Jan W Dash

Data Spike Cleaning with MSSA

This paper introduces a powerful method for detecting and fixing unphysical spikes in time series. The method utilizes Multiple Singular Spectrum Analysis (MSSA) to define local market trends used to identify outlier data spikes that are not caused by market movements, and then effectively correct the spikes. Various refinements for spike identification are proposed. This work extends previous work using MSSA to fill gaps or holes in time series.

Cleaning Financial Data Using SSA and MSSA

We introduce a powerful method for cleaning time series - Multi-Channel Singular Spectrum Analysis (MSSA). “Cleaning” means filling data gaps and removing unphysical spikes, which are chronic problems. MSSA utilizes all available information in “time” and “space” with autocorrelations, correlations, and lagged correlations. MSSA performs demonstrably better than other methods. Here we present tests using MSSA to fill data gaps, with positive results. Spike removal is in a separate paper.

Advanced Idiosyncratic Risk and Multi-Factor Models – Short Version

We introduce advanced idiosyncratic risk (“AI-Risk”), a parsimonious correlated residual correction to a predictive stress CAPM-like factor model, aimed to get more accurate stock-stock correlations. We find that AI-Risk can be significant for stock portfolios. Inclusion of AI-Risk gives a more realistic risk assessment, consistent with real-world correlation constraints. We also indicate the generalization of AI-Risk to cross-sectional regression factor models, of interest to PMs. This paper is an abridged version.

Non-Leading Eigenvalue Distributions, RMT, and Correlations

We showed that Singular Spectrum Analysis (SSA) applied to time series yields better correlations for risk simulations. This involved comparing SSA-based correlations with standard correlations and to noise, a zero correlation Wishart random matrix (WRM). We complete this testing here. We also present tractable analytic approximate WRM results that we used in the analysis: (1) leading and non-leading eigenvalue distributions of a WRM, (2) eigenvalue spacing of WRMs, and (3) eigenvector components of WRMs.

Predicting Equity Crises, Critical Exponents, and Earthquakes - II

We present further encouraging evidence for the Critical Exponent Earthquake Crisis (CEEC) Model that gives the probabilities of equity crises one year in advance. The CEEC model uses suitable precursor signals and is agnostic regarding dynamical origins of crises. The precursors accumulate in time between crises, like precursors to some earthquakes. The model uses a sophisticated noise filter to separate out crisis signals. The main metric is the anomalous exponent of an equity series describing the difference of the data variance scaling exponent from the Brownian variance scaling exponent of 1. No extra non-equity variables are used. The CEEC Model results for predicting crises are not perfect, but are much better than chance, including out-of-sample tests. The details here supplement our previous CEEC crisis paper (2013). In another paper (2016) we give details showing that various markets - not just equities - that are already in crisis are on the average described by a critical exponent of the nonlinear-diffusion Reggeon Field Theory (RFT), calculated in 1974, with no free parameters. Nonlinear diffusion naturally extends Brownian motion. Rich/cheap crisis behavior is suggested as a paradigm. This supplements our previous CEEC crisis paper (2013). The CEEC Model crisis predictions use the same scaling form described by the anomalous exponent as does the RFT. This consistency for crisis predictions and crisis behavior is significant.

Describing Crises with a Critical Exponent of the Reggeon Field Theory

We present evidence that markets in crisis can be described by a critical exponent of the nonlinear-diffusion Reggeon Field Theory, calculated 40 years ago, with no free parameters, translated to finance. We propose this as a benchmark for average crisis behavior, to which individual crises can be rich or cheap. In another paper we present a quantitative model for the probability of equity crises in advance. An earlier paper contained a summary.

Analytic Solution to the Two Dimension Merton Model

We present an exact analytic solution to the two-dimensional correlated default structural Merton model in the form of a local volatility problem using a conformal square-root transformation of the exact solution to a 2D hybrid barrier problem. We also give an approximation and evaluate it numerically to give an example. Finally we give an exact simpler solution for the zero correlation case.

Nearest Neighbor Technique for a Positive Definite Correlation Matrix in Advanced Stressed VAR

We present a new technique for obtaining a positive definite (PD) correlation matrix from a stressed target matrix within the context of Advanced Stressed Value at Risk, (cf. Dash ). The technique uses the spherical decomposition and a “nearest neighbor” technique. The advantage is that control over the scenario specified by the risk manager for the target matrix is achieved in that a maximal number of correlations specified by the target matrix scenario is maintained.

Stable Reduced-Noise 'Macro' SSA - Based Correlations for Long-Term Counterparty Risk Management

We introduce a methodology from geophysics, Singular Spectrum Analysis (SSA), to obtain stable, noise-cleaned correlations for long term risk (e.g. counterparty risk). SSA is applied to time series to smooth them in a robust manner. The SSA-smoothed time series are then used to obtain the correlations. We call these “macro�? correlations because they are determined with macroscopic time scales. Stable correlations are desirable to suppress noise from short time scales that make risk measures unstable. If correlations move around, risk measures also move around, making business decisions difficult. SSA-based correlations ameliorate this business problem.

Noise-Reduced Correlations, the Signal to Noise Ratio, and SSA

This is the second paper presenting noise-reduced, stable correlations for long-term risk measurement. We smooth time series using Singular Spectrum Analysis (SSA) and then form the correlations from these smoothed time series. These correlations have superior time stability and are cleaned of noise. Here we show that the Signal-to-Noise Ratio is larger for the SSA-based correlations than usual, and we perform other signal/noise tests. We use new results refining random matrix correlations.