Dynamic modeling of meanreverting spreads for statistical arbitrage
 K. Triantafyllopoulos,
 G. Montana
 … show all 2 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
Statistical arbitrage strategies, such as pairs trading and its generalizations rely on the construction of meanreverting spreads enjoying a certain degree of predictability. Gaussian linear statespace 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. Realtime estimation of the unobserved spread process can reveal temporary market inefficiencies which can then be exploited to generate excess returns. We embrace the statespace framework for modeling spread processes and extend this methodology along three different directions. First, we introduce timedependency in the model parameters, which allows for quick adaptation to changes in the data generating process. Second, we provide an online estimation algorithm that can be constantly run in realtime. Being computationally fast, the algorithm is particularly suitable for building aggressive trading strategies based on highfrequency 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 cointegration relationship involving two exchangetraded funds.
 Alexander C, Giblin I, Weddington W (2002) Cointegration and asset allocation: a new active hedge fund strategy. Tech Rep Discussion Paper 200308, ISMA Centre Discussion Papers in Finance Series
 Ameen, JRM, Harrison, PJ (1984) Discount weighted estimation. J Forecasting 3: pp. 285296 CrossRef
 Anderson, PL, Meerschaert, MM (2005) Parameter estimation for periodically stationary time series. J Time Ser Anal 26: pp. 489518 CrossRef
 Barberis, N (2000) Investing for the longrun when returns are predictable. J Finance 55: pp. 225264 CrossRef
 Carcano, G, Falbo, P, Stefani, S (2005) Speculative trading in mean reverting markets. Eur J Oper Res 163: pp. 132144 CrossRef
 Chan, SW, Goodwin, GC, Sin, KS (1984) Convergence properties of the riccati difference equation in optimal filtering of nonstabilizable systems. IEEE Trans Autom Control 29: pp. 1018 CrossRef
 Chaudhuri, K, Wu, Y (2003) Random walk versus breaking trend in stock prices: evidence from emerging markets. J Banking Finance 27: pp. 575592 CrossRef
 Cheng, X, Wu, Y, Du, J, Liu, H (1995) The zerocrossing rate of pthorder autoregressive processes. J Time Ser Anal 18: pp. 355374 CrossRef
 Dahlhaus, R (1997) Fitting time series models to nonstationary processes. Ann Stat 25: pp. 137 CrossRef
 d’Aspremont A (2008) Identifying small mean reverting portfolios. Tech rep, Princeton University
 Deaton, A, Laroque, G (1992) On the behavior of commodity prices. Rev Econ Stud 59: pp. 123 CrossRef
 Djurić, PM, Kotecha, JH, Esteve, F, Perret, E (2002) Sequential parameter estimation of timevarying nonGaussian autoregressive processes. EURASIP J Appl Signal Process 8: pp. 865875
 Elliott, R, Krishnamurthy, V (1999) New finitedimensional filters for parameter estimation of discretetime linear gaussian models. IEEE Trans Autom Control 44: pp. 938951 CrossRef
 Elliott, R, Hoek, J, Malcolm, W (2005) Pairs trading. Quant Finance 5: pp. 271276 CrossRef
 Engle, R, Granger, C (1987) Cointegration and error correction: representation, estimation, and testing. Econometrica 55: pp. 251276 CrossRef
 Fama, EF, French, K (1988) Permanent and temporary components of stock prices. J Polit Econ 96: pp. 246273 CrossRef
 Francq, C, Gautier, A (2004) Large sample properties of parameter least squares estimates for timevarying ARMA models. J Time Ser Anal 25: pp. 765783 CrossRef
 Francq, C, Zakoan, JM (2001) Stationarity of multivariate Markovswitching ARMA models. J Econom 102: pp. 339364 CrossRef
 Ghahramani Z, Hinton GE (1996) Parameter estimation for linear dynamical systems. Tech Rep Technical Report CRGTR922, Department of Computer Science, University of Toronto
 Ghosh, D (1989) Maximum likelihood estimation of the dynamic shockerror model. J Econom 41: pp. 121143 CrossRef
 Hargreaves C (1994) Nonstationary time series analysis and cointegration, Oxford, chap A review of methods of estimating cointegrating reiationships, pp 87–131
 Harrison, PJ, West, M (1991) Dynamic linear model diagnostics. Biometrika 78: pp. 797808 CrossRef
 Harvey, A (1989) Forecasting, structural time series models and the kalman filter. Cambridge University Press, Cambridge
 Johansen, S (1988) Statistical analysis of cointegration vectors. J Econ Dynam Control 12: pp. 231255 CrossRef
 Johansen, S (1991) Estimation and hypothesis testing of cointegration vectors in gaussian vector autoregression models. Econometrica 59: pp. 15511580 CrossRef
 Jorion, P, Sweeney, R (1996) Mean reversion in real exchange rates: evidence and implications for forecasting. J Int Money Finance 15: pp. 535550 CrossRef
 Kadane, JB, Chan, NH, Wolfson, LJ (1996) Priors for unit root models. J Econom 75: pp. 99111 CrossRef
 Kadiyala, KR, Karlsson, S (1997) Numerical methods for estimation and inference in Bayesian VARmodels. J Appl Econom 12: pp. 99132 CrossRef
 Kalaba, R, Tesfatsion, L (1988) The flexible least squares approach to timevarying linear regression. J Econ Dynam Control 12: pp. 4348 CrossRef
 Kalman, RE (1960) A new approach to linear filtering and prediction problems. J Basic Eng 82: pp. 3545
 Li, H, Xiao, Z (2003) Bootstrapping cointegrating regressions using blockwise bootstrap methods. J Stat Comput Simul 73: pp. 775789 CrossRef
 Li, WK (2004) Diagnostic checks in time series. Chapman and Hall, London
 Lin, Y, McCrae, M, Gulati, C (2006) Loss protection in pairs trading through minimum profit bounds: a cointegration approach. J Appl Math Decis Sci 2: pp. 114 CrossRef
 Lütkepohl, H (2006) New introduction to multiple time series analysis. Springer, New York
 McLachlan, GL, Krishnan, T (1997) The EM algorithm and extensions. Wiley Series in Probability and Statistics, Wiley
 Meinhold, RJ, Singpurwalla, ND (1983) Understanding the Kalman filter. Am Stat 37: pp. 123127 CrossRef
 Monahan, JF (1983) Fully Bayesian analysis of ARMA time series models. J Econom 21: pp. 307331 CrossRef
 Montana G, Parrella F (2008) Learning to trade with incremental support vector regression experts. In: Corchado E, Abraham WA amd Pedrycz (eds) Lecture notes in computer science, Springer, pp 591–598
 Montana, G, Parrella, F Data mining for algorithmic asset management. In: Cao, L, Yu, PS, Zhang, C, Zhang, H eds. (2009) Data mining for business applications. Springer, US, pp. 283295 CrossRef
 Montana G, Triantafyllopoulos K, Tsagaris T (2008) Data stream mining for marketneutral algorithmic trading. In: Proceedings of the ACM symposium on applied computing, pp 966–970
 Montana, G, Triantafyllopoulos, K, Tsagaris, T (2009) Flexible least squares for temporal data mining and statistical arbitrage. Expert Syst Appl 36: pp. 28192830 CrossRef
 Moulines, E, Priouret, P, Roueff, F (2005) On recursive estimation for time varying autoregressive processes. Ann Stat 33: pp. 26102654 CrossRef
 Ni, S, Sun, D (2003) Noninformative priors and frequentist risks of Bayesian estimators of vector autoregressive models. J Econom 115: pp. 159197 CrossRef
 Niedźwiecki, M (2000) Identification of timevarying processes. Wiley, New York
 Perron, P (1988) Trends and random walks in macroeconomic time series. J Econ Dynam Control 12: pp. 297332 CrossRef
 Phillips, P, Hansen, B (1990) Statistical inference in instrumental variables regression with I(1) process. Rev Econ Stud 57: pp. 99125 CrossRef
 Phillips, PCB, Ouliaris, S (1990) Asymptotic properties of residual based tests for cointegration. Econometrica 58: pp. 165193 CrossRef
 Pole A (2007) Statistical arbitrage. Algorithmic trading insights and techniques. Wiley Finance
 Poterba, JM, Summers, LH (1988) Mean reversion in stock prices: evidence and implications. J Financ Econom 22: pp. 2759 CrossRef
 Prado, R, Huerta, G (2002) Timevarying autoregressions with model order uncertainty. J Time Ser Anal 23: pp. 599618 CrossRef
 Saad D (ed) (1999) Online learning in neural networks. No. 17 in Publications of the Newton Institute, Cambridge
 Shumway, RH, Stoffer, DS (1982) An approach to time series smoothing and forecasting using the em algorithm. J Time Ser Anal 3: pp. 253264 CrossRef
 Sutcliffe C, Board J (2006) Encyclopedia of financial engineering and risk management, Fitzroy Dearborn, chap Index arbitrage
 Triantafyllopoulos, K (2007) Convergence of discount time series dynamic linear models. Commun Stat Theory Methods 36: pp. 21172127 CrossRef
 Triantafyllopoulos, K (2007) Covariance estimation for multivariate conditionally Gaussian dynamic linear models. J Forecasting 26: pp. 551569 CrossRef
 Vidyamurthy G (2004) Pairs trading. Wiley Finance
 West, M, Harrison, PJ (1997) Bayesian forecasting and dynamic models. Springer, New York
 West, M, Prado, R, Krystal, AD (1999) Evaluation and comparison of EEG traces: latent structures in nonstationary time series. J Am Stat Assoc 94: pp. 375387 CrossRef
 Zellner, A (1972) An introduction to Bayesian inference in econometrics. Wiley, New York
 Title
 Dynamic modeling of meanreverting spreads for statistical arbitrage
 Journal

Computational Management Science
Volume 8, Issue 12 , pp 2349
 Cover Date
 20110401
 DOI
 10.1007/s1028700901058
 Print ISSN
 1619697X
 Online ISSN
 16196988
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Mean reversion
 Statistical arbitrage
 Pairs trading
 State space model
 Timevarying autoregressive processes
 Dynamic regression
 Bayesian forecasting
 91B84
 91B28
 62M10
 Industry Sectors
 Authors

 K. Triantafyllopoulos ^{(1)}
 G. Montana ^{(2)}
 Author Affiliations

 1. Department of Probability and Statistics, University of Sheffield, Sheffield, S3 7RH, UK
 2. Department of Mathematics, Imperial College, 180 Queen’s Gate, London, SW7 2AZ, UK