Statistical Data Processing
Time series analysis


Outline of the lecture
•Time series
•Decomposition of the time series into
the trend, seasonal, cyclic, and random component
•The trend component
•The seasonal component
•Autocorrelation of the random component:  Durbin-Watson test
•Moving average:  simple, centred, and weighted moving average

Time series



Time series
•Instantaneous value type time series
  —  the measured value is taken at a particular time.
Examples:  the air temperature,  the wind speed
•
•Step accumulated value type time series
  —  the measured value is take over an entire interval of time
Example:  the rainfalls during the past hour

Time series



Time series



Time series



Time series



Time series



Time series:  Special cases



Time series:  Trend component



Time series:  Constant trend



Time series:  Linear trend



Time series:  Quadratic trend



Time series:  Polynomial trend



Time series:  Exponential trend



Time series:  Logarithmic trend



Time series:  Logistic trend



Time series:  Gompertz trend



Time series:  Which trend to choose?



Time series:  Seasonal component



Time series:  Seasonal component



Time series:  Seasonal component



Time series:  Seasonal component



Autocorrelation
of the random component
•Durbin-Watson test

Time series:  The Classical Assumption



Time series:  The Classical Assumption



Time series:  Autocorrelation



Time series:  Durbin-Watson test



Time series:  Durbin-Watson test



Time series:  Durbin-Watson test



Time series:  Durbin-Watson test



Time series:  Durbin-Watson test



Time series:  Durbin-Watson test



Moving average
•Simple moving average
•Weighted moving average

Moving average



Simple moving average



Simple moving average



Simple moving average:  Example



Simple moving average:  Example



Moving average



Moving average



Moving average:  Weighted moving average