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Introduction
• A time series is an ordered sequence of observations.
• The ordering of the observations is usually through time, but may
also be taken through other dimensions such as space.
• Time series analysis deal with relationship between observations
that are separated by k units of time or space (lagged observations).
• We are interested to know how the present depends upon the past.
• Time series occur in a variety of fields.
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Examples
• In agriculture, we observe annual crop production and prices.
• In economics, we observe daily stock prices, weekly interest rates,
monthly price indices, quarterly sales and yearly earnings.
• In engineering, we observe sound, electric signals and voltage.
• In meteorology, we observe hourly wind speed, daily temperature
and annual rainfall.
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Type of Time Series Data
• A time series that can be recorded continuously in time, is said to be
continuous. For example, electrical signals and voltage.
• A time series that is taken only at specific time intervals is said to be
discrete. For example, interest rates, volume of sales etc.
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Objectives
• Understanding and description of the generating mechanism.
• Modeling and inference.
• Forecasting and prediction.
• Optimal control of a system.
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Important note
• The basic nature of a time series is that its observations are
dependent or correlated, and the order of the observations is
therefore important.
• Statistical procedures and techniques that rely on independence
assumptions are no longer applicable.
• The statistical methodology available for analyzing time series is
referred to as time series analysis.
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Time versus Frequency Domain
• Time series approach, which uses autocorrelation and partial
autocorrelation functions to study the evolution of a time series
through parametric models, is known as frequency domain
analysis.
• An alternative approach, which uses spectral functions to study the
nonparametric decomposition of a time series into its different
frequency components, is known as frequency domain analysis.
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Graphical Methods
• The preliminary goal is to describe the overall (macro) structure of data
and to identify memory type of time series.
• There are two types of memories:
(1) Short memory – immediate past gives some information about
immediate future but less information about long-term future.
(2) Long memory – past gives (potentially) more information about
future (long term). Includes series with trends or cycles (seasonality).
• A basic useful graphical tool is a Time Series Plot. We plot the data
versus time.
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