A new algorithm for latent state estimation in non-linear time series models

Date, Paresh; Jalen, Luka; Mamon, Rogemar

doi:10.1016/j.amc.2008.04.028

Cited by 15 publications

(21 citation statements)

References 22 publications

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“…An HMM is used to drive the dynamics of model parameters; although the HMM in this discussion evolves in discrete time, it is also possible to modulate model parameters with an HMM in continuous time [10] with time-varying jump intensities. The HMM embedding in turn will enable the capturing of non-normality of returns [11], which is common in the spread portfolio. Lévy-type processes are noted to yield excellent statistical fit to the non-normal asset-returns process but they are difficult to interpret from a financial perspective.…”

Section: Background and Related Workmentioning

confidence: 99%

A computing platform for pairs-trading online implementation via a blended Kalman-HMM filtering approach

Tenyakov

Mamon

2017

J Big Data

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IntroductionPairs trading is an investment strategy used to exploit financial markets that are out of equilibrium. It consists of a long position in one security and a short position in another security at a predetermined ratio; see Elliott et al. [1]. Traders bet on the direction of the stocks relative to each other. Such a trading strategy is typically employed by hedge fund companies. Deviations in prices are monitored closely and used as basis for changing positions, taking advantage of market inefficiencies to obtain some profits. Hence, financial computing technologies with algorithmic trading capability, such as the one Abstract This paper addresses the problem of designing an efficient platform for pairs-trading implementation in real time. Capturing the stylised features of a spread process, i.e., the evolution of the differential between the returns from a pair of stocks, exhibiting a heavy-tailed mean-reverting process is also dealt with. Likewise, the optimal recovery of time-varying parameters in a return-spread model is tackled. It is important to solve such issues in an integrated manner to carry out the execution of trading strategies in a dynamic market environment. The Kalman and hidden Markov model (HMM) multiregime dynamic filtering approaches are fused together to provide a powerful method for pairs-trading actualisation. Practitioners' considerations are taken into account in the way the new filtering method is automated. The synthesis of the HMM's expectationmaximisation algorithm and Kalman filtering procedure gives rise to a set of self-updating optimal parameter estimates. The method put forward in this paper is a hybridisation of signal-processing algorithms. It highlights the critical role and beneficial utility of data fusion methods. Its appropriateness and novelty support the advancements of accurate predictive analytics involving big financial data sets. The algorithm's performance is tested on historical return spread between Coca-Cola and Pepsi Inc. 's equities. Through a back-testing trade, a hypothetical trader might earn a non-zero profit under the assumption of no transaction costs and bid-ask spreads. The method's success is illustrated by a trading simulation. The findings from this work show that there is high potential to gain when the transaction fees are low, and an investor is able to benefit from the proposed interplay of the two filtering methods. Tenyakov and Mamon J Big Data (2017) Data (2017) 4:46 put forward in this paper, are necessary for the efficient and successful implementation of a pairs trade. RESEARCHWhen the relative performance of the short position is better than that of the long position, this strategy is going to be profitable regardless of stock market regimes. So, a speculator who pairs a long position in a retail stock with a short position in a rival stock or an index ETF could end up with a profit. Pairs trading could be viewed alternatively as a mechanism to hedge both sector and market risks. When there is a financial crisis, two stoc...

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Section: Background and Related Workmentioning

confidence: 99%

A computing platform for pairs-trading online implementation via a blended Kalman-HMM filtering approach

Tenyakov

Mamon

2017

J Big Data

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“…The ensemble filter (EF) used in climatology is closely related to UKF; see [8] and references therein. An algorithm which combines some of the desirable properties of both UKF and EF has been proposed in [9]. In [10], approximate methods are developed to deal with the multiplicative uncertainty in the observation equation under sigma point filtering framework.…”

Section: Introductionmentioning

confidence: 99%

Higher order sigma point filter: A new heuristic for nonlinear time series filtering

Ponomareva

Date

2013

Applied Mathematics and Computation

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In this paper we present some new results related to the higher order sigma point filter (HOSPoF), introduced in [1] for filtering nonlinear multivariate time series. This paper makes two distinct contributions. Firstly, we propose a new algorithm to generate a discrete statistical distribution to match exactly a specified mean vector, a specified covariance matrix, the average of specified marginal skewness and the average of specified marginal kurtosis. Both the sigma points and the probability weights are given in closed-form and no numerical optimization is required. Combined with HOSPoF, this random sigma point generation algorithm provides a new method for generating proposal density which propagates the information about higher order moments. A numerical example on nonlinear, multivariate time series involving real financial market data demonstrates the utility of this new algorithm. Secondly, we show that HOSPoF achieves a higher order estimation accuracy as compared to UKF for smooth scalar nonlinearities. We believe that this new filter provides a new and powerful alternative heuristic to existing filtering algorithms and is useful especially in econometrics and in engineering applications.

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“…In this paper, we propose a scenario generation method that modifies the algorithm in [2] to match the given mean vector, the covariance matrix, the average marginal skewness as well as average marginal kurtosis (thus catering for assymetric marginals) of each individual component of the random vector, without needing an optimization procedure.…”

Section: Introductionmentioning

confidence: 99%

“…A modified version of the same method in [2] was used in [17] in the context of nonlinear time series filtering. However, to authors' knowledge, a moment-matching sigma point generation algorithm, which generates probability weights as well, has not been employed in the context of financial optimization before.…”

Section: Introductionmentioning

confidence: 99%

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An algorithm for moment-matching scenario generation with application to financial portfolio optimisation

Ponomareva

Roman

Date

2015

European Journal of Operational Research

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We present an algorithm for moment-matching scenario generation. This method produces scenarios and corresponding probability weights that match exactly the given mean, the covariance matrix, the average of the marginal skewness and the average of the marginal kurtosis of each individual component of a random vector. Optimisation is not employed in the scenario generation process and thus the method is computationally more advantageous than previous approaches. The algorithm is used for generating scenarios in a mean-CVaR portfolio optimisation model. For the chosen optimization example, it is shown that desirable properties for a scenario generator are satisfied, including in-sample and out-of-sample stability. It is also shown that optimal solutions vary only marginally with increasing number of scenarios in this example; thus, good solutions can apparently be obtained with a relatively small number of scenarios. The proposed method can be used either on its own as a computationally inexpensive scenario generator or as a starting point for non-convex optimisation based scenario generators which aim to match all the third and the fourth order marginal moments (rather than average marginal moments).

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A new algorithm for latent state estimation in non-linear time series models

Cited by 15 publications

References 22 publications

A computing platform for pairs-trading online implementation via a blended Kalman-HMM filtering approach

A computing platform for pairs-trading online implementation via a blended Kalman-HMM filtering approach

Higher order sigma point filter: A new heuristic for nonlinear time series filtering

An algorithm for moment-matching scenario generation with application to financial portfolio optimisation

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