R. G. Palmer

Time Series Properties of an Artificial Stock Market

This paper presents results from an experiemtal computer simulated stock market. In this market artificial intelligence algorithms take on the role of traders. They make predictions about the future, and buy and sell stock an indicated by their expectations of future risk and return.

Solution of 'Solvable model of a spin glass'

Abstract The Sherrmgton-Kirkpatrick model of a spin glass is solved by a mean field technique which is probably exact in the limit of infinite range interactions. At and above T c the solution is identical to that obtained by Sherrington and Kirkpatrick (1975) using the n → O replica method, but below T c the new result exhibits several differences and remains physical down to T = 0.

The process of recurrent choice

Recurrent choice has been studied for many years. A static law, matching, has been established, but there is no consensus on the underlying dynamic process. The authors distinguish between dynamic models in which the model state is identified with directly measurable behavioral properties (performance models) and models in which the relation between behavior and state is indirect (state models). Most popular dynamic choice models are local, performance models. The authors show that behavior in different types of discrimination-reversal experiments and in extinction is not explained by 2 versions of a popular local model and that the nonlocal cumulative-effects model is consistent with matching and that it can duplicate the major properties of recurrent choice in a set of discrimination-reversal experiments. The model can also duplicate results from several other experiments on extinction after complex discrimination training.

Mean exit times over fluctuating barriers

Abstract We investigate the problem of thermal activation over a fluctuating barrier. Three regimes are considered: the fluctuations slow compared to the mean crossing time τA of the average barrier height, fluctuations on roughly the same timescale as τA, and fluctuations extremely fast compared to τA. In the latter two cases, the mean barrier crossing time is reduced. The relevance of these results to a variety of problems in complex systems is discussed.

An artificial stock market

The Santa Fe Artificial Stock Market consists of a central computational market and a number of artificially intelligent agents. The agents choose between investing in a stock and leaving their money in the bank, which pays a fixed interest rate. The stock pays a stochastic dividend and has a price which fluctuates according to agent demand. The agents make their investment decisions by attempting to forecast the future return on the stock, using genetic algorithms to generate, test, and evolve predictive rules. The artificial market shows two distinct regimes of behavior, depending on parameter settings and initial conditions. One regime corresponds to the theoretically predicted rational expectations behavior, with low overall trading volume, uncorrelated price series, and no possibility of technical trading. The other regime is more complex, and corresponds to realistic market behavior, with high trading volume, high intermittent volatility (including GARCH behavior), bubbles and crashes, and the presence of technical trading. One parameter that can be used to control the regime is the exploration rate, which governs how rapidly the agents explore new hypotheses with their genetic algorithms. At a low exploration rate the market settles into the rational expectations equilibrium. At a high exploration rate it falls into the more realistic complex regime. The transition is fairly sharp, but close to the boundary the outcome depends on the agents’ initial “beliefs”—if they believe in rational expectations they occur and are a local attractor; otherwise the market evolves into the complex regime.

Ground States For Large Samples Of Two-Dimensional Ising Spin Glasses

We have developed a combinatoric matching method to find the exact groundstate energy for the 2-D Ising spin glass with the ± J distribution and equal numbers of positive and negative bonds. For the largest size (1800×1800 plaquettes of spins), we averaged results from 278 samples and for the smaller ones up to 374, 375 samples. We also studied the behavior of the distributions of computer time (CPU) and memory as functions of sample size. We present finite size scaling leading to a groundstate energy estimate of E∞=-1.40193±2 for the infinite system. We found that the memory scales as the square of sample length and that for a given size, the CPU time appears to have a skewed and high-tailed distribution.

Magnetic properties of a model spin glass and the failure of linear response theory

Zero-temperature computer simulations are reported for the Sherrington-Kirkpatrick random Ising model of a spin glass, including an external field. Results are presented for the internal field distribution P(H), and for the ground state energy and magnetisation as functions of field. P(H) has a linear rise from H=0 for all external fields. The zero-temperature susceptibility chi (0) is close to unity when equilibrium states are examined, in agreement with Parisis replica symmetry breaking theory and in conflict with linear response theory. The linear response result chi (0)=0 can be obtained by searching for metastable local energy minima close to the zero-field ground state in configuration space.

Internal field distributions in model spin glasses

The zero temperature probability distribution P(h) of internal magnetic fields is studied, both in the Sherrington-Kirkpatrick random Ising model of a spin glass and in its natural extension to classical vector spins. Theoretical predictions and computer simulations agree that P(h) is linear for small h in the Ising case, and has a hole-P(h)=0 for h< eta -in the vector spin case.

Error Estimation in the Histogram Monte Carlo Method

We examine the sources of error in the histogram reweighting method for Monte Carlo data analysis. We demonstrate that, in addition to the standard statistical error which has been studied elsewhere, there are two other sources of error, one arising through correlations in the reweighted samples, and one arising from the finite range of energies sampled by a simulation of finite length. We demonstrate that while the former correction is usually negligible by comparison with statistical fluctuations, the latter may not be, and give criteria for judging the range of validity of histogram extrapolations based on the size of this latter correction.

The thermodynamic limit and the replica method for short-range random systems

Short-range spin systems with random interactions are considered. A simple proof is given showing that the free energy of almost every sample converges to the average free energy in the thermodynamic limit. A stronger criterion, thermodynamic convergence, is also demonstrated. This implies that the N to infinity and n to 0 limits may be interchanged in the replica method.