smoothing Kalman filter estimation tvp_param1

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tvp

Time varying parameters estimation

CALLING SEQUENCE

[rtvp]=tvp(namey,varargin)

PARAMETERS

Input

• namey = a time series, a real (nx1) vector or a string equal to the name of a time series or a (nx1) real vector between quotes

• varargin = arguments which can be:

 * a time series

 * a real (nx1) vector

 * a string equal to the name of a time series or a (nx1) real vector between quotes

 * the string 'noprint' if the user doesn't want to print the results of the regression

 * 'priorb0=x' where x is (k x 1) vector with prior b0 values (default = ols(y,x))

 * 'priorv0=x' where x = (k x k) matrix with prior variance for Q (default = eye(k)*1e+5, a diffuse prior)

 * 'tvpmeth=x' where:

  * x = 1 (Q is diagonal and only Q and R are estimated)

  * or x=1a (no constraint on Q and only Q and R are estimated),

  * or x=2 (prirov0=0, Q is diagonal and priorb0, Q and R are estimated)

  * or x=2a (priorv0=0, no constraint on Q, and priorb0, Q and R are estimated) (default = 1)

 * 'Q=x' where x is a (kxk) initial value for Q

 * 'R=x' where x is an initial value for R

 * 'optmeth=x' where x is the optimization program used (optim or -default- maxlik)

Output

• rtvp = a results tlist with

  - rtvp('meth') = 'tvp'

  - rtvp('Q') = estimated Q

  - rtvp('R') = estimated R

  - rtvp('betat') = B(t/t)

  - rtvp('betaf') = B(t/t-1)

  - rtvp('betas') = B(t/T)

  - rtvp('sigmatt') = sigma(t/t)

  - rtvp('sigmatf') = sigma(t/t-1)

  - rtvp('sigmats') = sigma(t/T)

  - rtvp('param') = estimated parameters

  - rtvp('vcov') = variance-covariance matrix of estimated paramters

  - rtvp('tstat') = Student's t of estimated parameters

  - rtvp('y') = y

  - rtvp('x') = x

  - rtvp('yhat') = X(t)*B(t)

  - rtvp('resid') = y-X*B(t)

  - rtvp('like') = log-likelihood

  - rtvp('nobs') = # of observations

  - rtvp('nvar') = # of exogenous variables

  - rtvp('tR') = t-stat of estimated R variance

  - rtvp('tQ') = t-stat of estimated Q variance

  - rtvp('tpriorb0') = t-stat of estimated priorb0 (if method 1a or 2a are used)

  - rtvp('param') = estimated parameters in a vector form

  - rtvp('tstat') = their t-stat

  - rtvp('tvpmeth') = method used in tvp

  - rtvp('namey') = name of the endogenous variable

  - rtvp('namex') = name of the exogenous variable

  - rtvp('prests') = boolean indicating the presence or absence of a time series in the regression

  - rtvp('bounds') = if there is a timeseries in the regression, the bounds of the regression

DESCRIPTION

Time-varying parameter maximum likelihood estimation of the linear regression model y(t) = X(t)*B(t) + e(t), e(t) = N(0,R) B(t) = B(t-1) + v(t), v(t) = N(0,Q) NOTE: the methods '1a' and '2a' are not very robust; so I recommend to use them with much caution!

EXAMPLE

r1=tvp('con','inc','cte','R=sigu','Q=0.1*eye(2,2)','priorb0=b','priorv0=100000*eye(2,2)','tvpmeth=1')
// Example taken from function tvp_d1. Here the variance of the innovations of the time varying coefficients  is assumed to be diagonal and there is a diffuse prior for starting values (tvpmeth=1); endogenous variable is 'con', the exogenous ones are'inc' and 'cte'; starting values are given for R, Q and priorb0; priorv0 is imposed.

AUTHOR

Eric Dubois 2002
smoothing Kalman filter estimation tvp_param1