Time Series - STAT - EPFL

Comments
□ The measurements can be continuous (temperatures) or discrete (infectious disease counts) or a
mixture (rainfall), scalar or vector (seal position)
□ Mostly they are at regular intervals, but some are intermittent (quakes)
□ Some are instantaneous values, others are integrals (rain)
□ Some series exhibit strong trend and/or seasonality (CO 2 , infectious diseases, stock markets)
□ There can be missing observations and/or possible outliers (ozone, rainfall)
□ Series can be long (rainfall, temperatures) or very short (microarray)
□ May be one or a few or many series
□ Focus may be
– a possible change in the underlying series, so the dependence is a nuisance (e.g. ozone,
temperatures, beaver, microarray)
– dependence/interaction within or between series (quakes, diseases, stock markets)
– rare events (stock markets, rainfall, ozone)
– comparison of parallel series (microarray)
Time Series Autumn 2008 – slide 17
Objectives
Typically we have in mind one or more of the following general objectives:
□ Description
– Want a ‘simple’ summary of the series
□ Analysis
– Construct stochastic model(s), and try and answer questions with them
– Model will reflect knowledge about phenomenon under study and complexity of data available
– May just need to accommodate dependence as part of larger analysis
□ Monitoring/Control
– Blood pressure/chemical reactor temperature must be kept between x 0 and x 1
– Aim to detect changes as they occur and to influence process in real time
□ Forecasting
– ‘What will the market do tomorrow’ ‘What will the economy do next year’
– Sometimes the model is not so important (though economic models may be complex)
– Often combine different models to get best forecasts (‘model averaging’)
Time Series Autumn 2008 – slide 18
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