Abstract
In the present paper, we review the use of two-state, Generalized Auto Regressive Conditionally Heteroskedastic Markovian stochastic processes (MS-GARCH). These show the quantitative model of an active stock trading algorithm in the three main Latin-American stock markets (Brazil, Chile, and Mexico). By backtesting the performance of a U.S. dollar based investor, we found that the use of the Gaussian MS-GARCH leads, in the Brazilian market, to a better performance against a buy and hold strategy (BH). In addition, we found that the use of t-Student MS-ARCH models is preferable in the Chilean market. Lastly, in the Mexican case, we found that is better to use Gaussian time-fixed variance MS models. Their use leads to the best overall performance than the BH portfolio. Our results are of use for practitioners by the fact that MS-GARCH models could be part of quantitative and computer algorithms for active trading in these three stock markets.
Highlights
One of the main issues to be addressed in the investment management industry is the proper statistical parameter estimation of the behavior of a return time series
We present an introductory review of the MS and MS-Generalized Auto Regressive Conditional Heteroscedasticity (GARCH) models and their use in the trading algorithm
Since the original proposal made by Hamilton [14,15,16], MS and MS-GARCH models have been useful to characterize the behavior of a time series in S separate regimes
Summary
One of the main issues to be addressed in the investment management industry is the proper statistical parameter estimation of the behavior of a return time series (rt ). Following the modelling of the expected return with either an arithmetic mean (μr ) or an AutoRegressive Moving Average models-ARMA model, the novel proposal of Engle [7] and Bollerslev [8] lead to measure the risk exposure (variance) as a time-varying parameter This led to the widespread use of the Generalized Auto Regressive Conditional Heteroscedasticity (GARCH) models. This means that the studied time series has S − 1 structural breaks, which leads to S regimes or states of nature in the behavior of rt For this reason and departing from the seminal work of Hamilton [14,15,16], the expected return (μ) and risk (σ2r ) can be modelled in an S-state of the Gaussian or t-Student stochastic process.
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