A Dynamic Analysis of Moving Average Rules

The use of various moving average rules remains popular with financial market practitioners. These rules have recently become the focus of empirical studies. However there have been very few studies on the analysis of financial market dynamics resulting from the fact that some agents engage in such strategies. In this paper we seek to fill this gap in the literature by proposing a dynamic financial market model in which demand for traded assets has both a fundamentalist and a chartist component. The chartist demand is governed by the difference between a long run and a short run moving average. Both types of traders are boundedly rational in the sense that, based on a certain fitness measure, traders switch from a strategy with low fitness to the one with high fitness. We characterise first the stability and bifurcation properties of the underlying deterministic model via the reaction coefficient of the fundamentalists, the extrapolation rate of the chartists and the lag lengths used for moving averages. By increasing the switching intensity, we then examine various rational routes to randomness for different, but fixed, long run moving averages. The price dynamics of the moving average rule is also examined and it is found that an increase of the window length of the long moving average can destabilize an otherwise stable system, leading to more complicated, even chaotic behaviour. The analysis of the corresponding stochastic model is able to explain various market price phenomena, including market crashes, price switching between different levels and price resistance.moving averages; fundamentalis; trend followers; stability; bifurcation; volatility clustering

Bubbles and crashes: A vicious cycle of self-fulfilling investor sentiment

When traders expect an asset price to go up, they buy more, raising aggregate demand and driving up prices, write Te Bao, Cars Hommes and Tomasz Makarewic

Forward and Backward Dynamics in Implicitly Defined Overlapping Generations Models

In dynamic economic models derived from optimization principles, the forward equilibrium dynamics may not be uniquely de…fined, while the backward dynamics is well de…fined. We derive properties of the global forward equilibrium paths based on properties of the backward dynamics. We propose the framework of iterated function systems (IFS) to describe the set of forward equilibria, and apply the IFS framework to a one- and a two-dimensional version of the overlapping generations (OLG)-model. We show that, if the backward dynamics is chaotic and has a homoclinic orbit (a "snap-back repeller") the set of forward equilibrium paths converges to a fractal attractor. Forward equilibria may be interpreted as sunspot equilibria, where a random sunspot sequence determines equilibrium selection at each date.forward and backward dynamics, chaos, homoclinic orbit, snap-back repellor, sunspot equilibria, overlapping generations models.

Critical slowing down as an early warning signal for financial crises?

Financial crises have repeatedly been coined as a potential application area in the recent literature on constructing early warning signals through identifying characteristics of critical slowing down on the basis of time series observations. To test this idea, we consider four historical financial crises—Black Monday 1987, the 1997 Asian Crisis, the 2000 Dot-com bubble burst, and the 2008 Financial Crisis—and investigate whether there is evidence for critical slowing down prior to these market collapses. We find statistical evidence for critical slowing down before Black Monday 1987, while the results are mixed or insignificant for the more recent financial crises

Comparing Behavioural Heterogeneity Across Asset Classes

We estimate an endowment-based asset pricing model in which agents have heterogeneous and time-varying beliefs about the future price on a range of asset classes. This gives insight into the extent behaviour differs across assets, and what this implies for market stability. We find evidence for behavioural heterogeneity for all asset classes but equity. Heterogeneity is especially large and persistent in asset classes for which limits to arbitrage are more binding. In less constrained (financial) markets, agents update their beliefs more frequently. Consequently, the probability of behavioural bubbles and crashes is substantially higher in macroeconomic asset classes than in financial asset classes

Innovate or Imitate? Behavioural technological change

We propose a behavioural model of technological change with evolutionary switching between costly innovators and free imitators, and study the endogenous interplay of innovation decisions, market price dynamics and technological progress. Innovation and imitation are strategic substitutes and exhibit negative feedback. Endogenous technological change is the cumulative outcome of innovation decisions. There are three scenarios: market breakdown, Schumpeterian rents and learning curves. The latter is characterised by an increasing fraction of innovators when demand is elastic, while inelastic demand allows technological progress with shrinking innovation effort. Model simulations are compared to stylised features of empirical data in two industrial sectors

Bifurcation Routes to Volatility Clustering under Evolutionary Learning

A simple asset pricing model with two types of boundedly rational traders, fundamentalists and chartists, is studied. Fractions of trader types change over time according to evolutionary learning, with chartists conditioning their forecasting rule upon deviations from a benchmark fundamental. Volatility clustering arises endogenously and two generic mechanisms are proposed as an explanation: (1) coexistence of a stable steady state and a stable limit cycle, due to a so-called Chenciner bifurcation of the system and (2) intermittency and associated bifurcation routes to strange attractors. Economic intuition as to why these phenomena arise in nonlinear multi-agent evolutionary systems is provided