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Falsifying Generalized Wiener Processes. Melvin J. Hinich. Applied Research Laboratories University of Texas at Austin. hinich@austin.utexas.edu. http://web.austin.utexas.edu/hinich/. Black-Scholes Model. The Black-Scholes-Merton model is a central tool for

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Falsifying Generalized Wiener Processes

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Falsifying generalized wiener processes

Falsifying Generalized Wiener Processes

Melvin J. Hinich

Applied Research Laboratories

University of Texas at Austin



Black scholes model

Black-Scholes Model

The Black-Scholes-Merton model is a central tool for

pricing & hedging options & other derivatives securities.

The model employs a Wiener process

At present the derivatives business has become a more

than 415 trillion US$ market.

It has been implicated in the present world wide

financial crisis.


Generalized wiener process gwp

Generalized Wiener process(GWP)

bandlimited filter

non-gaussian i.i.d variates

fixed sampling rate

Bandlimited filter

Bandlimited Filter

Nyquist sampling rate

Falsifying generalized wiener processes

The generalized Wiener process (GWP) is linear

It is time reversiblesince the distribution of

is the same as the distribution of

The trispectrum

The Trispectrum

The principal domain of the trispectrum

in the cube of indices where

Falsifying generalized wiener processes

Normalized trispectrum

is the spectrum of

For the linear process GWP

Trispectrum based tests of linearity time reversibility

Trispectrum Based Tests of Linearity & Time Reversibility

The trispectrum version of the Hinich-Rothman (1998)

time reversibility test & the Hinich (1982) linearity test

can be used falsify the validity of the GWP model.


Estimating the trispectrum

Estimating the Trispectrum

Estimated normalized trispectrum

Testing linearity of a gwp

Testing Linearity of a GWP

Under this null hypothesis that the observed values of

are generated by a GWP when 0 < c < 1/3


has a uniform (0,1) distribution

Testing time reversibility of a gwp

Testing Time Reversibility of a GWP

has a uniform (0,1) distribution

Statistics of the 4 nyse returns

Statistics of the 4 NYSE Returns

Falsifying generalized wiener processes

Statistics after 10% Trimming of the Australian Returns

Nonlinearity test for nyse returns 73 trifreqs

Nonlinearity Test for NYSE Returns 73 Trifreqs

Falsifying generalized wiener processes

Nonlinearity Test Results for AU Returns 2,920 Trifreqs

Time reversibility test results

Time Reversibility Test Results

All TR p-values are < e-05

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