Time series data and Trends

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Time series data and Trends

• Dr. David Cornforth
• School of Information Technology and Electrical
  Engineering
• University of New South Wales _at_ ADFA

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Time Series Analysis
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What is a time series?

• An ordered sequence of data
• Usually ordered through time, e.g.
• Shop sales
• Visitors to a park
• Daily rainfall
• Factory production
• Weekly admissions to hospital
• Seasonal cpi trends

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What is time series analysis?

• The statistical interpretation of time series
• Uses of TSA
• Forecasting and projection
• Understanding temporal processes
• Methods
• Identify and model components
• trends, cycles, noise
• Build a composite model

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Components of TSA

• Trends
• Long-term changes in mean or variance
• Stationary series have no trends
• Cycles
• Repeating values eg seasonality
• Period, frequency, amplitude
• Noise
• Random fluctuations

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Time series
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Describing signals

• Trends
• Function of time or of another series
• Cyclic Components
• Period
• Amplitude
• Phase
• Noise
• Mean
• Standard Deviation

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Breakpoints

• Increase in flow in a stream (major storm)
• Increase in photosynthesis (morning sun)
• Surge in airline bookings (school holidays)

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Cumulative sums

• A visual aid to help locate breakpoints
• Exaggerate trends in mean or variance
• Change of slope means a break in the mean
• Change in amplitude means change of variance

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Cusums revisited
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Breakpoints in time series
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Filters

• Operations on series
• Moving average
• Mn aXn1 bXn cXn-1
• Autoregressive process
• An abXn bXn-1 bXn-2 cXn-3 ...
• Difference filter
• Dn bXn - cXn-1

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Filters
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Applications of filters