Introduction to Financial Time Series

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Introduction to Financial Time Series

• From Ruey. S. Tsays slides

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What is Financial Time Series Analysis

• Theory and practice of asset valuation over time.
• Different from other T.S. analysis?
• Close, but with some added uncertainty.
• For example, FTS must deal with the
  ever-changing business economic environment and
  the fact that volatility is not directly observed.

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Examples of financial time series

• Daily log returns of GE stock
• Quarterly earnings of Johnson Johnson
• Seasonal time series useful in
• earning forecasts
• pricing weather related derivatives (e.g. energy)
• modeling intraday behavior of asset returns
• US monthly interest rates
• Relations between the two series? Term structure
  of interest rates
• Exchange rate between US Dollar vs Japanese Yen
• Fixed income, hedging, carry trade
• Size of insurance claims
• Values of fire insurance claims from 1972 to
  1992.
• High-frequency financial data
• Tick-by-tick data of Boeing stock December 5,
  2005.

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Example of FTS
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Example of FTS (Cont.)
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Objective of the Course

• Provide some basic knowledge of financial time
  series data.
• Introduce some statistical tools econometric
  models useful for analyzing these series.
• Gain empirical experience in analyzing FTS.
• Design your own method to predict future FTS.

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Asset Returns

• From Ruey. S. Tsays slides

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Asset Returns
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Asset Return Example
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Asset Returns
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Compound Assert Returns
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Compound Assert Returns
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Compound Assert Returns
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Asset Returns

• Pt The price of an asset at time index t.
• One-period simple return, from t-1 to t
• Multi-period simple return, from t-k to t
• Annualized
• Continuously compounded return

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Asset Returns

• For multi-period returns, we have
• Captial Asset Price Model (CAPM)
• Consider the joint distribution of N return at a
  single time index t, Or, study the distribution
• We will focus on the dynamic structure of
  individual asset returns, in other words, we
  study the distribution of
  How to describe the joint distribution of

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Asset Returns

• For discrete case
• For continuous case

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Marginal Distribution of Asset Returnd

• When asset returns have weak empirical serial
  correlation, their marginal distributions are
  close to their conditional distributions. Thus
  the question is how to estimate marginal
  distributions.
• Several statistical distributions have been
  proposed for marginal distribution of asset
  returns
• Normal distribution
• Lognormal distribution
• Stable distribution
• Scale-Mixture Normal distribution

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Linear Time Series Analysis

• From Ruey. S. Tsays slides

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Linear Time Series (TS) Models
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Basic Concepts
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Basic Concepts (Cont.)
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Basic Concepts (Cont.)
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Basic Concepts (Cont.)
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(No Transcript)
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Univariate TS Analysis
Purpose
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Example of Linear Time Series
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Linear Financial Time Series
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AR Model
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AR Model (Cont.)
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AR Model (Cont.)
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AR Model (Cont.)
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AR(2) Model
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Building an AR Model
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Moving-Average (MA) Model
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MA(1) Model (Cont.)
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MA(2) Model
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Building MA Model
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Mixed ARMA Model
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Mixed ARMA Model (Cont.)
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Building an ARMA (1, 1) Model
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Three Model Comparisons
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Seasonal Time Series
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Examples of Seasonal Time Series (1)
Figure 1 Time plot of electricity demand of an
industrial sector 15th day of each month
from1972 to 1993.
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Example of Seasonal Time Series (2)
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Example of Seasonal Time Series (3)
Figure 3 Time plot of quarterly logged earnings
of Johnson and Johnson 1960-1980
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Seasonal Difference Model