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## Time Series

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**AS 90641 (internal)**3 credits Time Series**Time Series**• A time series is a set of values of a variable measured at regular intervals of time • E.g. temperature measured daily, monthly sales figures • Analysis looks for patterns of change over time • Try to predict future movements**Features of Time Series**• Long term trends • Random fluctuations (noise) • Periodic movements • Seasonal effects • Cyclical effects • Spikes/troughs (outliers) • Shifts (ramps)**Long term trend**• The tendency of the variable to increase or decrease (or stay constant) over a long period of time**Random fluctuations (noise)**• Unpredictable minor rises and falls which occur throughout the series • A value may rise or fall from one measurement to the other without necessarily indicating a long term change in the trend**Seasonal effects**• A regular fluctuation which results from changes of seasons, time of day, month of year, etc. • E.g. Hourly temperature higher at midday than at midnight**Cyclical effects**• Longer term patterns such as weather patterns (e.g. El Nino) or changes due to the expansion/contraction of economies • Typically less frequent than seasonal effects**Spike/trough (outlier)**• A value which is significantly higher or lower than what would be expected • Caused by a special event like extreme weather conditions, natural disasters, stock market crash, etc.**Shift (Ramp)**• New technology or an event causes a sudden, permanent step up or down in the pattern**Stable solve rate of around 90% until about 1940, decline**until about 1990, small improvement since then**Crime rate was low and stable until about 1950, then**dramatically increased until 1990, since then has dropped to about 10%**Textbook**• Pages 8-12 Exercise 1.01 • Questions 1ab, 2, 4 • Homework: page 5**Moving Mean**• Used to smooth out random and periodic variations in order to show the long term trend more clearly • Use a moving mean order “n” where “n” is the number of data in one cycle (e.g. 4 for quarterly, 12 for monthly) • Find the average of the first “n” terms and write result beside middle term**Moving Mean**• Calculate the moving means of order 3 for this data**Moving Mean**• Calculate the moving means of order 3 for this data**Moving Mean**• Calculate the moving means of order 3 for this data**Centred Moving Mean**• For odd order a moving mean is sufficient as you can place the MM in the middle of the periods you have averaged • For even order, you must do a second moving mean called a centred moving mean**Centred Moving Mean**• Calculate the CMM for this data**Centred Moving Mean**• Calculate the CMM for this data**Centred Moving Mean**• Calculate the CMM for this data**Centred Moving Mean**• Calculate the CMM for this data**Centred Moving Mean**• Calculate the CMM for this data**Centred Moving Mean**• Calculate the CMM for this data