M/Ph@dZddlZddlmcmZddlmZGddej Z Gddej Z Gdd ej Zejee dS) zH Markov switching regression models Author: Chad Fulton License: BSD-3 N)markov_switchingceZdZdZ dfd Zd Zd Zd Zed Z fd Z ddZ ddZ edZ edZfdZfdZxZS)MarkovRegressiona First-order k-regime Markov switching regression model Parameters ---------- endog : array_like The endogenous variable. k_regimes : int The number of regimes. trend : {'n', 'c', 't', 'ct'} Whether or not to include a trend. To include an intercept, time trend, or both, set `trend='c'`, `trend='t'`, or `trend='ct'`. For no trend, set `trend='n'`. Default is an intercept. exog : array_like, optional Array of exogenous regressors, shaped nobs x k. order : int, optional The order of the model describes the dependence of the likelihood on previous regimes. This depends on the model in question and should be set appropriately by subclasses. exog_tvtp : array_like, optional Array of exogenous or lagged variables to use in calculating time-varying transition probabilities (TVTP). TVTP is only used if this variable is provided. If an intercept is desired, a column of ones must be explicitly included in this array. switching_trend : bool or iterable, optional If a boolean, sets whether or not all trend coefficients are switching across regimes. If an iterable, should be of length equal to the number of trend variables, where each element is a boolean describing whether the corresponding coefficient is switching. Default is True. switching_exog : bool or iterable, optional If a boolean, sets whether or not all regression coefficients are switching across regimes. If an iterable, should be of length equal to the number of exogenous variables, where each element is a boolean describing whether the corresponding coefficient is switching. Default is True. switching_variance : bool, optional Whether or not there is regime-specific heteroskedasticity, i.e. whether or not the error term has a switching variance. Default is False. Notes ----- This model is new and API stability is not guaranteed, although changes will be made in a backwards compatible way if possible. The model can be written as: .. math:: y_t = a_{S_t} + x_t' \beta_{S_t} + \varepsilon_t \\ \varepsilon_t \sim N(0, \sigma_{S_t}^2) i.e. the model is a dynamic linear regression where the coefficients and the variance of the error term may be switching across regimes. The `trend` is accommodated by prepending columns to the `exog` array. Thus if `trend='c'`, the passed `exog` array should not already have a column of ones. See the notebook `Markov switching dynamic regression <../examples/notebooks/generated/markov_regression.html>`__ for an overview. References ---------- Kim, Chang-Jin, and Charles R. Nelson. 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications". MIT Press Books. The MIT Press. cNrTFnonec <ddlm} | |dd|_||_||_| |_t j|\|_}t|}d|_ |j|_ d}|dkrtj |df}d|_ n|dkr3tj|dzddtjf}d|_ n^|d krXtjtj |dftj|dzddtjff}d |_ |-||ntj||f}|xj |j z c_ t#|||||| | | |jd us |jd ur|jg|j z|_n,t|j|j kst'd|jd us |jd ur|jg|jz|_n,t|j|jkst'dtj|j|jft,|_|j|jd<|jrdgndg|jd<dS)Nr) string_liketrend)nrctt)optionsrr r )order exog_tvtpexogdatesfreqmissingTFz-Invalid iterable passed to `switching_trend`.z,Invalid iterable passed to `switching_exog`.rvariance)statsmodels.tools.validationr r switching_trendswitching_exogswitching_variancer prepare_exogk_exoglenk_trend_k_exognponesarangenewaxisc_super__init__ ValueErrorr_astypebooltolistswitching_coeffs parameters)selfendog k_regimesr rrrrrrrrrr nobs trend_exog __class__s r/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/tsa/regime_switching/markov_regression.pyr'zMarkovRegression.__init__Vs =<<<<< [9NOOO .,"4-9$?? T5zz {  C<<$++JDLL c\\)D//A-qqq"*}=JDLL d]]rway11 " $! 3QQQ ]C DEJDL  !!%::25T9I3JD LLDL (LL  9EYTdG  5 5 5  4 ' '4+?5+H+H$($8#9DL#HD T)**dl::LMM M  $ & &$*=*F*F#'#6"7$+"ED  T())T[88KLL L E$&%& ''-vd||FFHH  #'"7-1-D&Mqcc1# ###cBtj|d}tj|j|jf|j}t |jD]?}|jdkr2||j|df}tj |j |||<@|dddddfS)aj In-sample prediction, conditional on the current regime Parameters ---------- params : array_like Array of parameters at which to perform prediction. Returns ------- predict : array_like Array of predictions conditional on current, and possibly past, regimes r)ndmindtyperrN) r!arrayzerosr1r2r:ranger r.dotr)r/paramspredicticoeffss r5predict_conditionalz$MarkovRegression.predict_conditionals&***(DNDI6flKKKt~&& 7 7A|a6 :;VDIv66 qqq$z""r6cttj|||jd}|j|z S)Nr)axis)r!repeatrCr1r0)r/r?r@s r5_residzMarkovRegression._resids<)D44V<< N444zG##r6c(||}||jd}|jrt j||jddf}d|dzz|z dt jdtjz|zzz }|S)zS Compute loglikelihoods conditional on the current period's regime rrgr?) rGr.squeezerr!reshaper1logpi)r/r?residrconditional_loglikelihoodss r5_conditional_loglikelihoodsz,MarkovRegression._conditional_loglikelihoodss  F##$/*56>>@@  " Dz(T^Q,BCCH 5!8Oh &rva"%i(6J/K/K)K K #*)r6c"dttfiS)Nfit)MarkovRegressionResultsMarkovRegressionResultsWrapper)r/s r5 _res_classeszMarkovRegression._res_classess/689 9r6ct|\}}tj|j}d}|jdkrb|||j|j|j j d|}t|j D]}||||j |df<| ||j|j||||j d<||fS)z EM iteration Notes ----- This uses the inherited _em_iteration method for computing the non-TVTP transition probabilities and then performs the EM step for regression coefficients and variances. Nrrr)r& _em_iterationr!sqrtsmoothed_marginal_probabilitiesr _em_exogr0rr. switchingr=r1 _em_variance)r/params0resultparams1tmprBrAr4s r5rWzMarkovRegression._em_iterations ''//88gf<== ** @ @6linalgpinvanyrXrYr=r$)r/r^r0rr[r`rrBnonswitching_exognonswitching_coeffsrrA tmp_endogtmp_exogs r5rZzMarkovRegression._em_exogsVA4>6233vi   K $QQQ ] 3 ry~~&788%@@ $7F111yj= !BF#46IJJJE 6)   A!!!!Y,/N{gfDEE4>** A AFUN q6!!!RZ-0>AF29>>(33Y??q)|$$ r6c|dn |jd}|jrtj|j}t |jD]q}|dkr|tj|||z } n|} tj| dz|j|ztj|j|z ||<rnd}|tj |j}t |jD]m}|||z} |dkr>||ddtj f|z} | tj| ||z } n| } |tj| dzz }n||j z}|S)z' EM step for variances Nrrr) rbrr!r<r1r=r>sumrYrXr$r2) r/r^r0rbetasr`rrrArNrirjs r5r\zMarkovRegression._em_variancesl 1   " "x//H4>** G GA::!BF4q$:$::EE!EF5!8!A!DEFFF6A!DEEF  GH{gfDEE4>** - -FUN A::"1vaaam4t;H%xq(B(BBEE%EBF5!8,,,  !Hr6ctjj|}|jdkrt jt j|j |j }t j |j t j|j |z }t j |j r5t|jD]}|||jz z||j|df< n*|||jd<nt j |j }|jr.t j|dz ||j||jd<n|||jd<|S)a (array) Starting parameters for maximum likelihood estimation. Notes ----- These are not very sophisticated and / or good. We set equal transition probabilities and interpolate regression coefficients between zero and the OLS estimates, where the interpolation is based on the regime number. We rely heavily on the EM algorithm to quickly find much better starting parameters, which are then used by the typical scoring approach. rrg$@)numr)rMarkovSwitching start_paramsfgetr r!r>rdrerr0varrfr-r=r1r.rlinspace)r/r?betarrAs r5rqzMarkovRegression.start_params"sG"1>CCDII z0MarkovRegression.param_names..Xs5;P;P;P2;H 1~-;P;P;Pr6rz sigma2[%d]rsigma2)r!r;rrp param_namesrrobjectrfr-r=r1 exog_namesr.rr,)r/r}rAs @r5r}zMarkovRegression.param_namesJs9h  , 8 = =d C C 6$' ( ( C4>** P P;P;P;P;P?C;P;P;P DOAvI677 P48?K/ 0  " @4>** O O>JQ>N DOAzM:;; O8@K 3 4!!###r6ct|}||jd||jd<||jddz||jd<|S)a Transform unconstrained parameters used by the optimizer to constrained parameters used in likelihood evaluation Parameters ---------- unconstrained : array_like Array of unconstrained parameters used by the optimizer, to be transformed. Returns ------- constrained : array_like Array of constrained parameters which may be used in likelihood evaluation. rrr)r&transform_paramsr.)r/ unconstrained constrainedr4s r5rz!MarkovRegression.transform_paramsfsr$gg..  $/&1 2 DOF+, $/*5 6 9 DOJ/0r6ct|}||jd||jd<||jddz||jd<|S)a Transform constrained parameters used in likelihood evaluation to unconstrained parameters used by the optimizer Parameters ---------- constrained : array_like Array of constrained parameters used in likelihood evaluation, to be transformed. Returns ------- unconstrained : array_like Array of unconstrained parameters used by the optimizer. rrrI)r&untransform_paramsr.)r/rrr4s r5rz#MarkovRegression.untransform_paramssr"22  / 0 dof-.  3 4c 9 doj12r6) rNrNTTFNNr)N)__name__ __module__ __qualname____doc__r'rCrGrPpropertyrUrWrZr\rqr}rr __classcell__)r4s@r5rr sTFFPFGFJ<@7N7N7N7N7N7Nr###:$$$ ***$99X9<8@%%X%N$$X$6>r6rceZdZdZdS)rSa Class to hold results from fitting a Markov switching regression model Parameters ---------- model : MarkovRegression instance The fitted model instance params : ndarray Fitted parameters filter_results : HamiltonFilterResults or KimSmootherResults instance The underlying filter and, optionally, smoother output cov_type : str The type of covariance matrix estimator to use. Can be one of 'approx', 'opg', 'robust', or 'none'. Attributes ---------- model : Model instance A reference to the model that was fit. filter_results : HamiltonFilterResults or KimSmootherResults instance The underlying filter and, optionally, smoother output nobs : float The number of observations used to fit the model. params : ndarray The parameters of the model. scale : float This is currently set to 1.0 and not used by the model or its results. N)rrrrrxr6r5rSrSs8 Dr6rSceZdZdS)rTN)rrrrxr6r5rTrTsDr6rT)rnumpyr!statsmodels.base.wrapperbasewrapperwrap statsmodels.tsa.regime_switchingrrprMarkovSwitchingResultsrSMarkovSwitchingResultsWrapperrTpopulate_wrapperrxr6r5rs '''''''''======TTTTT'7TTTn      .E   @     6   4-/////r6