the correlation broke down, i.e. one stock traded up while the other traded down, they would sell the outperforming stock and buy the underperforming one, betting that the “spread” between the two would eventually converge.”

There are many ways you can implement the pairs trading framework. For this package, I used a very simple set of rules. Details can be found within code’s comments.

Please note that this package has been developed over the years and it will no longer exactly replicate the results from my 2007 paper.

Qualities of the package:

• Handles any number of assets
• Outputs separately the plot for the total cumulative profit from the long, short and combined positions.
• Provides the user a large amount of input choices for the pairs trading algorithm, including:
• amount of money to put in each position (long and short)
• value of transaction cost (in money unit)
• size of moving window for finding the pairs over the price data
• maximum number of days to keep any trade (without convergence).
• value of threshold variable

## State Space Models

This toolbox was designed to simulate and fit linear state space models.

The main literature I used for this particular package is Kim and Nelson (1999).

A state space model (without non stochastic coefficients) is given by:

y(t)=beta(t)x(t)’+e(t) beta(t)=u+Fbeta(t-1)+v(t)

e(t)~N(0,R) v(t)~N(0,Q)

Where x(t) is a vector of size (1,k), beta(t), u and v(t) are vectors with size [1,k] and F, Q are matrices of size [k,k]. More details about the model can be found at the reference.

The main advantage of this package is that the fitting function lets you build your own state space model by changing the input option optionsSpec. Please check the pdf document and the example scripts at the zip file for instructions of how to use it.

• So far it doesn’t handle autoregressive processes between series of the beta matrix. In other works, at the F matrix, the only estimated coefficients are in the diagonal (all non diagonal elements are zero).

• The model is estimated by Gaussian maximum likelihood with the function fminsearch. I also played around with fminunc(), but there was no improvement over fminsearch when it comes to robustness and speed.

• So far the code doesn’t handle state space models with mixture of non stochastic and stochastic coefficients, that is, when you want some variables to have stochastic coefficients and others not in the same model.

## Yahoo Finance and Matlab

This is a simple algorithm that downloads trading data from yahoo database. It is basically a large scale application of sqq.m which was originally submitted by Michael Boldin.

Some of the functionalities of the package:

• User defined ticker list.
• Choice for benchmark ticker in dates comparison