def _fit_start_params_hr(self, order):
"""
Get starting parameters for fit.
Parameters
----------
order : iterable
(p,q,k) - AR lags, MA lags, and number of exogenous variables
including the constant.
Returns
-------
start_params : array
A first guess at the starting parameters.
Notes
-----
If necessary, fits an AR process with the laglength selected according
to best BIC. Obtain the residuals. Then fit an ARMA(p,q) model via
OLS using these residuals for a first approximation. Uses a separate
OLS regression to find the coefficients of exogenous variables.
References
----------
Hannan, E.J. and Rissanen, J. 1982. "Recursive estimation of mixed
autoregressive-moving average order." `Biometrika`. 69.1.
"""
p, q, k = order
start_params = zeros((p + q + k))
endog = self.endog.copy() # copy because overwritten
exog = self.exog
if k != 0:
ols_params = GLS(endog, exog).fit().params
start_params[:k] = ols_params
endog -= np.dot(exog, ols_params).squeeze()
if q != 0:
if p != 0:
armod = AR(endog).fit(ic='bic', trend='nc')
arcoefs_tmp = armod.params
p_tmp = armod.k_ar
resid = endog[p_tmp:] - np.dot(
lagmat(endog, p_tmp, trim='both'), arcoefs_tmp)
if p < p_tmp + q:
endog_start = p_tmp + q - p
resid_start = 0
else:
endog_start = 0
resid_start = p - p_tmp - q
lag_endog = lagmat(endog, p, 'both')[endog_start:]
lag_resid = lagmat(resid, q, 'both')[resid_start:]
# stack ar lags and resids
X = np.column_stack((lag_endog, lag_resid))
coefs = GLS(endog[max(p_tmp + q, p):], X).fit().params
start_params[k:k + p + q] = coefs
else:
start_params[k + p:k + p + q] = yule_walker(endog, order=q)[0]
if q == 0 and p != 0:
arcoefs = yule_walker(endog, order=p)[0]
start_params[k:k + p] = arcoefs
return start_params
def _fit_start_params_hr(self, order):
"""
Get starting parameters for fit.
Parameters
----------
order : iterable
(p,q,k) - AR lags, MA lags, and number of exogenous variables
including the constant.
Returns
-------
start_params : array
A first guess at the starting parameters.
Notes
-----
If necessary, fits an AR process with the laglength selected according
to best BIC. Obtain the residuals. Then fit an ARMA(p,q) model via
OLS using these residuals for a first approximation. Uses a separate
OLS regression to find the coefficients of exogenous variables.
References
----------
Hannan, E.J. and Rissanen, J. 1982. "Recursive estimation of mixed
autoregressive-moving average order." `Biometrika`. 69.1.
"""
p,q,k = order
start_params = zeros((p+q+k))
endog = self.endog.copy() # copy because overwritten
exog = self.exog
if k != 0:
ols_params = GLS(endog, exog).fit().params
start_params[:k] = ols_params
endog -= np.dot(exog, ols_params).squeeze()
if q != 0:
if p != 0:
armod = AR(endog).fit(ic='bic', trend='nc')
arcoefs_tmp = armod.params
p_tmp = armod.k_ar
resid = endog[p_tmp:] - np.dot(lagmat(endog, p_tmp,
trim='both'), arcoefs_tmp)
if p < p_tmp + q:
endog_start = p_tmp + q - p
resid_start = 0
else:
endog_start = 0
resid_start = p - p_tmp - q
lag_endog = lagmat(endog, p, 'both')[endog_start:]
lag_resid = lagmat(resid, q, 'both')[resid_start:]
# stack ar lags and resids
X = np.column_stack((lag_endog, lag_resid))
coefs = GLS(endog[max(p_tmp+q,p):], X).fit().params
start_params[k:k+p+q] = coefs
else:
start_params[k+p:k+p+q] = yule_walker(endog, order=q)[0]
if q==0 and p != 0:
arcoefs = yule_walker(endog, order=p)[0]
start_params[k:k+p] = arcoefs
return start_params
def _stackX(self, k_ar, trend):
"""
Private method to build the RHS matrix for estimation.
Columns are trend terms then lags.
"""
endog = self.endog
X = lagmat(endog, maxlag=k_ar, trim='both')
k_trend = util.get_trendorder(trend)
if k_trend:
X = add_trend(X, prepend=True, trend=trend)
self.k_trend = k_trend
return X
def fit(self, nlags):
'''estimate parameters using ols
Parameters
----------
nlags : integer
number of lags to include in regression, same for all variables
Returns
-------
None, but attaches
arhat : array (nlags, nvar, nvar)
full lag polynomial array
arlhs : array (nlags-1, nvar, nvar)
reduced lag polynomial for left hand side
other statistics as returned by linalg.lstsq : need to be completed
This currently assumes all parameters are estimated without restrictions.
In this case SUR is identical to OLS
estimation results are attached to the class instance
'''
self.nlags = nlags # without current period
nvars = self.nvars
#TODO: ar2s looks like a module variable, bug?
#lmat = lagmat(ar2s, nlags, trim='both', original='in')
lmat = lagmat(self.y, nlags, trim='both', original='in')
self.yred = lmat[:,:nvars]
self.xred = lmat[:,nvars:]
res = np.linalg.lstsq(self.xred, self.yred)
self.estresults = res
self.arlhs = res[0].reshape(nlags, nvars, nvars)
self.arhat = ar2full(self.arlhs)
self.rss = res[1]
self.xredrank = res[2]
def fit(self, nlags):
'''estimate parameters using ols
Parameters
----------
nlags : integer
number of lags to include in regression, same for all variables
Returns
-------
None, but attaches
arhat : array (nlags, nvar, nvar)
full lag polynomial array
arlhs : array (nlags-1, nvar, nvar)
reduced lag polynomial for left hand side
other statistics as returned by linalg.lstsq : need to be completed
This currently assumes all parameters are estimated without restrictions.
In this case SUR is identical to OLS
estimation results are attached to the class instance
'''
self.nlags = nlags # without current period
nvars = self.nvars
#TODO: ar2s looks like a module variable, bug?
#lmat = lagmat(ar2s, nlags, trim='both', original='in')
lmat = lagmat(self.y, nlags, trim='both', original='in')
self.yred = lmat[:, :nvars]
self.xred = lmat[:, nvars:]
res = np.linalg.lstsq(self.xred, self.yred)
self.estresults = res
self.arlhs = res[0].reshape(nlags, nvars, nvars)
self.arhat = ar2full(self.arlhs)
self.rss = res[1]
self.xredrank = res[2]
[ 0.1, -0.1]]])
a31 = np.r_[np.eye(3)[None,:,:], 0.8*np.eye(3)[None,:,:]]
a32 = np.array([[[ 1. , 0. , 0. ],
[ 0. , 1. , 0. ],
[ 0. , 0. , 1. ]],
[[ 0.8, 0. , 0. ],
[ 0.1, 0.6, 0. ],
[ 0. , 0. , 0.9]]])
########
ut = np.random.randn(1000,2)
ar2s = vargenerate(a22,ut)
#res = np.linalg.lstsq(lagmat(ar2s,1)[:,1:], ar2s)
res = np.linalg.lstsq(lagmat(ar2s,1), ar2s)
bhat = res[0].reshape(1,2,2)
arhat = ar2full(bhat)
#print maxabs(arhat - a22)
v = Var(ar2s)
v.fit(1)
v.forecast()
v.forecast(25)[-30:]
ar23 = np.array([[[ 1. , 0. ],
[ 0. , 1. ]],
[[-0.6, 0. ],
a22 = np.array([[[1., 0.], [0., 1.]], [[-0.8, 0.], [0.1, -0.8]]])
a23 = np.array([[[1., 0.], [0., 1.]], [[-0.8, 0.2], [0.1, -0.6]]])
a24 = np.array([[[1., 0.], [0., 1.]], [[-0.6, 0.], [0.2, -0.6]],
[[-0.1, 0.], [0.1, -0.1]]])
a31 = np.r_[np.eye(3)[None, :, :], 0.8 * np.eye(3)[None, :, :]]
a32 = np.array([[[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]],
[[0.8, 0., 0.], [0.1, 0.6, 0.], [0., 0., 0.9]]])
########
ut = np.random.randn(1000, 2)
ar2s = vargenerate(a22, ut)
#res = np.linalg.lstsq(lagmat(ar2s,1)[:,1:], ar2s)
res = np.linalg.lstsq(lagmat(ar2s, 1), ar2s)
bhat = res[0].reshape(1, 2, 2)
arhat = ar2full(bhat)
#print maxabs(arhat - a22)
v = Var(ar2s)
v.fit(1)
v.forecast()
v.forecast(25)[-30:]
ar23 = np.array([[[1., 0.], [0., 1.]], [[-0.6, 0.], [0.2, -0.6]],
[[-0.1, 0.], [0.1, -0.1]]])
ma22 = np.array([[[1., 0.], [0., 1.]], [[0.4, 0.], [0.2, 0.3]]])
ar23ns = np.array([[[1., 0.], [0., 1.]], [[-1.9, 0.], [0.4, -0.6]],
