Behavioral finance FAQ / Glossary (Nonlinear)

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Dates of related message(s) in the
Behavioral-Finance group (*):

Year/month, d: developed / discussed,
i: incidental

Non-linearity, nonlinear
    ffect / system

00/6i,12i + see chaos theory,
fractals, bifurcation, percolation,
soft computing, dynamical system,
equilibrium + bfdef3

Expect bumps and potholes on the road.
Expect even some hairpin turns

Keep your hand on the wheel !

Definition:

Broken arrows

Non linear phenomena, systems and data are those
that do not evolve in a continuous fashion.

When measured and shown on a chart, they follow

  broken and discontinuous (aka "discrete") lines. 

Mind the gaps!

Their quantitative evolution does not obey linear (in the sense of
    continuous) mathematics (*).

(*) Not to be confused with "nonlinear equations" that are just equations
      in which
a variable has an exponent below or above 1.

Non linear evolutions are quite common
* in physical science

* as well as in human and social areas.

Financial markets, as seen below, are typical examples.

What kinds of discontinuities?

One grain at a time in the hourglass...

....And some occasional and violent glass breaks.


This non continuity reflects:

Either granular changes and jumps.
   Many phenomena are made of a succession or coexistence of separate
   units
:

Apples on market stalls, atoms in chemistry, cents for "penny stocks",
hairs upon the head...

Or full instability and disruptions.

Some of them leading to decisive changes of the general
direction
from upwards to downwards or the other way round, for
example in economic evolutions)

Non linear systems

Oscillating, bending or breaking?

Non-linearity is common in many dynamical systems
(see that phrase).

They are not static, not fully stable (even in apparent
stasis phases), they are in a permanent state of near
disequilibrium
.

Like you and me, as we are dynamical systems ;-)

The balance in such systems suffers various degrees of
instability , as it:

In ordinary "calm" times, tilts alternatively towards one

side and another in a small vibration / oscillation,

In crucial times, undergoes bifurcations, or chaotic moves,

Can even suffer sudden rare and excessive
   events

    (aka black swans and fat tails, how animalistic!)
.

Or, get into extremely disruptive situations, which makes the

system either mutate or ...die.

Spectacular categories of non linear phenomena that characterizes recurrently
some of those systems include fractals, bifurcations and percolations (see
those words).

Non-linearity in financial markets

Bumpy price road. Adapt your driving!


Market price fluctuations
in capital asset markets are typical nonlinear
moves.

Careful, looking at stock charts can make dizzy!

The buy and sell transactions do not evolve in a smooth flow

Prices move in zigzags of every sizes:

from short term "volatility" (see that word)

to long term "cycle-trends" (see those words).

Those instabilities are important sources of what is called "risk" or
"uncertainty"
(see those words)

They have several causes:

On the technical side, the random arrival of buying / selling

orders, which do not coincide fully at all times,

On the economic side, the flow of exogenous information and

"surprises" that reach the market,


On the behavioral side, the collective variations of

understanding (cognition) and mood (emotion).

When behaviors are at play, randomness is not total.
various alternating but "sticky" psychological phenomena
might affect the market crowd.

Non-stationary

02/11i + see uncertainty,
model

Hard to follow their track, Sheriff,
I suspect erratic misconduct!

Definition: largely unstable statistical relations are said to be mathematically
"non-stationary"

Not only the numbers might fluctuate in a non linear (see
that phrase) way, but also the mathematical relations
between the numbers change.

It even sometimes reverts - from one period to another.

Time to upgrade the old software, as the computer starts
to tell lies!

To take opposite examples:

In a pure random system (casinos for example), odds are stable,
   probabilities stay the same all the time,

In economical and financial matters, on the contrary,
   past statistics and measures of risks can be misleading, as the
   future
never repeats the past exactly.

In those fields, measurable risks under stable "probability laws" are mixed
with a degree of non measurable future instability /
uncertainty
/ "non-stationarity".

In such situations, many equations / models are no longer reliable,
however mathematically elegant they are.

Use them with care,  and sometimes forget them!


Beware, when "backtesting" your smart "make money" systems!

If they work with past data, better not be overconfident that they
will work with certainty in future situations.

Don't bet the farm on those models,

use them with precautions !

(*) To find those messages: reach that BF group and, once there,
      1) click "messages", 2) enter your query in "search archives".

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This page last update: 22/08/15  

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