Using Nelder–Mead to Initialize Nelson–Siegel–Svensson Estimation
Summary
The document outlines a bond-curve estimation procedure based on the Nelson–Siegel–Svensson model. Given bond cash flows and prices, the procedure calculates spot rates and discount factors, prices the bonds from those discount factors, and derives model-implied yields to maturity. It then minimizes the sum of squared differences between observed and fitted yields, using a numerical optimizer to estimate the curve parameters subject to a parameter constraint.
The central clarification is that “Simplex” in the cited paper most likely means the Nelder–Mead direct-search optimization method, which can find starting parameter values before a second optimization stage such as BHHH. It should not be confused with the linear-programming simplex algorithm. A response also notes that fixing the decay parameters may leave a linear least-squares fit for coefficients. The exchange offers interpretation rather than a full implementation; the precise objective, constraints, and optimizer behavior depend on the source paper and setup.
Key ideas
- The curve-fitting workflow converts bond cash flows and discount factors into model-implied prices and yields.
- The objective described is a sum of squared observed-versus-fitted yield errors.
- The paper’s “Simplex” likely refers to Nelder–Mead direct search for starting values, not linear-programming simplex.
- BHHH is described as a subsequent method for final parameter estimation.
- With decay parameters fixed, the remaining coefficient fit may reduce to linear least squares.
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# How do I use BIC (Bayesian Information Criterion) to estimated model AR (auto regressive) lag? # How do I use BIC (Bayesian Information Criterion) to estimated model AR (auto regressive) lag? In financial research papers, I have seen several times that the lag length in an ARMA model has been determined using BIC. Do the researchers estimate the lag length before considering other variables? Would you compare the BIC values of the just the dependent variable and its lags or would you compare the BIC of the full model with the other exogenous variables. Should I use method 1) BIC1 Y(t) = c + Y(t-1) BIC2 Y(t) = c + Y(t-1) + Y(t-2) ... or should I use method 2) BIC1 Y(t) = c + Y(t-1) + x1 + x2 + x3 BIC2 Y(t) = c + Y(t-1) + Y(t-2) + x1 + x2 + x3 ... ## Answer by Quantopik (score 0, accepted) https://quant.stackexchange.com/a/16542 Generally it depends on the model you need to compare; anyway, if I understood your question, you have to estimate the model (2) and in this case it is convenient to compare the Bayesian Information Criterion only for the model (2), since it is exactly what you want to run in the end. Said that, I suggest you to look at the different criteria that exists in literature (AIC, BIC, DIC, FIC, R2,...) in order to be able to choose the one that is more suitable for your needs. For instance, in my humble opinion, it is not convenient to use the BIC because of the fact it is neither a good estimator of the Kullback-Leibler's divergence (on which it is based) and asymptotically efficient, as suggested by Burnham & Anderson (2002). I suggest you to use the AIC in the place of the BIC, that, at least, it is more precise from a theoretical point of view. Of course, choose the model with the lowest statistic score (in both the case). ## Answer by Avinash Barnwal (score 0) https://quant.stackexchange.com/a/16607 To identify the best lags , try to fit models with different lag choices.Plotting of ACF and PACF could give a sense of different lags choices. Further to this BIC could be used to determine for which AR and MA lag BIC is getting minimised.
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