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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 compa...
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Context 1
... experiments were carried out with above LMS algorithm for empirical estimation of the selected Indian indices. Figure 2 presents the estimates using LMS estimator where = 20 (suitable choice of to get the convergence results of the estimates). Selected indices are estimated here with respect to Nifty returns ( t m r , ). ...
Context 2
... experiments were carried out with above LMS algorithm for empirical estimation of the selected Indian indices. Figure 2 presents the estimates using LMS estimator where = 20 (suitable choice of to get the convergence results of the estimates). Selected indices are estimated here with respect to Nifty returns ( t m r , ). ...
Citations
... Most like this study was that of Berardi et al. (2002), who used the Kalman filter to calculate VaR by estimating portfolio βs, treating the β parameter as if it were unobservable and followed a first order autoregressive process. Das (2019) introduced advancements in Adaptive Kalman Filters (AKFs) to address parameter inconsistency issues by incorporating adaptive noise covariances for estimating asset β and VaR. The empirical performance of the proposed filters was compared with the standard least square family and Kalman Filters, based on VaR backtesting, ES analysis, and in-sample forecasting. ...
... The adaptive Kalman filter demonstrated similar performance to an ordinary filter, reinforcing previous observations that sector β estimates are dynamic and not constant in nature. Das (2019) presents recent findings that highlight the efficacy of utilising the mathematical principles of Kalman in accurately estimating VaR. ...
Value at Risk (VaR) estimates the maximum loss a portfolio may incur at a given confidence level over a specified time, while expected shortfall (ES) determines the probability weighted losses greater than VaR. VaR has recently been replaced by (but remains a crucial step in the computation of) ES by the Basel Committee on Banking Supervision (BCBS) as the primary metric for banks to forecast market risk and allocate the relevant amount of regulatory market risk capital. The aim of the study is to introduce a more accurate approach of measuring VaR and hence ES determined using loss forecast accuracy. VaR (hence ES) is unobservable and depends on subjective measures like volatility, more accurate (loss forecast) estimates of both are constantly sought. Modelling the volatility of asset returns as a stochastic process, so a Kalman filter (which distinguishes and isolates noise from data using Bayesian statistics and variance reduction) is used to estimate both market risk metrics. A variety of volatility estimates, including the Kalman filter's recursive approach, are used to measure VaR and ES. Loss forecast accuracy is then computed and compared. The Kalman filter produces the most accurate loss forecast estimates in periods of both calm and volatile markets. The Kalman filter provides the most accurate forecasts of future market risk losses compared with standard methods which results in more accurate provision of regulatory market risk capital.
... Rockinger and Urga (2001). Meanwhile, Das (2019) proposed techniques for beta and VaR estimation of assets using adaptive Kalman filters based on National Stock Exchange of India indices. The results showed that sector betas are not constant but time-varying, and that modified adaptive Kalman filter techniques with unknown process and observation noise covariances perform at least as well as, or even better than, the traditional Kalman filters. ...
The main objective of this paper is to examine the Kalman approach to estimate the time-varying CAPM beta on the US stock market over the long time horizon of thirty-one years. We investigate the beta estimates on the basis of three specifications: random walk (RW), mean-reverting process (MR), and random coefficient of the beta parameter (RC) for companies listed on NYSE and NASDAQ in the period 1990-2021. We examine the prognostic power of beta estimates and ranked the results according to criteria of forecast accuracy. In terms of the adopted criteria, the estimation of the beta parameter assuming its variability in time proved to be better than the OLS, LAD and ROLS methods of the Sharpe model. We can conclude that the Kalman filter approach with the assumption of a random coefficient (RC) or mean-reversion (MR) for the CAPM beta parameter gives the best results.
... The VaR reflects the maximum amount of loss exposed in oil during a specific period. In the existing literature, there are many studies focus on the application and some alternative risk measures based on GARCH-type models [27][28][29][30][31]. However, these approaches often assume that the distribution of oil return is invariable across time. ...
Due to the crucial implication of oil risks for economic growth and policy making, the aim of this paper is to explore the heterogeneous interconnections of supply or demand in oil risks over time horizons and different countries. Specifically, we first examine the correlation of supply or demand in oil return risks and show the relationships in different countries based on wavelet coherence. Furthermore, we explore the time-varying interconnections between supply- or demand-side and oil return risks, as well as oil producers and demand countries. The empirical results show that the correlation between supply and oil return risks is relatively stable, whereas the linkage between demand and oil return risks shows greater volatility due to the impact of specific events. Further study indicates that there are heterogeneous interconnections between supply- or demand-side and oil return risks over sample periods. Specifically, the sign of response could be divided into four phases, i.e., 1997–2002, 2002–2010, 2010–2013 and 2014–2018. In addition, the interconnections of the demand side could be divided into three phases due to the sign of it. What is more, the dynamic interconnections of oil producers’ or countries’ demands behave quite heterogeneously in different countries. Thus policymakers should focus on the coordination level and space capacity in the global crude oil market.
