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RECH class

Create a RECH model object

Syntax 

Mdl = RECH(Specs,Name,Value)

Description

Mdl = RECH(Specs,Name,Value) returns RECH model object Mdl given particular specification Specs. Name and Value specify additional options using one or more name-value pair arguments. For example, users can specify different choices of priors for model parameters.

See: Input Arguments, Output Argument, Examples

Input Arguments

Specs - RECH model specification

Data type: string


Specification of the RECH model, specified as one of these values:

'SRN-GARCH' SRN-GARCH specification
'SRN-GJR' SRN-GJR specification
'SRN-EGARCH' SRN-EGARCH specification

See Nguyen et al. (2020) for mathematical description of specification of the RECH model.

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: 'Prior',{{'alpha','beta'},'Uniform',[0,1]},'Distribution','Normal' specifies that the prior distribution of parameters $\alpha$ and $\beta$ is a uniform distribution in $[0,1]$, and the innovation is standard normal.

'Prior' - Prior distribution of model parameters

Data Type: Cell Array


Prior distribution of the model parameters, specified as the comma-separated pair consisting of 'Prior' and a 2D cell array whose each row consists of:

  • Parameter names, specified as a cell array of strings.
  • Distribution name, specified as a string.
  • Distribution parameters, specified as an array of numerical number.

The RECH class use VarName property to store parameter names. The parameter names for each specification of the RECH model is defined as:

Specification Parameter names
'SRN-GARCH' 'alpha','beta','beta0','beta1','v0','v1','v2','w','b'
'SRN-GJR' 'alpha','beta','gamma','beta0','beta1','v0','v1','v2','w','b'
'SRN-EGARCH' 'alpha','beta','gamma','omega','beta0','beta1','v0','v1','v2','w','b'

The VBLab package provides following options for prior distribution of the RECH model parameters

Prior distribution Description
'Normal' Normal distribution $\mathcal{N}(\mu,\sigma^2)$
'Gamma' Gamma distribution $\Gamma(\alpha,\beta)$
'Inverse-Gamma' Inverse-Gamma distribution $\Gamma^{-1}(\alpha,\beta)$
'Beta' Beta distribution $\text{Beta}(\alpha,\beta)$
'Uniform' Uniform distribution $\mathcal{U}(\alpha,\beta)$

Default: The default priors for each specification of the RECH model are as following

Specification Prior
'SRN-GARCH' {{'alpha','beta'},'Uniform',[0,1]; {'beta0','beta1'},'Normal',[0,1];{'v0','v1','v2','w','b'},'Normal',[0,0.1]}
'SRN-GJR' {{'alpha','beta'},'Uniform',[0,1]; {'beta0','beta1'},'Normal',[0,1];{'v0','v1','v2','w','b'},'Normal',[0,0.1]}
'SRN-EGARCH' {{'alpha','beta'},'Uniform',[0,1]; {'beta0','beta1'},'Normal',[0,1];{'v0','v1','v2','w','b'},'Normal',[0,0.1]}

Example: 'Prior',{{'beta0','beta1'},'Normal',[0,0.1]}

'Distribution' - Conditional probability distribution of innovation process

Data Type: string


The probability of the innovation. The current version of the RECH model supports only standard normal innovation.

'Normal' Normal distribution (default)

Default: Normal

Example: 'Innovation','Normal'

'Description' - Model description

Data Type: string


Model description, specified as a string scalar or character vector. Provide additional information about the model.

Default: Empty string

Example: 'Description','SRG-GARCH with normal innovation'

Output Arguments

mdl - RECH Object

Data type: RECH Object


RECH is an object of the RECH class with pre-defined properties and functions.

Object Properties

The RECH object properties include information about model-specific information, coefficient estimates and fitting method.

Properties Data type Description{: .text-center}
ModelName string (r) Name of the model, which is 'RECH'
VarName cell array (r) Model parameter names. Stored in a cell array of strings
NumParams integer (+) Number of model parameters
Post * struct Information about the fittedd method used to estimate model paramters
• RECH models can only be fitted by MGVB technique
Coefficients * Cell array • Estimated Mean of weights of Deep Neuron Network
• Used to doing point estimation for new test data
CoefficientVar * cell array (r) Variance of coefficient estimates
LogLikelihood * double (r) Loglikelihood of the fitted model.

Notation:

  • * $\rightarrow$ object properties which are only available when the model is fitted. Default value is None.
  • (+) $\rightarrow$ positive number.
  • (r) $\rightarrow$ read-only properties.

Object Methods

Use the object methods to initialize model parameters, predict responses, and to visualize the prediction.

vbayesInit Initialization method of model parameters
vbayesPredict Predict responses of fitted DeepGLM models

Examples

To be updated…

Reference

[1] Nguyen, T.-N., Tran, M.-N., and Kohn, R. (2020). Recurrent conditional heteroskedasticity. arXiv:2010.13061. Read the paper

See Also

LogisticRegression $\mid$ DeepGLM $\mid$ Custom model $\mid$ MGVB