1,170 research outputs found
Filtering and Forecasting Spot Electricity Prices in the Increasingly Deregulated Australian Electricity Market
Modelling and forecasting the volatile spot pricing process for electricity presents a number of challenges. For increasingly deregulated electricity markets, like that in the Australian state of New South Wales, there is need to price a range of derivative securities used for hedging. Any derivative pricing model that hopes to capture the pricing dynamics within this market must be able to cope with the extreme volatility of the observed spot prices. By applying wavelet analysis, we examine both the price and demand series at different time locations and levels of resolution to reveal and differentiate what is signal and what is noise. Further, we cleanse the data of leakage from the high frequency, mean reverting price spikes into the more fundamental levels of frequency resolution. As it is from these levels that we base the reconstruction of our filtered series, we need to ensure they are least contaminated by noise. Using the filtered data, we explore time series models as possible candidates for explaining the pricing process and evaluate their forecasting ability. These models include one from the threshold autoregressive (AR) model. What we find is that models from the TAR class produce forecasts that best appear to capture the mean and variance components of the actual data.electricity; wavelets, time series models; forecasting
A Tractable State-Space Model for Symmetric Positive-Definite Matrices
Bayesian analysis of state-space models includes computing the posterior
distribution of the system's parameters as well as filtering, smoothing, and
predicting the system's latent states. When the latent states wander around
there are several well-known modeling components and
computational tools that may be profitably combined to achieve these tasks.
However, there are scenarios, like tracking an object in a video or tracking a
covariance matrix of financial assets returns, when the latent states are
restricted to a curve within and these models and tools do not
immediately apply. Within this constrained setting, most work has focused on
filtering and less attention has been paid to the other aspects of Bayesian
state-space inference, which tend to be more challenging. To that end, we
present a state-space model whose latent states take values on the manifold of
symmetric positive-definite matrices and for which one may easily compute the
posterior distribution of the latent states and the system's parameters, in
addition to filtered distributions and one-step ahead predictions. Deploying
the model within the context of finance, we show how one can use realized
covariance matrices as data to predict latent time-varying covariance matrices.
This approach out-performs factor stochastic volatility.Comment: 22 pages: 16 pages main manuscript, 4 pages appendix, 2 pages
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Dynamic Mode Decomposition for Compressive System Identification
Dynamic mode decomposition has emerged as a leading technique to identify
spatiotemporal coherent structures from high-dimensional data, benefiting from
a strong connection to nonlinear dynamical systems via the Koopman operator. In
this work, we integrate and unify two recent innovations that extend DMD to
systems with actuation [Proctor et al., 2016] and systems with heavily
subsampled measurements [Brunton et al., 2015]. When combined, these methods
yield a novel framework for compressive system identification [code is publicly
available at: https://github.com/zhbai/cDMDc]. It is possible to identify a
low-order model from limited input-output data and reconstruct the associated
full-state dynamic modes with compressed sensing, adding interpretability to
the state of the reduced-order model. Moreover, when full-state data is
available, it is possible to dramatically accelerate downstream computations by
first compressing the data. We demonstrate this unified framework on two model
systems, investigating the effects of sensor noise, different types of
measurements (e.g., point sensors, Gaussian random projections, etc.),
compression ratios, and different choices of actuation (e.g., localized,
broadband, etc.). In the first example, we explore this architecture on a test
system with known low-rank dynamics and an artificially inflated state
dimension. The second example consists of a real-world engineering application
given by the fluid flow past a pitching airfoil at low Reynolds number. This
example provides a challenging and realistic test-case for the proposed method,
and results demonstrate that the dominant coherent structures are well
characterized despite actuation and heavily subsampled data
Determining The Value-at-risk In The Shadow Of The Power Law: The Case Of The SP-500 Index
In extant financial market models, including the Black-Scholes’ contruct, the dramatic events of October 1987 and August 2007 are totally unexpected, because these models are based on the assumptions of ‘independent price fluctuations’ and the existence of some ‘fixed-point equilibrium’. This paper argues that the convolution of a generalized fractional Brownian motion (into an array in frequency or time domain) and their corresponding amplitude spectra describes the surface of the attractor driving the evolution of prices. This more realistic approach shows that the SP-500 Index is characterized by a high long term Hurst exponent and hence by a ‘black noise’ with a power spectrum proportional to f-b (b > 2). In that set up, the above dramatic events are expected and their frequencies are determined. The paper also constructs an exhaustive frequency-variation relationship which can be used as practical guide to assess the ‘value at risk’.Market Collapse; Fractional Brownian Motion; Fractal Attractors; Maximum Hausdorff Dimension of Markets and Affine Profiles; Hurst Exponent; Power Spectrum Exponent; Value at Risk
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