VoseTimeSeasonalGBM | Vose Software

VoseTimeSeasonalGBM

VoseTimeSeasonalGBM(Mu, Sigma, {S1}, P1, {S2}, P2, Log Return, Initial Value)

Array function that models a Seasonal Geometric Brownian Motion time series model.

You can provide an array with seasonal indices (e.g. 7 values, one for each day of the week) that will be run through periodically, starting at position P1.

Optionally you can provide a second optional cycle within each period of the first cycle, useful for modelling, say, week/day or day/hour patterns.

• Mu - mean log return of the underlying GBM;

• Sigma - standard deviation of the log returns of the underlying GBM;

• {S1} - array of seasonality factors for the first (outer) cycle. For example: if outer cycle is week of year, inner cycle is day of week, this value would be a list of 52 values representing the multiplying factor (with average of 1) to apply to each week;

• P1 - the starting index for cycle 1. For example, the week of the year (a value from 1 to 52);

• {S2} - array of seasonality factors for the second (inner) cycle. For example: if outer cycle is week of year, inner cycle is day of week, this value would be a list of 7 values representing the multiplying factor (with average of 1) to apply to each day of the week;

• P2 - the starting index for cycle 2. For example, the day of the week (a value from 1 to 7);

• Log Return - an optional parameter. Function generates log returns if set to TRUE, or variable values if set to FALSE or omitted;

• Initial Value - starting value (at time zero). The generated time series values will continue on from this value. Should only be provided if the Log Return parameter is set to FALSE or omitted.

As the ModelRisk Time Series functions typically take a lot of parameters, we recommend for these in particular to use the Time Series window.

Equations

where:

- a sample from a Normal(0,1)

- if   is the value of the variable at time t, then is the log return defined as

- log return mean

- standard deviation of log return

{f1} - set of outer loop multipliers

{f2} - set of inner loop multipliers

VoseFunctions for this time series

VoseTimeSeasonalGBM - generates an array of random values from this time series.

VoseTimeSeasonalGBMFit - generates an array of random values from this time series fitted to data.

VoseTimeSeasonalGBMFitP - returns the parameters of this time series fitted to data.