SimulateGaussianMixture
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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
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Output type / Parameter details
Output type: Double()
Parameter Name | Variable Type | Description |
InputMeans | Double() | Array containing means for each state (p x n in size) |
InputVariances | Double() | Array containing covariance matrix for each state (p x n x n in size) |
StateTransitionFromToMatrix | Double() | Array containing state transition matrix (p x p in size) |
IsStartStateKnown | Boolean | Indicates if start state is known |
GivenStartState | Integer | If start state is known then this indicates what it is (0 to p-1) |
StartStateProbabilities | Double() | If start state not known then this indicates probabilities of each state (p in size) |
NumberSimulations | Integer | Number of simulations (s) |
NumberTimePeriods | Integer | Number of time periods for each simulation (t) |
NumberStates | Integer | Number of states or regimes that are included in the mixture (p) |
NumberVariables | Integer | Number of individual variables simulated in each time step (n) |
RandSeed | Double | Random number seed |
WeightToEndState | Double | Indicates proportion of behaviour coming from end period state (as opposed to start period state) |
UseEqualQuantileSpacingsForTransitions | Boolean | If true then transition probabilities are spread evenly across quantiles (across simulations) |
UseEqualQuantileSpacingsWithinStates | Boolean | If true then outcomes for each individual variable are spread evenly across quantiles (across simulations) |
Links to:
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Interactively run function
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Interactive instructions
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Example calculation
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Output type / Parameter details
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Illustrative spreadsheet
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Other Markov processes functions
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Computation units used
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