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)
X = np.column_stack(
(lagmat(endog, p, 'both')[p_tmp + (q - p):],
lagmat(resid, q, 'both'))) # stack ar lags and resids
coefs = GLS(endog[p_tmp + q:], 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]
def _stackX(self, k_ar, trend):
"""
Private method to build the RHS matrix for estimation.
Columns are trend terms, then exogenous, then lags.
"""
endog = self.endog
exog = self.exog
X = lagmat(endog, maxlag=k_ar, trim='both')
if exog is not None:
X = np.column_stack((exog[k_ar:, :], X))
# Handle trend terms
if trend == 'c':
k_trend = 1
elif trend == 'nc':
k_trend = 0
elif trend == 'ct':
k_trend = 2
elif trend == 'ctt':
k_trend = 3
if trend != 'nc':
X = add_trend(X, prepend=True, trend=trend)
self.k_trend = k_trend
return X
def _stackX(self, k_ar, trend):
"""
Private method to build the RHS matrix for estimation.
Columns are trend terms, then exogenous, then lags.
"""
endog = self.endog
exog = self.exog
X = lagmat(endog, maxlag=k_ar, trim='both')
if exog is not None:
X = np.column_stack((exog[k_ar:,:], X))
# Handle trend terms
if trend == 'c':
k_trend = 1
elif trend == 'nc':
k_trend = 0
elif trend == 'ct':
k_trend = 2
elif trend == 'ctt':
k_trend = 3
if trend != 'nc':
X = add_trend(X,prepend=True, trend=trend)
self.k_trend = k_trend
return X
a22 = np.array([[[1.0, 0.0], [0.0, 1.0]], [[-0.8, 0.0], [0.1, -0.8]]])
a23 = np.array([[[1.0, 0.0], [0.0, 1.0]], [[-0.8, 0.2], [0.1, -0.6]]])
a24 = np.array([[[1.0, 0.0], [0.0, 1.0]], [[-0.6, 0.0], [0.2, -0.6]], [[-0.1, 0.0], [0.1, -0.1]]])
a31 = np.r_[np.eye(3)[None, :, :], 0.8 * np.eye(3)[None, :, :]]
a32 = np.array(
[[[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[0.8, 0.0, 0.0], [0.1, 0.6, 0.0], [0.0, 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, 0.0], [0.0, 1.0]], [[-0.6, 0.0], [0.2, -0.6]], [[-0.1, 0.0], [0.1, -0.1]]])
ma22 = np.array([[[1.0, 0.0], [0.0, 1.0]], [[0.4, 0.0], [0.2, 0.3]]])
ar23ns = np.array([[[1.0, 0.0], [0.0, 1.0]], [[-1.9, 0.0], [0.4, -0.6]], [[0.3, 0.0], [0.1, -0.1]]])
def acorr_lm(x, maxlag=None, autolag='AIC', store=False):
'''Lagrange Multiplier tests for autocorrelation
not checked yet, copied from unitrood_adf with adjustments
check array shapes because of the addition of the constant.
written/copied without reference
This is not Breush-Godfrey. BG adds lags of residual to exog in the
design matrix for the auxiliary regression with residuals as endog,
see Greene 12.7.1.
Notes
-----
If x is calculated as y^2 for a time series y, then this test corresponds
to the Engel test for autoregressive conditional heteroscedasticity (ARCH).
TODO: get details and verify
'''
x = np.asarray(x)
nobs = x.shape[0]
if maxlag is None:
#for adf from Greene referencing Schwert 1989
maxlag = 12. * np.power(
nobs / 100., 1 / 4.) #nobs//4 #TODO: check default, or do AIC/BIC
xdiff = np.diff(x)
#
xdall = lagmat(x[:-1, None], maxlag, trim='both')
nobs = xdall.shape[0]
xdall = np.c_[np.ones((nobs, 1)), xdall]
xshort = x[-nobs:]
if store: resstore = ResultsStore()
if autolag:
#search for lag length with highest information criteria
#Note: I use the same number of observations to have comparable IC
results = {}
for mlag in range(1, maxlag):
results[mlag] = sm.OLS(xshort, xdall[:, :mlag + 1]).fit()
if autolag.lower() == 'aic':
bestic, icbestlag = max((v.aic, k) for k, v in results.iteritems())
elif autolag.lower() == 'bic':
icbest, icbestlag = max((v.bic, k) for k, v in results.iteritems())
else:
raise ValueError("autolag can only be None, 'AIC' or 'BIC'")
#rerun ols with best ic
xdall = lagmat(x[:, None], icbestlag, trim='forward')
nobs = xdall.shape[0]
xdall = np.c_[np.ones((nobs, 1)), xdall]
xshort = x[-nobs:]
usedlag = icbestlag
else:
usedlag = maxlag
resols = sm.OLS(xshort, xdall[:, :usedlag + 1]).fit()
fval = resols.fvalue
fpval = resols.f_pvalue
lm = nobs * resols.rsquared
lmpval = stats.chi2.sf(lm, usedlag)
# Note: degrees of freedom for LM test is nvars minus constant = usedlags
return fval, fpval, lm, lmpval
if store:
resstore.resols = resols
resstore.usedlag = usedlag
return fval, fpval, lm, lmpval, resstore
else:
return fval, fpval, lm, lmpval
def acorr_lm(x, maxlag=None, autolag='AIC', store=False):
'''Lagrange Multiplier tests for autocorrelation
not checked yet, copied from unitrood_adf with adjustments
check array shapes because of the addition of the constant.
written/copied without reference
This is not Breush-Godfrey. BG adds lags of residual to exog in the
design matrix for the auxiliary regression with residuals as endog,
see Greene 12.7.1.
Notes
-----
If x is calculated as y^2 for a time series y, then this test corresponds
to the Engel test for autoregressive conditional heteroscedasticity (ARCH).
TODO: get details and verify
'''
x = np.asarray(x)
nobs = x.shape[0]
if maxlag is None:
#for adf from Greene referencing Schwert 1989
maxlag = 12. * np.power(nobs/100., 1/4.)#nobs//4 #TODO: check default, or do AIC/BIC
xdiff = np.diff(x)
#
xdall = lagmat(x[:-1,None], maxlag, trim='both')
nobs = xdall.shape[0]
xdall = np.c_[np.ones((nobs,1)), xdall]
xshort = x[-nobs:]
if store: resstore = ResultsStore()
if autolag:
#search for lag length with highest information criteria
#Note: I use the same number of observations to have comparable IC
results = {}
for mlag in range(1,maxlag):
results[mlag] = sm.OLS(xshort, xdall[:,:mlag+1]).fit()
if autolag.lower() == 'aic':
bestic, icbestlag = max((v.aic,k) for k,v in results.iteritems())
elif autolag.lower() == 'bic':
icbest, icbestlag = max((v.bic,k) for k,v in results.iteritems())
else:
raise ValueError("autolag can only be None, 'AIC' or 'BIC'")
#rerun ols with best ic
xdall = lagmat(x[:,None], icbestlag, trim='forward')
nobs = xdall.shape[0]
xdall = np.c_[np.ones((nobs,1)), xdall]
xshort = x[-nobs:]
usedlag = icbestlag
else:
usedlag = maxlag
resols = sm.OLS(xshort, xdall[:,:usedlag+1]).fit()
fval = resols.fvalue
fpval = resols.f_pvalue
lm = nobs * resols.rsquared
lmpval = stats.chi2.sf(lm, usedlag)
# Note: degrees of freedom for LM test is nvars minus constant = usedlags
return fval, fpval, lm, lmpval
if store:
resstore.resols = resols
resstore.usedlag = usedlag
return fval, fpval, lm, lmpval, resstore
else:
return fval, fpval, lm, lmpval
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]],