Seasonal time series

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.

Handling seasonality

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.

Seasonality index method

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

 

ModelRisk

Monte Carlo simulation in Excel. Learn more

Tamara

Adding risk and uncertainty to your project schedule. Learn more

Navigation

FREE MONTE CARLO SIMULATION SOFTWARE

For Microsoft Excel

Download your free copy of ModelRisk Basic today. Professional quality risk modeling software and no catches

Download ModelRisk Basic now

FREE PROJECT RISK SOFTWARE

For Primavera & Microsoft Project

Download your free copy of Tamara Basic today. Professional quality project risk software and no catches.

Download Tamara Basic now
-->