B ¤ŠãZNfã @sdZddlmZmZmZddlmZddlmZddl Z ddl Z ddl mZddlmZddlmZmZmZdd lmZdd lmZmZddlmmZe  d d d ddgdddddgdddddgg¡ZGdd„deƒZ Gdd„deƒZ!Gdd„deƒZ"e #e"e!¡dS) zL Recursive least squares model Author: Chad Fulton License: Simplified-BSD é)ÚdivisionÚabsolute_importÚprint_function)Úwarn)Ú OrderedDictN)ÚOLS)Ú_is_using_pandas)ÚMLEModelÚ MLEResultsÚMLEResultsWrapper)ÚBunch)Úcache_readonlyÚresettable_cachegŸâ8ð*ñ?gö7Fü”ó?gp`r£Èºõ?g¤‰£aGø?g!*C ¿ ú?gü´@q¶oå¿gÚsO²på¿gÜÅêE£qå¿g“›ò2Ôrå¿gRƒÄÑ°så¿g\b§×œâ¿gÿRP›‚†ç¿gZÞ°È Yì¿gXŽ<[ñ¿gÏ£Éó¿csveZdZdZ‡fdd„Zed‡fdd„ ƒZdd„Zd‡fd d „ Zd‡fd d „ Z e dd„ƒZ e dd„ƒZ dd„Z ‡ZS)Ú RecursiveLSa… Recursive least squares Parameters ---------- endog : array_like The observed time-series process :math:`y` exog : array_like Array of exogenous regressors, shaped nobs x k. Notes ----- Recursive least squares (RLS) corresponds to expanding window ordinary least squares (OLS). This model applies the Kalman filter to compute recursive estimates of the coefficients and recursive residuals. References ---------- .. [*] Durbin, James, and Siem Jan Koopman. 2012. Time Series Analysis by State Space Methods: Second Edition. Oxford University Press. c sât|dƒst |¡}t|dƒ}|s,t |¡}|jdkrV|sL|dd…df}n t |¡}|jd|_|  d|j¡|  dd¡|  dd¡t t |ƒj |f|j|dœ|—Ž|j dd…dd…dfj|d<t |j¡|d <d |d <dS) NéÚloglikelihood_burnZinitializationZapproximate_diffuseZinitial_variancegeÍÍA)Úk_statesÚexogZdesignZ transitiongð?)Úobs_covrr)rÚnpZ asanyarrayZasarrayÚndimÚpdZ DataFrameÚshapeÚk_exogÚ setdefaultÚsuperrÚ__init__rÚTZeyer)ÚselfZendogrÚkwargsZexog_is_using_pandas)Ú __class__©úBlib/python3.7/site-packages/statsmodels/regression/recursive_ls.pyr8s$          zRecursiveLS.__init__Ncstt|ƒ |||¡S)z8 Not implemented for state space models )rr Ú from_formula)ÚclsZformulaÚdataZsubset)r r!r"r#^szRecursiveLS.from_formulacCs>|jdd}|jd}t ||¡|j|j}||d<| ¡S)z€ Fits the model by application of the Kalman filter Returns ------- RecursiveLSResults T)Ú return_ssmr)rrr)ÚsmoothÚstandardized_forecasts_errorrÚinnerÚnobsr)rZsmoother_resultsZresidZsigma2r!r!r"Úfites   zRecursiveLS.fitFc sptt|ƒjgfddddœ|—Ž}|sl|jdd…df}d|jdd…dd…dfddœ}tt|||d|d ƒ}|S) NTÚnone)Ú transformedÚcov_typer&éÿÿÿÿÚ nonrobustz^Parameters and covariance matrix estimates are RLS estimates conditional on the entire sample.)Úcustom_cov_typeÚcustom_cov_paramsÚcustom_descriptionÚcustom)r.Úcov_kwds)rrÚfilterÚfiltered_stateÚfiltered_state_covÚRecursiveLSResultsWrapperÚRecursiveLSResults)rr&rÚresultÚparamsr5)r r!r"r6ys  zRecursiveLS.filterc sptt|ƒjgfddddœ|—Ž}|sl|jdd…df}d|jdd…dd…dfddœ}tt|||d|d ƒ}|S) NTr,)r-r.r&r/r0z^Parameters and covariance matrix estimates are RLS estimates conditional on the entire sample.)r1r2r3r4)r.r5)rrr'r7r8r9r:)rr&rr;r<r5)r r!r"r's  zRecursiveLS.smoothcCs|jS)N)Ú exog_names)rr!r!r"Ú param_names§szRecursiveLS.param_namescCs t d¡S)Nr)rZzeros)rr!r!r"Ú start_params«szRecursiveLS.start_paramscKsdS)a Update the parameters of the model Updates the representation matrices to fill in the new parameter values. Parameters ---------- params : array_like Array of new parameters. transformed : boolean, optional Whether or not `params` is already transformed. If set to False, `transform_params` is called. Default is True.. Returns ------- params : array_like Array of parameters. Nr!)rr<rr!r!r"Úupdate°szRecursiveLS.update)N)F)F)Ú__name__Ú __module__Ú __qualname__Ú__doc__rÚ classmethodr#r+r6r'Úpropertyr>r?r@Ú __classcell__r!r!)r r"rs &  rcs„eZdZdZd‡fdd„ Zedd„ƒZedd„ƒZed d „ƒZ ed d „ƒZ ddd„Z ddd„Z ddd„Z ddd„Zd dd„Z‡ZS)!r:aÛ Class to hold results from fitting a recursive least squares model. Parameters ---------- model : RecursiveLS instance The fitted model instance Attributes ---------- specification : dictionary Dictionary including all attributes from the recursive least squares model instance. See Also -------- statsmodels.tsa.statespace.kalman_filter.FilterResults statsmodels.tsa.statespace.mlemodel.MLEResults Úopgc sFtt|ƒj||||f|Žtj|_|j ¡|_t fd|jj iŽ|_ dS)Nr) rr:rrÚinfZdf_residÚmodelZ_get_init_kwdsZ _init_kwdsr rÚ specification)rrJr<Úfilter_resultsr.r)r r!r"rÜs   zRecursiveLSResults.__init__cCsŠd}|j}d}}||j}t|j||…|j||…||…fdd|d}|jdk rd|j||…|_|jdk r†|j||…||…f|_|S)a7 Estimates of regression coefficients, recursively estimated Returns ------- out: Bunch Has the following attributes: - `filtered`: a time series array with the filtered estimate of the component - `filtered_cov`: a time series array with the filtered estimate of the variance/covariance of the component - `smoothed`: a time series array with the smoothed estimate of the component - `smoothed_cov`: a time series array with the smoothed estimate of the variance/covariance of the component - `offset`: an integer giving the offset in the state vector where this component begins Nr)ÚfilteredÚ filtered_covÚsmoothedÚ smoothed_covÚoffset) rKrr r7r8Zsmoothed_staterOZsmoothed_state_covrP)rÚoutÚspecÚstartrQÚendr!r!r"Úrecursive_coefficientsês    z)RecursiveLSResults.recursive_coefficientscCs|jj ¡|jjddS)a9 Recursive residuals Returns ------- resid_recursive : array_like An array of length `nobs` holding the recursive residuals. Notes ----- The first `k_exog` residuals are typically unreliable due to initialization. )rrgà?)rLr(Zsqueezer)rr!r!r"Úresid_recursives z"RecursiveLSResults.resid_recursivecCs4|j}t |j|jd…¡tj|j|d…ddS)aÜ Cumulative sum of standardized recursive residuals statistics Returns ------- cusum : array_like An array of length `nobs - k_exog` holding the CUSUM statistics. Notes ----- The CUSUM statistic takes the form: .. math:: W_t = \frac{1}{\hat \sigma} \sum_{j=k+1}^t w_j where :math:`w_j` is the recursive residual at time :math:`j` and :math:`\hat \sigma` is the estimate of the standard deviation from the full sample. Excludes the first `k_exog` datapoints. Due to differences in the way :math:`\hat \sigma` is calculated, the output of this function differs slightly from the output in the R package strucchange and the Stata contributed .ado file cusum6. The calculation in this package is consistent with the description of Brown et al. (1975) References ---------- .. [*] Brown, R. L., J. Durbin, and J. M. Evans. 1975. "Techniques for Testing the Constancy of Regression Relationships over Time." Journal of the Royal Statistical Society. Series B (Methodological) 37 (2): 149-92. Nr)Úddof)rrÚcumsumrWZstd)rÚllbr!r!r"Úcusum)s)zRecursiveLSResults.cusumcCs*t |j|jd…d¡}|d}||S)a˜ Cumulative sum of squares of standardized recursive residuals statistics Returns ------- cusum_squares : array_like An array of length `nobs - k_exog` holding the CUSUM of squares statistics. Notes ----- The CUSUM of squares statistic takes the form: .. math:: s_t = \left ( \sum_{j=k+1}^t w_j^2 \right ) \Bigg / \left ( \sum_{j=k+1}^T w_j^2 \right ) where :math:`w_j` is the recursive residual at time :math:`j`. Excludes the first `k_exog` datapoints. References ---------- .. [*] Brown, R. L., J. Durbin, and J. M. Evans. 1975. "Techniques for Testing the Constancy of Regression Relationships over Time." Journal of the Royal Statistical Society. Series B (Methodological) 37 (2): 149-92. Nér/)rrYrWr)rZnumerZdenomr!r!r"Ú cusum_squaresVs"z RecursiveLSResults.cusum_squaresrçš™™™™™©?ú upper leftNcCs*t|ttfƒr|g}t|ƒ}|jj}x0t|ƒD]$}||} t| tƒr.| | ¡||<q.Wddlm } ddl m } m } | ƒ} | ||ƒ}x˜t|ƒD]Š}||} |  |d|d¡}t|jdƒrÔ|jjdk rÔ|jj ¡}n t |j¡}|j}|j}|j||d…|j| |d…fd|| d| ¡\}}|dk rò|  d|d ¡}t |j| | dd…f¡}|j| ||}|j| ||}|j||d…||d…||d…d d }d d|d }|dkrò| jddd| ¡dd}|  |¡|  |¡|j!|||d||dkrŽ|j" #g¡qŽW| $¡|S)aI Plot the recursively estimated coefficients on a given variable Parameters ---------- variables : int or str or iterable of int or string, optional Integer index or string name of the variable whose coefficient will be plotted. Can also be an iterable of integers or strings. Default is the first variable. alpha : float, optional The confidence intervals for the coefficient are (1 - alpha) % legend_loc : string, optional The location of the legend in the plot. Default is upper left. fig : Matplotlib Figure instance, optional If given, subplots are created in this figure instead of in a new figure. Note that the grid will be created in the provided figure using `fig.add_subplot()`. figsize : tuple, optional If a figure is created, this argument allows specifying a size. The tuple is (width, height). Notes ----- All plots contain (1 - `alpha`) % confidence intervals. r)Únorm)Ú _import_mplÚcreate_mpl_figrÚdatesNzRecursive estimates: %s)Úlabelg@gš™™™™™É?)Úalphaz$%.3g \%%$ confidence intervaléd)rr)Zfc)Úloc)%Ú isinstanceÚintÚstrÚlenrJr=ÚrangeÚindexZ scipy.statsr`Ústatsmodels.graphics.utilsrarbÚ add_subplotÚhasattrr%rcÚ _mpl_reprrÚaranger*rrVÚplotrMZget_legend_handles_labelsZppfZsqrtrNZ fill_betweenZ RectangleZ get_facecolorÚappendÚlegendZxaxisZset_ticklabelsZ tight_layout)rZ variablesreÚ legend_locÚfigÚfigsizeZ k_variablesr=ÚiZvariabler`rarbÚpltÚaxrcrZZcoefZhandlesÚlabelsZcritical_valueZ std_errorsZci_lowerZci_upperZci_polyZci_labelÚpr!r!r"Úplot_recursive_coefficient|sT      &     z-RecursiveLSResults.plot_recursive_coefficientcs„|dkrd‰n$|dkrd‰n|dkr*d‰ntdƒ‚|j‰|jˆ|d‰‡‡‡fd d „}|d krrt ˆ|jg¡}||ƒ ||ƒfS) a— Parameters ---------- alpha : float, optional The significance bound is alpha %. ddof : int, optional The number of periods additional to `k_exog` to exclude in constructing the bounds. Default is zero. This is usually used only for testing purposes. points : iterable, optional The points at which to evaluate the significance bounds. Default is two points, beginning and end of the sample. Notes ----- Comparing against the cusum6 package for Stata, this does not produce exactly the same confidence bands (which are produced in cusum6 by lw, uw) because they burn the first k_exog + 1 periods instead of the first k_exog. If this change is performed (so that `tmp = (self.nobs - llb - 1)**0.5`), then the output here matches cusum6. The cusum6 behavior does not seem to be consistent with Brown et al. (1975); it is likely they did that because they needed three initial observations to get the initial OLS estimates, whereas we do not need to do that. g{®Gáz„?g}?5^ºIò?gš™™™™™©?g¼t“Vî?gš™™™™™¹?gffffffî?zInvalid significance level.gà?csˆˆdˆ|ˆˆS)Nr\r!)Úx)rZÚscalarÚtmpr!r"Ú sz?RecursiveLSResults._cusum_significance_bounds..N)Ú ValueErrorrr*rÚarray)rrerXÚpointsÚ upper_liner!)rZr€rr"Ú_cusum_significance_boundsász-RecursiveLSResults._cusum_significance_boundsc Csúddlm}m}|ƒ}|||ƒ}| ddd¡}t|jdƒrT|jjdk rT|jj ¡} n t  |j ¡} |j } |j | | d…|j dd|jd| | | dd d d | |¡\} } |j | | | dg| d d |dd|  | | | dg| d ¡|j|d|S)a Plot the CUSUM statistic and significance bounds. Parameters ---------- alpha : float, optional The plotted significance bounds are alpha %. legend_loc : string, optional The location of the legend in the plot. Default is upper left. fig : Matplotlib Figure instance, optional If given, subplots are created in this figure instead of in a new figure. Note that the grid will be created in the provided figure using `fig.add_subplot()`. figsize : tuple, optional If a figure is created, this argument allows specifying a size. The tuple is (width, height). Notes ----- Evidence of parameter instability may be found if the CUSUM statistic moves out of the significance bounds. References ---------- .. [*] Brown, R. L., J. Durbin, and J. M. Evans. 1975. "Techniques for Testing the Constancy of Regression Relationships over Time." Journal of the Royal Statistical Society. Series B (Methodological) 37 (2): 149-92. r)rarbrrcNZCUSUM)rdr/Úkg333333Ó?)Zcolorrezk--z%d%% significancerf)rg)rnrarbrorpr%rcrqrrrr*rrsr[Zhlinesr‡ru) rrervrwrxrarbrzr{rcrZÚ lower_liner†r!r!r"Ú plot_cusums "   zRecursiveLSResults.plot_cusumc CsÈ|j}d|j|d}ydddddg |d¡}Wntk rPtd ƒ‚YnXtd d …|f}|d |d|d||d|d }|d kr¦t ||jg¡}|||j|}||||fS) aÐ Notes ----- Comparing against the cusum6 package for Stata, this does not produce exactly the same confidence bands (which are produced in cusum6 by lww, uww) because they use a different method for computing the critical value; in particular, they use tabled values from Table C, pp. 364-365 of "The Econometric Analysis of Time Series" Harvey, (1990), and use the value given to 99 observations for any larger number of observations. In contrast, we use the approximating critical values suggested in Edgerton and Wells (1994) which allows computing relatively good approximations for any number of observations. gà?rgš™™™™™¹?gš™™™™™©?gš™™™™™™?g{®Gáz„?g{®Gázt?r\zInvalid significance level.Nrgø?)rr*rmrƒÚ_cusum_squares_scalarsrr„) rrer…rZÚnZixZscalarsZcritÚliner!r!r"Ú"_cusum_squares_significance_boundsLs,z5RecursiveLSResults._cusum_squares_significance_boundscCsddlm}m}|ƒ}|||ƒ}| ddd¡}t|jdƒrT|jjdk rT|jj ¡} n t  |j ¡} |j } |j | | d…|j ddt  | |j ¡| |j | } |j | | d…| dd d | |¡\} } |j | | | d g| d d |dd|  | | | d g| d ¡|j|d|S)a Plot the CUSUM of squares statistic and significance bounds. Parameters ---------- alpha : float, optional The plotted significance bounds are alpha %. legend_loc : string, optional The location of the legend in the plot. Default is upper left. fig : Matplotlib Figure instance, optional If given, subplots are created in this figure instead of in a new figure. Note that the grid will be created in the provided figure using `fig.add_subplot()`. figsize : tuple, optional If a figure is created, this argument allows specifying a size. The tuple is (width, height). Notes ----- Evidence of parameter instability may be found if the CUSUM of squares statistic moves out of the significance bounds. Critical values used in creating the significance bounds are computed using the approximate formula of [1]_. References ---------- .. [*] Brown, R. L., J. Durbin, and J. M. Evans. 1975. "Techniques for Testing the Constancy of Regression Relationships over Time." Journal of the Royal Statistical Society. Series B (Methodological) 37 (2): 149-92. .. [1] Edgerton, David, and Curt Wells. 1994. "Critical Values for the Cusumsq Statistic in Medium and Large Sized Samples." Oxford Bulletin of Economics and Statistics 56 (3): 355-65. r)rarbrrcNzCUSUM of squares)rdrˆg333333Ó?)rer/zk--z%d%% significancerf)rg)rnrarbrorpr%rcrqrrrr*rrsr]rŽru)rrervrwrxrarbrzr{rcrZZref_liner‰r†r!r!r"Úplot_cusum_squaresms")   z%RecursiveLSResults.plot_cusum_squares)rH)rr^r_NN)rN)r^r_NN)N)r^r_NN)rArBrCrDrrFrVr rWr[r]r~r‡rŠrŽrrGr!r!)r r"r:Çs &  - & c / ; !r:c@s0eZdZiZe eje¡ZiZe ej e¡Z dS)r9N) rArBrCZ_attrsÚwrapZ union_dictsr Z _wrap_attrsZ_methodsZ _wrap_methodsr!r!r!r"r9²s r9)$rDZ __future__rrrÚwarningsrZstatsmodels.compat.collectionsrZnumpyrZpandasrZ#statsmodels.regression.linear_modelrZstatsmodels.tools.datarZ#statsmodels.tsa.statespace.mlemodelr r r Zstatsmodels.tools.toolsr Zstatsmodels.tools.decoratorsr rZstatsmodels.base.wrapperÚbaseÚwrapperrr„r‹rr:r9Zpopulate_wrapperr!r!r!r"Ús.       *n