Constrained Kalman Filtering: Additional Results

Pizzinga, Adrian

doi:10.1111/j.1751-5823.2010.00098.x

Cited by 39 publications

(12 citation statements)

References 44 publications

(74 reference statements)

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“…[24]), but we did not use any specific libraries to assist in the implementation of the Kalman filter and/or improve the process of maximizing the likelihood function, including their initial exact versions (see Sections 4.4 and 4.5). We should emphasize that the diffuse version of the log-likelihood presented in (17) has proven to be more stable when compared with the competing, big kappa version in (16); the latter encountered severe numerical difficulties during the estimation processes.…”

Section: The Inflation Index Used To Calculate Nominal Payments Is Thmentioning

confidence: 99%

“…According to Pizzinga , the reduced restricted Kalman filter is the most natural way of imposing the portfolio restriction on the dynamic asset class factor model (to be discussed in Section 5) properly converted into a linear state space model. Briefly, this method of implementing the Kalman filter under linear restrictions consists of rephrasing some coordinates of the state vector as appropriate affine functions (that is, linear functions plus an intercept term) of the others, placing the result in the measurement equation, and applying the usual Kalman filter with the modified (i.e., reduced) model.…”

Section: Linear State Space Models and The Kalman Filtermentioning

confidence: 99%

“…g g As Pizzinga claims, there is no loss of generality in considering that such a matrix is nonsingular, as there is always the possibility of rewriting the measurement and state equations to make such a partition attainable.…”

mentioning

confidence: 99%

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Restricted Kalman filter applied to dynamic style analysis of actuarial funds

Marques¹,

Pizzinga

Vereda

2011

Appl Stoch Models Bus & Ind

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We use dynamic style analysis to unveil the strategies followed by Brazilian actuarial funds from January 2004 to August 2008 and investigate whether managers' decisions were compatible with the intention of protecting the investor against the negative effects of inflation. The main goal of this paper is to show that this methodology is suitable for allowing insurance companies to increase their capacity to monitor the behavior of portfolios and to control the amount of risk they assume. The basic steps of the method are to build and/or choose market indexes capable of characterizing the returns of the main securities available and to apply restricted linear state space models estimated with a Kalman filter with exact initialization. The main conclusions of this paper are the following: (1) the use of exact initialization of the Kalman filter promotes numerical stability; (2) there is no need to consider the entire set of market indicators because a subset containing only three indexes spans the relevant space of investment opportunities; and (3) the actuarial funds' resources were primarily invested in inflation-indexed bonds, but fund managers also left room to adjust their exposure to other assets not directly related to the objective of providing protection against inflation. a Inflation-indexed assets or liabilities are those with returns protected against inflation, which means that their purchasing power does not decrease over time. b Loosely speaking, an exposure (or an allocation) is the proportion of total investment resources that is directed to a specific market or asset class. For instance, equity funds invest the bulk of their resources in buying shares; therefore, they have a higher exposure to some indexes that follow the returns provided by this kind of asset (such as the Dow Jones or the S&P 500 indexes in the US financial market). From a statistical point of view, they are nothing more than the coefficients of the time series regression models considered within. In our framework, a time-varying exposure is a random coefficient of a time series regression model. Bus. Ind. 2012, 28 558-570 d The acronym WN stands for 'White Noise', a term used for (possibly multivariate) second-order stochastic processes with uncorrelated components with zero mean and common variance. Because the covariance matrices H t and Q t can be time-varying, the use of the term here is perhaps inappropriate. Appl. Stochastic Models

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Section: The Inflation Index Used To Calculate Nominal Payments Is Thmentioning

confidence: 99%

Section: Linear State Space Models and The Kalman Filtermentioning

confidence: 99%

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Restricted Kalman filter applied to dynamic style analysis of actuarial funds

Marques¹,

Pizzinga

Vereda

2011

Appl Stoch Models Bus & Ind

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“…Both identities in (3) were originally dealt with in Doran [7], but a very quick, general, Gaussianbased proof is offered in Pizzinga and Fernandes [8]. Here, this is reproduced in Appendix A.…”

Section: Theorem 1 (The Gaussian Restricted Kalman Filtering)mentioning

confidence: 99%

Semi‐strong dynamic style analysis with time‐varying selectivity measurement: Applications to Brazilian exchange‐rate funds

Pizzinga

Vereda

Atherino

et al. 2007

Appl Stoch Models Bus & Ind

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SUMMARYThis paper deals with restricted linear state space models for dynamic style analysis with time-varying selectivity measurement. Implementation and interpretation of the models are pertinently discussed. Empirical contributions lie on the understanding of how managers of Brazilian US Dollar/Real exchange-rate funds behaved along 2001 and 2002, a period of some political turbulence especially due to the 2002 Brazilian presidential election.

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“…In practice, filtering problems often have certain inherent and known constraints in the physical dynamic systems [1], for example, target tracking [2,3], robotics [4], multisensor data fusion [5,6], vision-based systems [7], econometric modeling [8], biomedical systems [9] and others [10,11]. For equality-constrained state estimation, numerous approaches have been developed, for example, the model reduction method [5,6,12], the pseudo measurement method [13][14][15][16][17][18], the estimate projection method [19,20], the system projection method [21], the gain projection method [22], and some other methods [11,23].…”

Section: Introductionmentioning

confidence: 99%

New Viewpoints about Pseudo Measurements Method in Equality-Constrained State Estimation

Zhu

Luo

Zhu

2015

Mathematical Problems in Engineering

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We discuss the pseudo measurement method which is one of the main approaches to equality-constrained state estimation for a dynamic system. We demonstrate by the fundamental theory of Kalman filtering that reviewing the equality constraint as a pseudo measurement seems questionable. The main reason is that the additional pseudo measurement is actually a constant here which cannot help to estimate the state. More specifically, when the states in an unconstrained dynamic system model have already satisfied the equality constraint, the extra constraint is obviously not necessary. When the true equality-constrained states do not satisfy the unconstrained dynamic process equation, the effect of pseudo measurement is projecting the estimate which is not optimal onto the constraint set. However, since the performance of a projected estimate is also certainly influenced by its original estimate, we show through a numerical example that the pseudo measurement method is not always a good choice, especially when the process equation mismatch is large.

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Constrained Kalman Filtering: Additional Results

Cited by 39 publications

References 44 publications

Restricted Kalman filter applied to dynamic style analysis of actuarial funds

Restricted Kalman filter applied to dynamic style analysis of actuarial funds

Semi‐strong dynamic style analysis with time‐varying selectivity measurement: Applications to Brazilian exchange‐rate funds

New Viewpoints about Pseudo Measurements Method in Equality-Constrained State Estimation

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