financial econometrics introduction
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FINANCIAL ECONOMETRICS:
SCOPE AND METHODS
By Prabath. S. Morawakage
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Financial Econometrics
Concerns A mission for models that describe financial
time series such as prices, returns, interestrates, financial ratios, defaults etc.
Reason for the existence of such subject?
Main Question in Financial Econometrics
Its a multi discipline
Finance Economics
Mathematics
Statistics
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The universe cannot be read until we havelearnt the language and become familiar withthe characters in which it is written. It iswritten in the language of mathematics; theletters are triangles, circles, and othergeometrical figures, without which it is
humanly impossible to comprehend a singleword.
Galileo -1623
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It was only in the second half of the 20thcentury that a quantitative description ofeconomics became a mainstream discipline:econometrics (i.e., the quantitative science ofeconomics) was born.
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Data Generating Process
We write mathematical models, that is, relationshipsbetween different variables and/or variables indifferent moments and different places.
The basic tenet of quantitative science is that thereare relationships that do not change regardless ofthe moment or the place under consideration sea waves - random movement
in every moment and location the basic laws of hydrodynamics
hold without change
asset price - random movement
but econometric laws should hold in every moment and forevery set of assets
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Econometric models model the economy orfinancial markets
Information efficiency today Vs yesterday
Because the economy and financial markets areartifacts subject to change, econometric modelsare not unique representations valid throughouttime; they must adapt to the changingenvironment.
financial econometrics uses both continuoustime and discrete time models Derivatives Pricing CAPAM
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What is Data generating Process In a discrete dynamic model the mathematical relation ship
between variables at different time is called the datagenerating process
E.g. pt + 1 = + pt+ t+ 1
if we consider any two consecutive instants of time,there is a combination of prices that behave as randomnoise E.g. pt+ 1 pt= t + 1
an econometric model can be regarded as amathematical device that reconstructs a noise sequencefrom empirical data.
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Static models (i.e, models that involve onlyone instant) are used to express relationshipsbetween different variables at any giventime.
Static models are used, for example, to
determine exposure to different risk factors.
However, because they involve only one instant,static models cannot be used to make forecasts;
forecasting requires models that link variables intwo or more instants in time.
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Financial Econometrics at
WorkApplying financial econometrics involves threkey steps:
1. Model selection 2. Model estimation
3. Model testing
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Modeling issues
How do we apply statistics given that there is only one realization of
financial series?
Given a sample of historical data, how do we choose between linear
and nonlinear models, or the different distributional assumptions ordifferent levels of model complexity?
Can we exploit more data using, for example, high-frequency data?
How can we make our models more robust, reducing model risk?
How do we measure not only model performance but also the abilityto realize profits?
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Important factors to be
considered Time horizon
Model Riskiness
Model Robustness
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APPLICATIONS
There has been a greater use of econometricmodels in investment management since theturn of the century. Application areas include:
Portfolio construction and optimization
Risk management
Asset and liability management