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Flashcards · 0479 · Topic 12

Time series flashcards

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Topic 12: Time series

What is a time series?
Values of one quantity recorded at regular intervals, such as every quarter or every school day, and plotted in time order.
What is the trend of a time series?
The long-term direction of the series (rising, falling or flat) once short repeating ups and downs are removed.
What is seasonal variation?
A regular swing around the trend that returns after the same number of periods each time. A "season" can be a quarter, a day of the week or a month.
What is a moving average?
The mean of a fixed number of consecutive values, moved along the series one value at a time.
How many points should each moving average use?
The length of one cycle: 4 for quarterly data, 12 for monthly data with a yearly pattern, 5 for school days, 7 for days of the week. A full cycle in each average cancels the seasonal swings, leaving the trend.
When must moving averages be centred, and how?
When the number of points is even, because each average then sits between two time periods. Centre by taking the mean of each pair of neighbouring moving averages.
A series has 20 values. How many four-point moving averages are there, and how many after centring?
20 − 4 + 1 = 17 four-point moving averages, and 16 after centring.
How do you calculate a seasonal component?
For each period find actual value − moving average. Group these differences by season and take the mean of each group. The components should add to roughly zero.
How do you predict a future value from a time series?
Predicted value = trend value (read from the trend line) + seasonal component. Example: trend 53.5 and component −6.5 → 47.0.
Where should the trend line be drawn?
By eye through the plotted moving averages, not through the raw data, with each moving average plotted at the time of its middle value.
Why may a time series prediction be unreliable?
It assumes the trend continues in a straight line and each season keeps the same effect; a trend line drawn by eye varies between people; and one-off events are not in the model. Reliability falls the further ahead you predict.

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