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Download a pdf copy of this help file here |
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Download a pdf copy of this help file here |
See also: Time series introduction, Time series modeling in finance
Many random variables exhibit some degree of seasonality over time: that is, some quality of the probability distribution of their values (usually the mean and spread, but in principle the minimum, maximum, etc) has a repeated pattern with a defined period.
For example:
A nation's unemployment rate has a yearly period because of seasonal labour, school and university leavers, etc. That's why seasonally-adjusted figures are presented on the news;
Delays on a railway system have a yearly period because a sudden leaf fall causes the trains to loose grip, very high temperatures make electrical connections expand and short out, very cold temperatures cause freezing of points, etc;
Some strikes have a yearly period, because pilots walk out just before the holidays, refuse collectors walk out when it's high summer (the smell), etc;
Electricity demand is higher in some countries in summer (air conditioning) and winter (heating);
Most of our lives follow a weekly work and school cycle, and along with that go shop revenue, traffic, TV viewing, etc;
Electricity demand is higher in a city centre from Monday to Friday (offices);
Over a day, ... okay, you get the point.
Seasonality is probably only relevant to us if:
The decision option is to have a seasonal impact;
Seasonal peaks or troughs represent a constraint on your system;
The seasonal variation has an impact on other variables you are trying to estimate;
The data we have covers a fraction of some period; or
Breaking down a time series into components helps us better estimate the series as a whole;
if you can, aggregate estimates over complete seasonal periods which will allow you to use a simpler model.
The effect of seasonality is modelled two different ways:
1. A set of seasonality indices {I1 to In} where you are modeling n individual forecasts within the seasonality period. This is the method implemented in VoseTimeSeasonalGBM.
2. A set of periodic functions (like a sin function) with different amplitudes and frequencies (not recommended).
Read on: Bounded random walk