/

SimulateGaussianMixture

[this page | pdf]

Function Description

Returns an array providing simulated output from a multivariate time series model of the world involving one or more states or regimes, each of which is characterised by a Gaussian (i.e. multivariate normal) distribution, with a Markov chain process indicating how likely it is to move between each state over a given time period. The output is 2 dimensional, with the first dimension characterising the simulation and the time period and the second dimension providing a vector of the variables themselves.

 

Models where each state itself consists of a predefined (distributional) mixture of multivariate normal distributions can be accommodated in such a model by defining the Markov chain appropriately.

 

The function includes parameters that:

 

(a)    define the starting state or how it may itself be simulated

(b)   include a random number seed so that the results can be reproduced subsequently

(c)    include sampling algorithms that help to reduce run times by sampling in a uniform manner across the quantile range that the individual random variables can take

 


NAVIGATION LINKS
Contents | Prev | Next


Output type / Parameter details

Output type: Double()
Parameter NameVariable TypeDescription
InputMeansDouble()Array containing means for each state (p x n in size)
InputVariancesDouble()Array containing covariance matrix for each state (p x n x n in size)
StateTransitionFromToMatrixDouble()Array containing state transition matrix (p x p in size)
IsStartStateKnownBooleanIndicates if start state is known
GivenStartStateIntegerIf start state is known then this indicates what it is (0 to p-1)
StartStateProbabilitiesDouble()If start state not known then this indicates probabilities of each state (p in size)
NumberSimulationsIntegerNumber of simulations (s)
NumberTimePeriodsIntegerNumber of time periods for each simulation (t)
NumberStatesIntegerNumber of states or regimes that are included in the mixture (p)
NumberVariablesIntegerNumber of individual variables simulated in each time step (n)
RandSeedDoubleRandom number seed
WeightToEndStateDoubleIndicates proportion of behaviour coming from end period state (as opposed to start period state)
UseEqualQuantileSpacingsForTransitionsBooleanIf true then transition probabilities are spread evenly across quantiles (across simulations)
UseEqualQuantileSpacingsWithinStatesBooleanIf true then outcomes for each individual variable are spread evenly across quantiles (across simulations)

Links to:

-          Interactively run function

-          Interactive instructions

-          Example calculation

-          Output type / Parameter details

-          Illustrative spreadsheet

-          Other Markov processes functions

-          Computation units used


Note: If you use any Nematrian web service either programmatically or interactively then you will be deemed to have agreed to the Nematrian website License Agreement


Desktop view | Switch to Mobile