Simplified Samuelson Conditions for Cubic and Quartic Equations*

Farebrother, R. W.

doi:10.1111/j.1467-9957.1973.tb00090.x

Cited by 59 publications

(28 citation statements)

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“…The following set of inequalities imposed on the coefficients of the characteristic polynomial (36) provide a necessary and sufficient condition for all the eigenvalues of (32) to be of modulus smaller than unity (Farebrother (1973)), which implies a locally asymptotically stable steady state:…”

mentioning

confidence: 99%

Heterogeneous speculators, endogenous fluctuations and interacting markets: A model of stock prices and exchange rates

Dieci

Westerhoff

2010

Journal of Economic Dynamics and Control

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We develop a discrete-time model in which the stock markets of two countries are linked via and with the foreign exchange market. The foreign exchange market is characterized by nonlinear interactions between technical and fundamental traders. Such interactions may generate complex dynamics and recurrent switching between "bull" and "bear" market phases via a well-known pitchfork and period-doubling bifurcation path, when technical traders become more aggressive. The two stock markets are populated by fundamentalists, and prices tend to evolve towards stable steady states, driven by linear laws of motion. A connection between such markets is established by allowing investors to trade abroad, and the resulting three-dimensional dynamical system is analyzed. One goal of our paper is to explore potential spill-over effects between foreign exchange and stock markets. A second, related goal is to study how the bifurcation sequence which characterizes the market with heterogeneous speculators is modified in the presence of interactions with other markets.

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confidence: 99%

Heterogeneous speculators, endogenous fluctuations and interacting markets: A model of stock prices and exchange rates

Dieci

Westerhoff

2010

Journal of Economic Dynamics and Control

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“…Together with the policy rule it becomes a 3 × 3 system of difference equations. Using the criterion of stability of a 3 × 3 system from Farebrother (1973) and our particular parameter values α 1 = 0.5, α 2 = 0.15, β 1 = 0.9, β 2 = 0.75, we conclude that the system is stable if and only if T 1 > 0, T 2 > 0, T 3 > 0, T 4 > 0 (see the online-appendix for more details), where…”

Section: Stability Of Non-optimal Rulesmentioning

confidence: 95%

An experimental test of Taylor-type rules with inexperienced central bankers

Engle‐Warnick

Turdaliev

2010

Exp Econ

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“…Si on fixe -θ 2 = -θ 2 0 = (θ 20 , ..., θ p0 )′, le problème se réduit à la résolution de polynômes du second degré en θ 1 . Plus précisément, Farebrother (1973Farebrother ( , 1974aFarebrother ( , 1974bFarebrother ( , 1974cFarebrother ( , 1976Farebrother ( , 1987.…”

Section: Processus Autorégressif Généralunclassified

Méthodes d’inférence exactes pour des processus autorégressifs : une approche fondée sur des tests induits

Dufour

Neifar

2004

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Simplified Samuelson Conditions for Cubic and Quartic Equations*

Cited by 59 publications

References 1 publication

Heterogeneous speculators, endogenous fluctuations and interacting markets: A model of stock prices and exchange rates

Heterogeneous speculators, endogenous fluctuations and interacting markets: A model of stock prices and exchange rates

An experimental test of Taylor-type rules with inexperienced central bankers

Méthodes d’inférence exactes pour des processus autorégressifs : une approche fondée sur des tests induits

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