Performance evaluation of modified adaptive Kalman filters, least means square and recursive least square methods for market risk beta and VaR estimation

Atanu Das; Atanu Das

doi:10.3934/QFE.2019.1.124

Quantitative Finance and Economics

2019, Volume 3, Issue 1: 124-144. doi: 10.3934/QFE.2019.1.124

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Research article Special Issues

Performance evaluation of modified adaptive Kalman filters, least means square and recursive least square methods for market risk beta and VaR estimation

Atanu Das ^,

Department of Computer Science and Engineering, Netaji Subhash Engineering College, Kolkata, India

Received: 17 December 2018 Accepted: 29 March 2019 Published: 26 March 2019
JEL Codes: C13, C32, C35, C81, G12

Adaptive Kalman Filters (AKFs) are well known for their navigational applications. This work bridges the gap in the evolution of AKFs to handle parameter inconsistency problems with adaptive noise covariances. The focus is to apply proposed techniques for beta and VaR estimation of assets. The empirical performance of the proposed filters are compared with the standard least square family and KF with respect to VaR backtesting, expected shortfall analysis and in-sample forecasting performance analysis using Indian market data. Results show that the Modified AKFs are performing at par with the bench mark even with these adaptive noise covariance assumptions.
- adaptive estimation,
- noise covariance adaptation,
- recursive least square,
- least mean square,
- modified AKF,
- market risk,
- beta,
- value-at-Risk
Citation: Atanu Das. Performance evaluation of modified adaptive Kalman filters, least means square and recursive least square methods for market risk beta and VaR estimation[J]. Quantitative Finance and Economics, 2019, 3(1): 124-144. doi: 10.3934/QFE.2019.1.124

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Abstract

Adaptive Kalman Filters (AKFs) are well known for their navigational applications. This work bridges the gap in the evolution of AKFs to handle parameter inconsistency problems with adaptive noise covariances. The focus is to apply proposed techniques for beta and VaR estimation of assets. The empirical performance of the proposed filters are compared with the standard least square family and KF with respect to VaR backtesting, expected shortfall analysis and in-sample forecasting performance analysis using Indian market data. Results show that the Modified AKFs are performing at par with the bench mark even with these adaptive noise covariance assumptions.

References

[1]	Almagbile A, Wang J, Ding W (2010) Evaluating the Performances of Adaptive Kalman Filter Methods in GPS/INS Integration. J Glob Position Syst 9: 33–40. doi: 10.5081/jgps.9.1.33
[2]	Berardi A, Corradin S, Sommacampagna C (2002) Estimating Value at Risk with the Kalman Filter. University of Trieste, Italy.
[3]	Bel H, Ayed A, Loeper G, et al. (2017) Forecasting trends with asset prices. Quant Financ 17: 369–382. doi: 10.1080/14697688.2016.1206959
[4]	Barth JR, Han S, Joo S, et al. (2018) Forecasting net charge-off rates of banks: What model works best? Quant Financ Econ 2: 554–589. doi: 10.3934/QFE.2018.3.554
[5]	Das A (2014) Estimation and Prediction in Finance-A Review, In: N. Chaudhary, Dynamics of Commerce and Management in the New Millennium, Int. Research Pub. House, New Delhi, India: 267–306.
[6]	Das A (2016) Higher Order Adaptive Kalman Filter for Time Varying Alpha and Cross Market Beta Estimation in Indian Market. Econ Comput Econ Cybern Stud 50: 211–228.
[7]	Das A, Ghoshal TK (2010) Market Risk Beta Estimation using Adaptive Kalman Filter. Int J Eng Sci Technol 2: 1923–1934.
[8]	Das A, Basu PN, Das SC (2008) A re-look at the VaR computation method recommended by National Stock Exchange of India. ICFAI J Appl Finance 14: 45–53.
[9]	Ding W, Wang J, Rizos C (2007) Improving adaptive Kalman estimation in GPS/INS integration. J Navig 60: 517–529. doi: 10.1017/S0373463307004316
[10]	Gastaldi M, Nardecchia A (2003) The Kalman Filter Approach For Time-Varying β Estimation. Syst Anal Model Simul 43: 1033–1042. doi: 10.1080/0232929031000150373
[11]	Haykin S (2001) Adaptive Filter Theory, 4th ed., Prentice Hall.
[12]	Kai RW, Leschinski CH, Sibbertsen P (2018) The memory of volatility. Quant Financ Econ 2: 137–159. doi: 10.3934/QFE.2018.1.137
[13]	Kownacki C (2015) Design of Adaptive Kalman Filter to Eliminate Measurement Faults of a Laser Rangefinder Used in the UAV System. Aerosp Sci Technol 41: 81–89. doi: 10.1016/j.ast.2014.12.008
[14]	Mehra RK (1972) Approaches to adaptive filtering. IEEE Trans Autom Control 17: 693–698. doi: 10.1109/TAC.1972.1100100
[15]	Mergner S (2008) Applications of Advanced Time Series Models to Analyze the Time-varying Relationship between Macroeconomics, Fundamentals and Pan-European Industry Portfolios. Georg-August-University at Gottingen, Germany.
[16]	Mohamed AH, Schwar KP (1999) Adaptive Kalman Filtering for INS/GPS. J Geod 73: 193–203. doi: 10.1007/s001900050236
[17]	Nazin AV, Ljung L (2002) Asymptotically optimal smoothing of averaged LMS estimates for regression parameter tracking. Autom 38: 1287–1293. doi: 10.1016/S0005-1098(02)00028-6
[18]	Senyurek VY, Baspinar U, Varol HS (2014) A Modified Adaptive Kalman Filter For Fibre Optic Gyroscope. Rev Roum Sci Tech-Ser Electro 59: 153–162.
[19]	Shah A, Moonis SA (2003) Testing for time variation in beta in India. J Emerg Mark Financ 2: 163–180. doi: 10.1177/097265270300200202
[20]	Simon D (2006) Optimal State Est.: Kalman, H-infinity, and Nonlinear Approaches, John Wiley & Sons.
[21]	Snyder RD, Saligari GR (1996) Initialization of the Kalman filter with partially diffuse initial conditions. J Time Ser Anal 17: 409–424. doi: 10.1111/j.1467-9892.1996.tb00285.x
[22]	Wang Z, Woodward WA, Gray HL (2009) The application of the Kalman filter to nonstationary time series through time deformation. J Time Ser Anal 30: 559–574. doi: 10.1111/j.1467-9892.2009.00628.x
[23]	Yamai Y, Yoshiba T (2002) Comparative analyses of expected shortfall and VaR (2): expected utility maximization and tail risk. Monetary Econ Stud 20: 95–115.

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