Financial Econometrics

Session II

12/23/2013 1Introduction to Financial Time series

Why return series more engaging?

• Return of an asset is a complete and scale-free summary of the investment opportunity.

• Second, return series are easier to handle than price series because the former have more attractive statistical properties.

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Return and Prices

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Descriptive statistics

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Naked Eye Observations

• Plots of all indices show that volatility clustering.• Large (Small) shocks followed by large (Small) shocks.• Lots of large observations implying lots of observations

are on the tail of the corresponding distribution. So Distributions are of THICK TAILS.

• Table shows that all the return distributions are slightly positively skewed---right tail is larger than the left tail.

• High kurtosis coefficients---thick tails.• Thick tail has a serious implication in themeasurement of Value-at-Risk.

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Data Types of Financial Variables and corresponding Analysis

• The price of a financial asset evolves over time and forms a stochastic process, which is a statistical term used to describe the evolution of a random variable over time. The observed prices are a realization of the underlying stochastic process.

• The theory of stochastic process is the basis on which the observed prices are analyzed and statistical inference is made.

• a statistical process involving a number of random variables depending on a variable parameter (which is usually time).

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Stochastic Process

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The Type of Process we will analyse

• Two types of stochastic process• (1) the discrete-time stochastic process, in which the

price changes at discrete time points so when T is a set of integers, representing specific time points .

• (2) continuous-time process, in which the price changes continuously, even though the price is only observed at discrete time points.

• If T is the real line (or some interval of the real line) we have a stochastic process in continuous time and we change the notation slightly, writing X(t) rather than Xt.

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The Type of Process we will analyse

• For both types of process, the price can be continuous or discrete.

• Discrete time continuous process(mostly): the Ex: Daily closing price of IBM stock on the New York Stock Exchange-Main theme of our analysis

• Discrete time discrete Process: The high frequency data in finance are the transaction-by-transaction or trade-by-trade data in security markets: the tick-by-tick return of an individual stock.

• Continuous time discrete Process : ECG Graph• Continuous time continuous process: Financial

Mathematics

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Discrete time discrete Process

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What we will do?

the capital asset pricing model (CAPM) of Sharpe (1964) focus on the joint distribution of N returns at a single time index t (i.e., the distribution of

Our main concern first:

Then second:

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Linear Time series Analysis

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12/23/2013 17Introduction to Financial Time series

12/23/2013 18Introduction to Financial Time series

12/23/2013 19Introduction to Financial Time series

12/23/2013 20Introduction to Financial Time series

12/23/2013 21Introduction to Financial Time series

12/23/2013 22Introduction to Financial Time series

Linear Time series analysis

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ProgramR

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Programlecture2

Data files: m-gs10,m-gs1,m-ibmvwewsp2603txt

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