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Time Series Analysis

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by

Maier Jessica

on 21 January 2014

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Transcript of Time Series Analysis

Time Series Analysis
Conclusion
In summary, time series analysis represents an
important field of statistics
and is
used
in
various fields
of application.

"The best qualification of a prophet is to have a good memory."

Marquis of Halifax
of Time Series Analysis in General
Classical Component Model
of Time Series Analysis
Specific Models
of Time Series Analysis
Typical Examples of a Time Series
Classical Component Model
of Time Series Analysis
Daily
closing prices
of market-listed derivatives
Monthly measured
unemployment rates
Annual
production rates
of a steel plant
Quarterly
revenue
of a company
Time Series Analysis in General
Classical Component Model
of Time Series Analysis
A time series is a sequence of observed values
of a certain characteristic, which are chronologically in succession and mostly periodical
among the same carrier.
Definition of Time Series
Valuable to identify
seasonal variations
Often practiced method
, probably more then theoretical methods
There are
no completely true components
Validity of hypotheses
are only partially verifiable
Components have to be
functions of time
Moving average
Exponential smoothing
Trend extrapolation
Box-Jenkins

Moving Average
Aim:
calculate an average
for the trend of historic data and
smooth out a time series
Differentiation into:
simple, exponential and weighted
moving average
Arithmetic mean of defined number of
successive values
within a specific time frame
Categorization into moving average of
even and uneven
order

Application of the Moving Average
Moving average of
uneven
order:
Moving average of
even
order:
Application of the Moving Average
Database for
Example in Lecture
of the Moving Average
Simple, practicable, and effective
in use
Basic mathematical tools
are sufficient
Easy in terms of
comprehensibility
Difficult to decide about
number of considered values
Simple moving average states an
equal weighting
for all values
It is suggested that the time series has an
regular cycle
Exponential Smoothing
Mathematical-statistical method for
short-term
to maximum
medium-term
horizons
Differentiation into:
single, double
and
triple
exponential smoothing
Recent
observed values are
more meaningful
for the prediction of the future than
earlier observed

Values are exponentially
increasing
from
past
to
present

Application of Exponential Smoothing
Application of Exponential Smoothing
of Exponential Smoothing
Trend Extrapolation
Simplest way to
define forecasts
Extrapolation relates to a
single time series
Historic data with
regularities
is continued into future

--> Trends in data must be
valid for future
as well
Based on the regularities in the historic data
trends are extrapolated into the future
Application of Trend Extrapolation
Possibility to use the
free-hand method
by sense of proportion
Mathematical way is
more appropriate
Different mathematical approaches
--> linear, parabolic, exponential and logistic trend, as well as gompertz curve

Application of Trend Extrapolation
Box-Jenkins methodology
Box-Jenkins methodology
Origin:
George Box and Gwilym Jenkins
in 1970
Main condition for the application:
stationarity
(mean variance and autocorrelation function that are essentially constant through time)
Principle of parsimony
: The more parameters to estimate, the more errors.
Aim: finding a good model
that describes how observations in a time series are related to each other

Comparison to classical model
Consideration of stochastic processes
instead of deterministic processes in order to model a time series.
Classical model: Cyclical movements are modeled as stationary processes around the deterministic trend.
Box-Jenkins:
random shocks are considered
and can have a
permanent effect on subsequent time series
data.

Basic Box-Jenkins Processes
Autoregressive
Process AR (p)
Basic Box-Jenkins Processes
Autoregressive Moving Average Process
ARMA
(p, q)
The Box-Jenkins model building process
Single
Exponential Smoothing:
Simple
, robust, easy to use
Possible to utilize
very short time
series
Not an art
to
update
if new data is available
Overly simplistic
and inflexible
Not optimal
for capturing any
linear dependence
in data
Hard
to forecast in the
long run
as values are
highly influenced
by
recent
happenings in the history of the time series
Database for
Example in Lecture
Application of Exponential Smoothing
Moving Average
Process MA (q)
Treatment of non-stationary processes:
ARIMA
(p, d, q)
Application of the trend extrapolation based on the linear trend states a
mathematical function
Multiplicative
Hybrid form
of Trend Extrapolation
Simple
to use
Time
as
only element
to change in function
Can be used to define
short-, medium- and long-term forecasts
Fluctuations in business cycle are
not considered
In a practical view it is
no longer sufficient
to extrapolate trends
Regularities of the past are
suggested to be valid
in future as well
Smooth Component
Wide spectrum of software programs
enables simulation of various types of models with correspondent results
Consideration of random shocks
which have a permanent effect on subsequent time series data
Reduction of errors
due to the principle of parsimony