MSVAR (Markov-Switching Vector AutoRegressions)

Overview

MSVAR is an Ox package designed for the econometric modelling of univariate and multiple time series subject to shifts in regime. It provides the statistical tools for the maximum likelihood estimation (EM algorithm) and model evaluation of Markov-Switching Vector Autoregressions as discussed in my book of the same name.
A variety of model specifications regarding the number of regimes, regime-dependence versus invariance of parameters etc. provides the necessary flexibility for empirical research and will be of use to econometricians intending to construct and use models of dynamic, non-linear, non-stationary or cointegrated systems.
MSVAR can be used by writing a small Ox program. Ox is an object-oriented matrix language with a comprehensive mathematical and statistical function library. As MSVAR derives from the Modelbase class, it allows the easy use and exchange with other classes such as PcFiml.
In conjunction with Ox Professional, MSVAR can be used interactively via the user-friendly interface OxPack in combination with GiveWin 2 for data input and graphical and text output.

Quick Start
MSVAR download and links
Research on MS-VARs

MSVAR modelling
MSVAR examples
MSVAR functions

Quick Start

Working with MSVAR: Ox 3.4 console version

MSVAR 1.32a contains a series of new features which are not documented yet in the paper. But with the help of the provided examples, you should be able to run your existing programs. Note that there are two important changes when compared to MSVAR 1.00:
1. A link to hmk is no longer required. So just use:
  
  It is imperative to let MSVAR know that you do not call it via OxPack:
For more information, consider the example contained in the zip file. The Ox file kroto.ox estimates an MS(3)-VECM(1) of output and employment growth in the US (see paper). The data are provided in the GiveWin files kroto.in7 and kroto.bn7.

Working with MSVAR: OxPack

If you have an Ox3 Professional licence and want to use MSVAR interactively via OxPack, you can add MSVAR under "Add/Remove Package" in the Package Menu:
- Package oxo file:
  
  Package class name:
where [Path] denotes the location of the msvar130.oxo file, for example: c:\program files\GiveWin2\bin.
The interface is similar to the ones of PcGive10 and PcGets1, so hopefully it is self-explaining.

MSVAR download and links

The MSVAR package is offered as is, and without any warranties. Unfortunately, I am unable to answer any queries related to the package, and suggest trying the ox-users discussion list instead.
To facilitate replication and validation of empirical findings, MSVAR should be cited in all reports and publications involving its application. The appropriate form is to cite MSVAR in the list of references.
Download:
- MSVAR1.32a for Ox 3.4
- MSVAR examples
For more information regarding Ox, visit:
- Jurgen Doornik's workpage.
- OxMetrics.

MSVAR modelling

The model

The statistical model of the K-dimensional time series vector y_t=(y_1t,...,y_Kt) is defined conditional upon the regime s_tÎ{1,...,M}. :

p(y_t|Y_t-1,X_t,s_t)={

f(y_t|Y_t-1,X_t,q₁) if s_t=1

f(y_t|Y_t-1,X_t,q_M) if s_t=M.

where p(y_t|Y_t-1,X_t,s_t) is the probability density function of the vector of endogenous variables y_t=(y_1t,...,y_Kt)' conditional upon the history of the process, Y_t-1={y_t-i}_i=1^¥, some (strongly) exogenous variables X_t={x_t-i}_i=0^¥ and the regime variable s_t.. q_m is the parameter vector present in regime m. It is usually assumed that the statistical model is linear in each regime, say s_t=m. In the following we focus on autoregressive processes

y_t=n_m+a_m1y_t-1+...+a_mpy_t-p+e_t, e_t~IID(0,s_m²),

and their multivariate generalization: the vector autoregressive (VAR) process

y_t=n_m+A_m1y_t-1+...+A_mpy_t-p+e_t, e_t~IID(0,S_m).

Models with shifts in the intercept as above imply a smooth adjustment of the time series after regime shifts. In contrast, there is a once-and-for-all jump in the time series when the conditional process is subject to shifts in the mean:

y_t-m(s_t)=A₁(s_t)( y_t-1-m(s_t-1)) +...+A_p(s_t)( y_t-p-m(s_t-p)) +u_t,

If the stochastic process of y_t is defined conditionally upon the (unobservable) regime s_t, a complete description of the data generating mechanism requires the specification of the stochastic process which generates the regime:

Pr (s_t|Y_t-1,S_t-1,X_t;r)

where the history S_t-1={s_t-j}_j=1^¥ of the state variable might be unobserved but will be "reconstructed" from the observations and the vector r collects the parameters of the regime generating process. The models within this class differ in their assumptions concerning the stochastic process generating the regime.

Model types

The following types of regime-switching models can be estimated by MSVAR:

Structural change and switching regression model
The regime variable is observable:
Pr (s_t|Y_t-1,S_t-1,X_t;r) = I( s_t )

where the I( s_t ) is an indicator function . In structural change models, `time' is the regime variable:

I( s_t )={

1 for t>t

0 for t£t.
Threshold model
In the threshold autoregressive model, the regime shifts are triggered by an observable, exogenous transition variable x_t crossing a threshold c:

y_t=( n₁+å_i=1^pa_1iy_t-i) ( 1-I( x_t;c) ) +( n₂+å_i=1^pa_2iy_t-i) I( x_t;c) +e_t

where e_t~IID(0,s²). The indicator function I( x_t;c) is of the type

I(x;c)={

1 if g(x_t)>c

0 if g(x_t)£c.

For x_t=t a model with a structural break at time t=c occurs If the transition variable is a lagged endogenous variable y_t-d with delay d>0, the self-exciting threshold autoregressive (SETAR) model results:

y_t=( n₁+å_i=1^pa_1iy_t-i) ( 1-I( y_t-d;c) ) +( n₂+å_i=1^pa_2iy_t-i) I( y_t-d;c) +e_t

where e_t~IID(0,s²). In the SETAR model, the regime-generating process is not assumed to be exogenous but directly linked to the lagged endogenous variable y_t-d.

Markov-switching model

The unobservable regime variable s_tÎ{1,...,M} is generated by an ergodic Markov chain defined by the transition probabilities:

p_ij= Pr (s_t+1=j|s_t=i), å_j=1^Mp_ij=1 "i,jÎ{1,...,M}.

A major advantage of the MS-VAR is its flexibility, see Krolzig (1997):

Special MS-VAR Models

MSM specification MSI specification

m varying m invariant n varying n invariant

A_j invariant S invariant MSM--VAR linear MVAR MSI--VAR linear VAR

S varying MSMH--VAR MSH--MVAR MSIH--VAR MSH--VAR

A_j varying S invariant MSMA--VAR MSA--MVAR MSIA--VAR MSA--VAR

S varying MSMAH--VAR MSAH--MVAR MSIAH--VAR MSAH--VAR

		MSM specification	MSI specification
		m varying	m invariant	n varying	n invariant
A_j invariant	S invariant	MSM--VAR	linear MVAR	MSI--VAR	linear VAR
S varying	MSMH--VAR	MSH--MVAR	MSIH--VAR	MSH--VAR
A_j varying	S invariant	MSMA--VAR	MSA--MVAR	MSIA--VAR	MSA--VAR
S varying	MSMAH--VAR	MSAH--MVAR	MSIAH--VAR	MSAH--VAR

Model formulation

The following steps are involved in model formulation:

Create a object.
Load your data into the database using the facilities of the Database class.
Transform the data.
Use Select to formulate the model. A constant will be included by default.
Use SetSample to specify the sample.
Use SetModel for a different specification of the model, for example:
- time-invariant intercept;
- regime-dependent intercept;
- regime-dependent mean.
For reports of the progress of the EM algorithm, use SetPrint.
For changes of convergence threshold and the maximum number of iteration, use SetEmOptions.
By default, a graphic presentation of the results is shown, standard errors are calculated, and gwg files of all givewin graphics saved. Use SetOptions to change this.
Finally, use Estimate for estimation.

MSVAR examples

Markov-switching AR: Hamilton (Econometrica, 1989)
Hamilton's model of the US business cycle fostered a great deal of interest in the MS--AR model as an empirical vehicle for characterizing macroeconomic fluctuations, and there have been a number of subsequent extensions and refinements (see the literature discussed in Krolzig, 1997). The model is an MSM(2)-AR(4) of the quarterly percentage change in US real GNP from 1953 to 1984:

Dy_t-m(s_t)=a₁( Dy_t-1-m(s_t-1)) +...+a₄( Dy_t-p-m(s_t-4)) +u_t,

where u_t~NID(0,s²), and the conditional mean m(s_t) switches between two states:

m(s_t)={

m₁<0 if s_t=1 (`expansion' or `boom'),

m₂>0 if s_t=2 (`contraction' or `recession').

The variance of the disturbance term, s², is assumed to be the same in both regimes. Thus, contractions and expansions are modelled as switching regimes of the stochastic process generating the growth rate of real GNP. The regimes are associated with different conditional distributions of the growth rate of real GNP, where, for example,the mean is positive in the first regime (`expansion') and negative in the second regime (`contraction'). The transition probabilities are constant:

p₂₁ = Pr ( contraction in t | expansion in t-1),

p₁₂ = Pr ( expansion in t | contraction in t-1).

By inferring the probabilities of the unobserved regimes conditional on an available information set, it is then possible to reconstruct the regimes.
Markov-switching VAR: Krolzig (1997)
In Krolzig (1997), Hamilton's model of the U.S. business cycle is generalized to a Markov-switching vector autoregressive (MS-VAR) time series model. This examples analyzes regime shifts in the stochastic process of economic growth of six major OECD countries over the last three decades. An MSMH(3)-VAR(1) model is applied to six series of quarterly GNP growth rates:

Dy_t' =
( Dy_t^USA, Dy_t^JAP, Dy_t^FRG, Dy_t^UK, Dy_t^CAN, Dy_t^AUS )

For all countries, business cycles can be identified as regime shifts in the mean growth rate occurring mainly simultaneously across countries.
Markov-switching VECM: Krolzig and Toro (1999)
This example replicates the results of the Markov-switching vector equilibrium correction model (MS-VECM) of US Output and Employment proposed by Krolzig and Toro (1999). An MS-VECM is a vector equilibrium correction model with shifts in the drift d(s_t) and in the long-run equilibrium m(s_t):

Dx_t-d(s_t)=a( b'x_t-1-m(s_t)-gt) +å_k=1^p-1G_i( Dx_t-k-d(s_t)) +u_t

and the innovations u_t are conditionally Gaussian, u_t|s_t~NID(0,S(s_t) ). The parameters d and m depend upon a stochastic, unobservable regime variable s_tÎ{1,...,M} The stochastic process for generating the unobservable regimes is an ergodic Markov chain defined by the transition

p_ij= Pr (s_t+1=j|s_t=i), å_j=1^Mp_ij=1 "i,jÎ{1,...,M}.

By following the two-stage procedure proposed in Krolzig (1996), the cointegration properties of the output, y_t, and employment, n_t, data are studied within a linear vector autoregressive representation using the maximum likelihood techniques (as provided by the PcFiml class). Conditional on the estimated cointegration matrix, we get the following representation:

Dx_t=n(s_t)+G₁Dx_t-1+az_t-1+u_t

where z_t-1=y_t-1-n_t-1-g^{^} t-m has been normalized such that E[z_t]=0.
ML estimation of the MSIH-VARX model is then based on the Expectation-Maximization (EM) algorithm of the MSVAR class.
Threshold model
Tiao and Tsay (1994) and Potter (1995) analyse two-regime SETAR models of the quarterly growth rate of US output Dy_t of the type:

Dy_t=m(s_t)+å_i=1⁵a_i(s_t)Dy_t-i+u_t, u_t~IID(0,s²(s_t))

where the delay d=2 and the threshold c»0. In the example, we estimate a two-regime SETAR(4) for the Hamilton data set.
Switching regression
In this example, we again consider an AR(4) of the quarterly growth rate of US output Dy_t over sample period analysed in the other examples, but now conditioned on the NBER business cycle dating. So regime 1 corresponds to NBER expansions (s_t=0) and regime 2 to NBER recessions (s_t=1) .

MSVAR exported member functions

The documentation only includes the exported member functions of MSVAR. The non-exported member functions are not documented here as they are only called from other MSVAR function members. Some functions are quite complex, and should be approached with care.

Notation:

K	number of endogenous variables,
M	number of regimes,
N	dimension of the state vector (MSIxx: M, MSMxx: M^p+1)
p	order of the VAR,
r	cointegration rank
R	number of regressors (excluding constant),
T	number of observations.

CycleDating

CycleDating();

Description: Reports the regime classification based on the smoothed regime probabilities.

DeSelect

DeSelect();

Description: Clears the model formulation, i.e. clears previous calls to Select() and SetSample().

DynamicAnalysis

DynamicAnalysis();

Description: Prints dynamic analysis.

Estimate

Estimate(const mMu, const mB, const m_mSigma, const Trans);
Estimate(const mProbSt);
Estimate(const );

`mMu`	in:	K ×M matrix of means or intercepts (MSAx: K ×1)
`mB`	in:	K ×R matrix of coefficients (MSxAx: K ×MR)
`mSigma`	in:	K ×M variance matrix (MSxxH: K ×MK)
`mTrans`	in:	M ×M transition matrix (transposed matrix of transition probabilities)
`mProbSt`	in:	M ×T matrix of initial regime probabilities

Description: Estimates the model and prints the results, unless this is switched off by SetPrint(). Use Select, SetSample and SetModel prior to Estimate to formulate the model.
When initial parameter values or regime probabilities are not given, Estimate() will calculate them.

DrawErrors

DrawErrors(const fAcf);

`fAcf`	in:	integer, `TRUE`: draw error analysis

Description: Calculates and draws the one-step prediction errors y_t-E[y_t|Y_t-1] and standardized residuals of each equation. If fAcf is TRUE a graphic analysis of one-step prediction errors and standardized residuals is undertaken. The error analysis includes the estimated ACF, spectral density, histogram and a QQ plot.

DrawFit

DrawFit();

Description: Draws actual and fitted values for all series.

DrawModelAnalysis

DrawModelAnalysis();

Description: Illustrates some essential properties of the estimated model.

DrawResults

DrawResults();

Description: Draws the series, the Markov chain component as well as the smoothed, filtered and predicted probabilities for all regimes m=1,...,M.

Forecast

Forecast(const h, const fFoTable, const fFoGraph, const fFoCum);

`h`	in:	integer, number of periods
`fFoTable`	in:	integer, `TRUE`: print table
`fFoGraph`	in:	integer, `TRUE`: show graphs
`fFoCum`	in:	integer, `TRUE`: cumulates forecasts

Description: Forecasts.

GetA, GetB, GetMu, GetSigma, GetTrans, GetAIC, GetHQ, GetLogLik, GetSC, GetT, GetU, GetProbS, GetProbSt, GetProbF, GetProbFt, GetProbP, GetProbPt, GetProbErg, GetProbInit, GetProbLast, GetEmOptions, GetModel, GetCovar

Description

Return value

`GetA()`	gets VAR matrices
`GetAIC()`	returns Akaike Information Criterion
`GetB()`	returns K ×R matrix of coefficients (MSxAx: K ×MR)
`GetCovar()`	returns variance-covariance matrix of ML estimates
`GetEmOptions()`	returns an array with the EM algorithm options as set using `SetEmOptions`
`GetHQ()`	returns Hannan Quinn Information Criterion
`GetLogLik()`	returns log-likelihood
`GetModel()`	returns an array with the model options as set using `SetModel`
`GetMu()`	returns K ×M matrix of means or intercepts (MSAx: K ×1)
`GetProbInit()`	gets M ×1 vector of initial regime probabilies (MSMx: M^p ×1)
`GetProbErg()`	gets M ×1 vector of ergodic regime probabilies
`GetProbLast()`	gets N ×1 vector of smoothed regime probabilies at time T
`GetProbF()`	gets N ×T matrix of filtered regime probabilies
`GetProbFt()`	gets M ×T matrix of filtered regime probabilies
`GetProbP()`	gets N ×T matrix of predicted regime probabilies
`GetProbPt()`	gets M ×T matrix of predicted regime probabilies
`GetProbS()`	gets N ×T matrix of smoothed regime probabilies
`GetProbSt()`	gets M ×T matrix of smoothed regime probabilies
`GetSC()`	returns Schwarz Information Criterion
`GetSigma()`	returns K ×K variance matrix (MSxxH: K ×MK)
`GetT()`	gets number of observations T
`GetTrans()`	returns M ×M transition matrix (transposed matrix of transition probabilities)
`GetU()`	gets K ×NT matrix of residuals

Description: Most of these functions can be only called after the data has been loaded for estimation, or after successful estimation.

Impulse

Impulse(const h, const fIrCum, const fIrOrth);

`h`	in:	integer, number of periods
`fIrCum`	in:	integer, `TRUE`: cumulates responses
`fIrOrth`	in:	integer, `TRUE`: orthogonalizes impulses

Description: Draws impulse response functions for MS-VARs.

ImpulseVecm

ImpulseVecm(const mAlpha, const mBeta, const h, const fIrOrth);

`mAlpha`	in:	K ×r matrix of adjustment parameters
`mBeta`	in:	K ×r matrix of cointegration vectors
`h`	in:	integer, number of periods
`fIrOrth`	in:	integer, `TRUE`: orthogonalizes impulses

Description: Draws impulse response functions for MS-VECMs.

IsConverged

IsConverged();

Description
Return value: Returns 1 if the EM algorithm converged, -1 if the algorithm stopped at the maximum number of iteration, and 0 otherwise.

IsOxPack

IsOxPack(const fOxPack);

`fOxPack`	in:	integer, `FALSE`: use MSVAR with the console version of Ox

Description: It is imperative to let MSVAR know that you do not call it via OxPack.

MSVAR

MSVAR();

Description: Constructor function.

MsvarFor

MsvarFor(const mY, const fModel, const cM, const vProb,
         const mMu, const mA, const mTrans, const max_h);

`mY`	in:	K ×T data
`fModel`	in:	integer, model type
`cM`	in:	integer, number of regimes
`vProb`	in:	M ×T matrix of initial regime probabilities
`mMu`	in:	K ×M matrix of means or intercepts (MSAx: K ×1)
`mB`	in:	K ×R matrix of coefficients (MSxAx: K ×MR)
`mTrans`	in:	M ×M transition matrix (transposed matrix of transition probabilities)
`max_h`	in:	integer, number of periods

Description: Forcasts MS-VAR processes.

MsvecmFor

MsvecmFor(const mY, const fModel, const cM, const vProb,
          const mMu, const mAlpha, const mBeta, mGamma, const pmA,
          const vDelta, const mTrans, const cT, const max_h);

`mY`	in:	K ×T data
`fModel`	in:	integer, model type
`cM`	in:	integer, number of regimes
`vProb`	in:	M ×T matrix of initial regime probabilities
`mMu`	in:	K ×M matrix of means or intercepts (MSAx: K ×1)
`mAlpha`	in:	K ×r matrix of adjustment parameters
`mBeta`	in:	K ×r matrix of cointegration vectors
`mGamma`	in:	K ×R matrix of coefficients (MSxAx: K ×MR)
`pmA`	in:
`mDelta`	in:	K ×R matrix of coefficients (MSxAx: K ×MR)
`mTrans`	in:	M ×M transition matrix (transposed matrix of transition probabilities)
`cT`	in:
`max_h`	in:	integer, number of periods

Description: Forecasts MS-VECM processes.

Load, LoadIn7, LoadDht, LoadFmtVar, LoadObs, LoadVar, LoadWks, LoadXls

Load(const sFilename);
LoadIn7(const sFilename); 
LoadDht(const sFilename, const iYear1, const iPeriod1, const iFreq); 
LoadFmtVar(const sFilename);
LoadObs(const sFilename, const cVar,const cObs, const iYear1,
        const iPeriod1, const iFreq, const fOffendMis); 
LoadVar(const sFilename, const cVar,const cObs, const iYear1,
        const iPeriod1, const iFreq, const fOffendMis);
LoadWks(const sFilename);
LoadXls(const sFilename);

`sFilename`	in:	string, filename
`cVar`	in:	int, number of variables
`cObs`	in:	int, number of observations
`iYear1`	in:	int, start year
`iPeriod1`	in:	int, start period
`iFreq`	in:	int, frequency
`fOffendMis`	in:	int, `TRUE:` offending text treated as missing value `FALSE:` offending text skipped

Description

Identical to the functions of the underlying database class:

Load creates the database and loads the specified data file from disk. The file type is derived from the extension.

LoadDht creates the database and loads the specified Gauss data file from disk.

LoadIn7 creates the database and loads the specified GiveWin file (PcGive 7 data file) from disk.

LoadFmtVar creates the database and loads the ASCII file with formatting information from disk. In GiveWin this is called `Data with load info'. Such a file is human-readable, with the data ordered by variable, and each variable preceded by a line of the type:

    > name year1 period1 year2 period2 frequency

LoadObs and LoadVar create the database and load the specified human-readable data file from disk. The data is ordered by observation (LoadObs), or by variable. Since there is no information on the sample or the variable names in these files, the sample must be provided as function arguments. The variable names are set to Var1, Var2, etc., use Rename to rename the variables.

LoadWks and LoadXLS create the database and load the specified spreadsheet file from disk. A .wks or .wk1 file is a Lotus file, an .xls file is an Excel worksheet.

LogLik

LogLik(const vP, const adFunc, const avScore, const amHess);

`vP`	in:	1 ×1 matrix, with current t
`adFunc`	in:	address of variable
	out:	loglikelihood at t
`avScore`	in:	should be 0
`amHess`	in:	should be 0

Description
Return value: Returns 1 if the likelihood can be evaluated, 0 otherwise.

Description: Uses the BHLK filter to evaluate the likelihood.

PrintCovar

PrintCovar();

Description: Prints variance-covariance matrix of ML estimates.

PrintStdErr

PrintStdErr();

Description: Prints standard errors.

Select

Select(const iGroup, const aSel);

`iGroup`	in:	int, group indicator: `Y_VAR`, `X_VAR`, `S_VAR`, `T_VAR`
`aSel`	in:	array, specifying database name, start lag, end lag

Description

Selects variables by name and with specified lags, and assigns the iGroup status to the selection. The aSel argument is an array consisting of sequences of three values: name, start lag, end lag.

The following types of variables are supported:

Y_VAR dependent and lagged dependent variable

X_VAR exogenous regressors

S_VAR regime variable (s_t Î{1,...,M})

T_VAR threshold variable

Each Select() adds to the current selection. Use DeSelect() to start afresh. Note: SetSample() checks for data availability; in case of missing observations it uses the largest available sample within the selection.

SetB, SetMu, SetSigma, SetTrans

SetB(const mB);
SetMu(const mMu);
SetSigma(const mSigma);
SetTrans(const mTrans);

`mMu`	in:	K ×M matrix of means or intercepts (MSAx: K ×1)
`mB`	in:	K ×R matrix of coefficients (MSxAx: K ×MR)
`mSigma`	in:	K ×K variance matrix (MSxxH: K ×MK)
`mTrans`	in:	M ×M transition matrix (transposed matrix of transition probabilities)

Description: Set parameter matrices of the MS-VAR model.

SetEmOptions

SetEmOptions(const dTol, const iIt);
SetEmOptions(const dTol, const iIt, const iItMsm);

`dTol`	in:	double, tolerance level for convergence of the Em algorithm as percentage change of the log-likelihood (1e-6 by default).
`cItMsm`	in:	integer, maximum number of iterations of the EM algorithm (100 by default).
`cItMsm`	in:	integer, number of internal iterations at each M-step (2 by default).

Description: Specifies options of the EM algorithm. Note that the third option only effects MSMx-VAR models.

SetModel

SetModel(const fModel, const M);

`fModel`	in:	integer, specification of the MS-VAR, see below.
`M`	in:	integer

Description

Set the specification of the MS-VAR and the number of regimes to be used in the model. Use Select() prior to SetModel() to formulate the model.

The following model specifications are supported:

MSH regime-dependent heteroscedasticity

MSI regime-dependent intercept

MSIH regime-dependent intercept and heteroscedasticity

MSM regime-dependent mean

MSHH regime-dependent mean and heteroscedasticity

MSIA regime-dependent intercept

MSIAH regime-dependent intercept and heteroscedasticity

MSIA regime-dependent intercept

MSIAH regime-dependent intercept and heteroscedasticity

SETAR (self-exciting) threshold autoregression

SR switching regression

Note: The computational burden associated with MSMx-VAR models can be quite high (compared to an MSIx-VAR the factor is M^p where p is the order of the VAR). In general it is not advised to work with a number of regimes M ³4 due to local maxima and parameter inflation.

SetOptions

SetOptions(const fStdErr, const fShowDrawResults, const fSaveDrawWindow);

`fStdErr`	in:	integer, `TRUE`: calculate automatically standard errors
`fShowDrawResults`	in:	integer, `TRUE`: calls automatically DrawResults
`fSaveDrawWindow`	in:	integer, `TRUE`: saves gwg files of all MSVAR graphics

Description: Sets general options for the MSVAR class.

SetPrint

SetPrint(const fPrintResults, const fPrintSteps);

`fPrintResults`	in:	int, `TRUE` or `FALSE`
`fPrintSteps`	in:	int, `TRUE` or `FALSE`

Description: Switches printing on (TRUE) or off (FALSE). By default printing is on. If fPrintSteps is TRUE the progress of the EM algorithm is printed after each iteration.

SetSample

SetSample(const iYear1, const iPeriod1, const iYear2,  const iPeriod2);

`iYear1`	in:	integer, start year.
`iPeriod1`	in:	integer, start period.
`iYear2`	in:	integer, end year.
`iPeriod2`	in:	integer, end period.

Description: By default, the whole sample is used. This function selects a subsample in the time dimension. Observations before the specified start sample point and after the end are omitted from estimation.

StdErr

StdErr();

Description: Calculations standard errors based on numerical calculations of the Hessian. If the Hessian is singular the generalized inverse is calculated. As the transition probabilities p_ij are restricted to the [0,1] interval, the parameters are transformed logits p_ij= log ( p_ij/1-p_ij ) which avoids problems if one or more of the p_ij is close to the border. If one of the transition parameters is estimated to lie on the border, p_ijÎ{0,1}, then the parameter is taken as being fixed and eliminated from the parameter vector (under construction).
Note: The computational burden is proportional to the squared number of parameters. For systems with more than 100 parameters it is suggested to turn the automatical calculation off. Use PrintStdErr to print standard errors and t-values.

TestAsy

TestAsy();

Description: Performs the Clements and Krolzig (2003) test for business cycle asymmetries.

`Y_VAR`	dependent and lagged dependent variable
`X_VAR`	exogenous regressors
`S_VAR`	regime variable (s_t Î{1,...,M})
`T_VAR`	threshold variable

`MSH`	regime-dependent heteroscedasticity
`MSI`	regime-dependent intercept
`MSIH`	regime-dependent intercept and heteroscedasticity
`MSM`	regime-dependent mean
`MSHH`	regime-dependent mean and heteroscedasticity
`MSIA`	regime-dependent intercept
`MSIAH`	regime-dependent intercept and heteroscedasticity
`MSIA`	regime-dependent intercept
`MSIAH`	regime-dependent intercept and heteroscedasticity
`SETAR`	(self-exciting) threshold autoregression
`SR`	switching regression

MSVAR (Markov-Switching Vector AutoRegressions)

Overview

Contents

Quick Start

Working with MSVAR: Ox 3.4 console version

Working with MSVAR: OxPack

MSVAR download and links

MSVAR modelling

The model

Model types

Model formulation

MSVAR examples

MSVAR exported member functions

CycleDating

DeSelect

DynamicAnalysis

Estimate

DrawErrors

DrawFit

DrawModelAnalysis

DrawResults

Forecast

GetA, GetB, GetMu, GetSigma, GetTrans, GetAIC, GetHQ, GetLogLik, GetSC, GetT, GetU, GetProbS, GetProbSt, GetProbF, GetProbFt, GetProbP, GetProbPt, GetProbErg, GetProbInit, GetProbLast, GetEmOptions, GetModel, GetCovar

Impulse

ImpulseVecm

IsConverged

IsOxPack

MSVAR

MsvarFor

MsvecmFor

Load, LoadIn7, LoadDht, LoadFmtVar, LoadObs, LoadVar, LoadWks, LoadXls

LogLik

PrintCovar

PrintStdErr

Select

SetB, SetMu, SetSigma, SetTrans

SetEmOptions

SetModel

SetOptions

SetPrint

SetSample

StdErr

TestAsy