7,740 research outputs found
Dynamic modeling of mean-reverting spreads for statistical arbitrage
Statistical arbitrage strategies, such as pairs trading and its
generalizations, rely on the construction of mean-reverting spreads enjoying a
certain degree of predictability. Gaussian linear state-space processes have
recently been proposed as a model for such spreads under the assumption that
the observed process is a noisy realization of some hidden states. Real-time
estimation of the unobserved spread process can reveal temporary market
inefficiencies which can then be exploited to generate excess returns. Building
on previous work, we embrace the state-space framework for modeling spread
processes and extend this methodology along three different directions. First,
we introduce time-dependency in the model parameters, which allows for quick
adaptation to changes in the data generating process. Second, we provide an
on-line estimation algorithm that can be constantly run in real-time. Being
computationally fast, the algorithm is particularly suitable for building
aggressive trading strategies based on high-frequency data and may be used as a
monitoring device for mean-reversion. Finally, our framework naturally provides
informative uncertainty measures of all the estimated parameters. Experimental
results based on Monte Carlo simulations and historical equity data are
discussed, including a co-integration relationship involving two
exchange-traded funds.Comment: 34 pages, 6 figures. Submitte
Dynamic Covariance Models for Multivariate Financial Time Series
The accurate prediction of time-changing covariances is an important problem
in the modeling of multivariate financial data. However, some of the most
popular models suffer from a) overfitting problems and multiple local optima,
b) failure to capture shifts in market conditions and c) large computational
costs. To address these problems we introduce a novel dynamic model for
time-changing covariances. Over-fitting and local optima are avoided by
following a Bayesian approach instead of computing point estimates. Changes in
market conditions are captured by assuming a diffusion process in parameter
values, and finally computationally efficient and scalable inference is
performed using particle filters. Experiments with financial data show
excellent performance of the proposed method with respect to current standard
models
Bayesian Lattice Filters for Time-Varying Autoregression and Time-Frequency Analysis
Modeling nonstationary processes is of paramount importance to many
scientific disciplines including environmental science, ecology, and finance,
among others. Consequently, flexible methodology that provides accurate
estimation across a wide range of processes is a subject of ongoing interest.
We propose a novel approach to model-based time-frequency estimation using
time-varying autoregressive models. In this context, we take a fully Bayesian
approach and allow both the autoregressive coefficients and innovation variance
to vary over time. Importantly, our estimation method uses the lattice filter
and is cast within the partial autocorrelation domain. The marginal posterior
distributions are of standard form and, as a convenient by-product of our
estimation method, our approach avoids undesirable matrix inversions. As such,
estimation is extremely computationally efficient and stable. To illustrate the
effectiveness of our approach, we conduct a comprehensive simulation study that
compares our method with other competing methods and find that, in most cases,
our approach performs superior in terms of average squared error between the
estimated and true time-varying spectral density. Lastly, we demonstrate our
methodology through three modeling applications; namely, insect communication
signals, environmental data (wind components), and macroeconomic data (US gross
domestic product (GDP) and consumption).Comment: 49 pages, 16 figure
Matrix-State Particle Filter for Wishart Stochastic Volatility Processes
This work deals with multivariate stochastic volatility models, which account for a time-varying variance-covariance structure of the observable variables. We focus on a special class of models recently proposed in the literature and assume that the covariance matrix is a latent variable which follows an autoregressive Wishart process. We review two alternative stochastic representations of the Wishart process and propose Markov-Switching Wishart processes to capture different regimes in the volatility level. We apply a full Bayesian inference approach, which relies upon Sequential Monte Carlo (SMC) for matrix-valued distributions and allows us to sequentially estimate both the parameters and the latent variables.Multivariate Stochastic Volatility; Matrix-State Particle Filters; Sequential Monte Carlo; Wishart Processes, Markov Switching.
Covariance estimation for multivariate conditionally Gaussian dynamic linear models
In multivariate time series, the estimation of the covariance matrix of the
observation innovations plays an important role in forecasting as it enables
the computation of the standardized forecast error vectors as well as it
enables the computation of confidence bounds of the forecasts. We develop an
on-line, non-iterative Bayesian algorithm for estimation and forecasting. It is
empirically found that, for a range of simulated time series, the proposed
covariance estimator has good performance converging to the true values of the
unknown observation covariance matrix. Over a simulated time series, the new
method approximates the correct estimates, produced by a non-sequential Monte
Carlo simulation procedure, which is used here as the gold standard. The
special, but important, vector autoregressive (VAR) and time-varying VAR models
are illustrated by considering London metal exchange data consisting of spot
prices of aluminium, copper, lead and zinc.Comment: 21 pages, 2 figures, 6 table
Modeling electricity prices: international evidence
This paper analyses the evolution of electricity prices in deregulated markets. We present a general model that simultaneously takes into account the possibility of several factors: seasonality, mean reversion, GARCH behaviour and time-dependent jumps. The model is applied to equilibrium spot prices of electricity markets from Argentina, Australia (Victoria), New Zealand (Hayward), NordPool (Scandinavia), Spain and U.S. (PJM) using daily data. Six different nested models were estimated to compare the relative importance of each factor and their interactions. We obtained that electricity prices are mean-reverting with strong volatility (GARCH) and jumps of time-dependent intensity even after adjusting for seasonality. We also provide a detailed unit root analysis of electricity prices against mean reversion, in the presence of jumps and GARCH errors, and propose a new powerful procedure based on bootstrap techniques
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