p7]c@sdZddlmZddlZddlZddlmZm Z m Z ddl m Z ddl mZddlmZddlmZdd lmZmZmZdd lmZdd lmZddljjZd Zd Z dZ!dZ"dZ#dZ$dZ%dZ&dZ'dZ(dZ)i ej&ddf6ej'ddf6ej$de*f6ej(ddf6ej)ddf6ej%de*f6ej"e*df6ej!e*df6ej e*e*f6Z+i e&ddf6e'ddf6e$de*f6e(ddf6e)ddf6e%de*f6e"e*df6e!e*df6e e*e*f6Z,defdYZ-defdYZ.ee.e-defdYZ/de/fd YZ0d!e/fd"YZ1dS(#s$ Notes ----- Code written using below textbook as a reference. Results are checked against the expected outcomes in the text book. Properties: Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2014. Author: Terence L van Zyl Modified: Kevin Sheppard i(t string_typesN(t basinhoppingtbrutetminimize(t sqeuclidean(t inv_boxcox(tboxcox(tResults(tpopulate_wrappert union_dictstResultsWrapper(tTimeSeriesModel(tfreq_to_periodcCs|||jtj<|d \}}}} } } d|} d|} ||}d|(d|(| |d<| |d<||| | | |fS(s"Initialization for the Holt Modelsiii(tastypetnptbool(txtxitptytltbtalphatbetat_tl0tb0tphitalphactbetacty_alpha((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pyt _holt_inits     c Csvt||||||\} } } } }}x9td|D](}||d| ||d|| Additive Seasonal Minimization Function (,A) gi(R-R R(RRRRRRR!R"R#R$RRR)RRRR+RR,R%((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pyt_holt_win__adds9 2>c  Csbt||||||||\ } } } } }}}}}| | dkrP| S| | ksl| d| krp| Sxtd|D]}||d||d|||d| ||d||<| ||||d|| ||d||<||d||d| ||d|||d|||d0sicCsygt|jjdd}|jjd|}|jjd||}|jj|jd|d|SWn0ttfk r|jjd||jjSXdS(s% Out-of-sample forecasts Parameters ---------- steps : int The number of out of sample forecasts from the end of the sample. Returns ------- forecast : array Array of out of sample forecasts tfreqiiR?R@thN( tgetattrR;t_indexR>R<tAttributeErrort ValueErrort_predictt fcastvalues(R:tstepsRAR?R@((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pytforecastIs#c Csdddlm}ddlm}|j}|jjd}d}t|jjt j rm|jjj d}n*t|jjt j r|jjj }n|jjd.krd.n |jj}idd6dd 6d d 6d d 6d d.6}|jd}|rtnt} t|tr|n |jd} t| trFdj| } nd|gfd|jjgfdttj|jgfd||jjgfd||jjgfdt|gfdt| gfdt| gfg} dtt|jjgfddj|jgfddj|jgfddj|jgfddj|j gfd/d0g} |} | j!|d!| d"| d#||j"}d$}g}xi|j#D][\}}|j$||j%d%d&j|j%dd&jtt&|j%d'gqW||d(d)d*d+gd#d,d-t'|j(}| j)j$|| S(1s6 Summarize the fitted Model Returns ------- smry : Summary instance This holds the summary table and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary i(tSummary(t SimpleTables Model ResultstendogitAdditiveR5tadditivetMultiplicativeR4tmultiplicativetNonet use_boxcoxtlamdas {:>10.5f}sDep. Variable:sModel:s Optimized:sTrend:s Seasonal:sSeasonal Periods:sBox-Cox:sBox-Cox Coeff.:sNo. Observations:tSSEs{:5.3f}tAICtBICtAICCsDate:sTime:tglefttgrightttitlecSstj|}d}|dkr9ttj|}n|dksQ|dkr^dj|Std|d}dj|}|j|S(Niiiis {:>20.5g}is {{:>20.{0}f}}(Rtabstinttlog10tformattmin(Rtabs_xtscaletdectfmt((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pyt_fmts  is{0:>20}itheaderstcoefftcodet optimizedttstubsN(sDate:N(sTime:N(*tstatsmodels.iolib.summaryRKtstatsmodels.iolib.tableRLR;t __class__t__name__t isinstanceRMtpdt DataFrametcolumnstSeriestnametseasonalRRtseasonal_periodsR<tTruetFalseRtfloatR_tstrRtanyRittrendtlentssetaictbictaicctadd_table_2colstparams_formattedtiterrowstappendtilocRtlisttindexttables(R:RKRLR;R[t dep_variableRwtlookupt transformtbox_cox_transformt box_cox_coeffttop_leftt top_righttsmryt formattedRettabRtvalst params_table((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pytsummaryas^ $ "     *N(Rot __module__t__doc__R9RRR>RJR(((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pyR6s 1  tHoltWintersResultsWrappercBsieZidd6dd6dd6dd6dd6ZeejeZidd6dd6ZeejeZRS( trowst fittedvaluestleveltresidtseasontslopetdatesR>RJ(RoRt_attrsR R t _wrap_attrst_methodst _wrap_methods(((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pyRs    tExponentialSmoothingc BseZdZdeddddddZdddZddddeeeeddded ZdZ ddddddddddddd Z RS(sY Holt Winter's Exponential Smoothing Parameters ---------- endog : array-like Time series trend : {"add", "mul", "additive", "multiplicative", None}, optional Type of trend component. damped : bool, optional Should the trend component be damped. seasonal : {"add", "mul", "additive", "multiplicative", None}, optional Type of seasonal component. seasonal_periods : int, optional The number of periods in a complete seasonal cycle, e.g., 4 for quarterly data or 7 for daily data with a weekly cycle. Returns ------- results : ExponentialSmoothing class Notes ----- This is a full implementation of the holt winters exponential smoothing as per [1]_. This includes all the unstable methods as well as the stable methods. The implementation of the library covers the functionality of the R library as much as possible whilst still being Pythonic. References ---------- .. [1] Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2014. tnonec Cstt|j|d||d||jjtj|_|d krdidd6dd6|}n||_||_ |d kridd6dd6|}n||_ |dk|_ |dk|_ |jdks|j dkrtj |dkrtdn|j r(|j r(tdn|j r|||_|dkr[t|j|_n|jd krtd qn d |_t|j|_dS(NtmissingRORQR5R4gsWendog must be strictly positive when using multiplicative trend or seasonal components.s#Can only dampen the trend componentis'seasonal_periods must be larger than 1.i(RORQ(RORQ(R4R5(R4R5(R8RR9RRRMR RtdoubleR}tdampedRvttrendingt seasoningR|RFRwR t _index_freqR~tnobs( R:RMR}RRvRwRRAR((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pyR9s0      3    cCs|dkr5t|jdd}|jd|}n|jd|d|\}}}}|dkr}|jd||}n|jdd|}|j|||d!S( s Returns in-sample and out-of-sample prediction. Parameters ---------- params : array The fitted model parameters. start : int, str, or datetime Zero-indexed observation number at which to start forecasting, ie., the first forecast is start. Can also be a date string to parse or a datetime type. end : int, str, or datetime Zero-indexed observation number at which to end forecasting, ie., the first forecast is start. Can also be a date string to parse or a datetime type. Returns ------- predicted values : array RAiiR?R@iRBN(RRRCRDt_get_prediction_indexRGt fittedfcast(R:R<R?R@RAt out_of_sampletprediction_indextres((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pyR>s   c 4Cs|d(k rt|nd(} |d(k r6t|nd(}|d(k rTt|nd(}|d(k rrt|nd(}| d(k rt| nd(|_| d(k rt| nd(|_|j}|j}|j}|j}|j}|j }|j }d(}|r |nd}|dkr5d}t ||}nTt |tr\|}t ||}n-|rwt |\}}nd(}|j }tj|dkrtdntj|dtj|_}tj|j}tj|j}tj|j|d}tjd|}tjtjj}|j\} }!}"tj|dtj}#|rH| d(k rw| ndt|d}$|d(k r|n|rd |$n|}%d(}&|d(k r|nd }'|rk|d(k r|n d d|$}&tj| d(k|o|d(k|d(k| d(k|o5| d(k|d(koD|gtg|}#t||f}(n|rtj| d(k|d(kt| d(k| d(k|d(ko|gtg|}#td(|f}(nBtj| d(ktt| d(kttgtg|}#td)}(|$|%|&| |!|'g|"|(tj|#r|#tjttttttgtg|@})|)j tj})tjd*d+d,d-d.d/gd0g|}*|)j tj!|||||||j|f }+| d(krBtj|)rB| rBt"|(|*|)|+d d dtdd(},|,\||)<}}-}-n| d(k rtj#tj | } t$| |#j%krtdj&t$|#t$| n| ||# 7}4| |||d|d|g}5|5| | j#7}5t$t%d |5}5t j&|5}5| d4kr t jt'|3d!t j(}6n| j)t j(}6t*||t*||g}7|7t*g|7}7t+j,gt-|3|5|6D]\}8}9}:|8|9|:g^q6 d"d#d$d%gd&|4}5|5j.|7}5t/||j!d'|*d(|*| d d)|*| dd*|,d+|+d,|'d-|(d.|.d/|1d0|0d1|2d2|-d3|5d%|6};t0|;S(5s Helper prediction function Parameters ---------- h : int, optional The number of time steps to forecast ahead. g?Rgis!Only 1 dimensional data supportediR4R5cSs|S(N((RR((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pytQRjcSsdS(Ni((RR((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pyRURjcSsdS(Ni((RR((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pyRYRjiiRRRRRRRRSRTRRRR)sl.0sb.0Rss.{0}sinitial_seasons.{0}cSs|dkrtjS|S(N(RRRtnan(tv((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pyRRjRRsRutparamRiRRRRHRRRRRRRRtkRN(1RMRRRR}RvRwRRpRzRRRRRtNotImplementedErrorRRtcumsumtrepeatRtmultiplyR5tdividetsubtracttpowerR tcopyRRRtinfRRR<R_ttolistRtmapRR~RR RxRqRrtziptlocR6R(<R:RBRRRRRRRRSRTRRRRR)RR7RRRR}RvR"RRR,RRR+RRR!tphi_httrendedtdetrendtdampenRR%RRtjtfittedRRRRt aicc_penaltyRRRtcodestidxRRitincludedtctftoR((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pyRGs8             !   W           1#1#C 1#5#C 1'! %(  1    , ,  !=  N( RoRRRRRyR9R>RxRRRG(((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pyRs!     9   tSimpleExpSmoothingcBs/eZdZdZdeddedZRS(s? Simple Exponential Smoothing Parameters ---------- endog : array-like Time series Returns ------- results : SimpleExpSmoothing class Notes ----- This is a full implementation of the simple exponential smoothing as per [1]_. `SimpleExpSmoothing` is a restricted version of :class:`ExponentialSmoothing`. See Also -------- ExponentialSmoothing Holt References ---------- .. [1] Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2014. cCstt|j|dS(N(R8RR9(R:RM((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pyR9sc Cs1tt|jd|d|d|d|d|S(s8 Fit the model Parameters ---------- smoothing_level : float, optional The smoothing_level value of the simple exponential smoothing, if the value is set then this value will be used as the value. optimized : bool, optional Estimate model parameters by maximizing the log-likelihood start_params: array, optional Starting values to used when optimizing the fit. If not provided, starting values are determined using a combination of grid search and reasonable values based on the initial values of the data initial_level: float, optional Value to use when initializing the fitted level. use_brute: bool, optional Search for good starting values using a brute force (grid) optimizer. If False, a naive set of starting values is used. Returns ------- results : HoltWintersResults class See statsmodels.tsa.holtwinters.HoltWintersResults Notes ----- This is a full implementation of the simple exponential smoothing as per [1]. References ---------- [1] Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2014. RRiRRR(R8RR(R:RRiRRR((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pyRs% N(RoRRR9RRRxR(((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pyRs  tHoltc Bs>eZdZeedZdddedddedZRS(s Holt's Exponential Smoothing Parameters ---------- endog : array-like Time series exponential : bool, optional Type of trend component. damped : bool, optional Should the trend component be damped. Returns ------- results : Holt class Notes ----- This is a full implementation of the Holt's exponential smoothing as per [1]_. `Holt` is a restricted version of :class:`ExponentialSmoothing`. See Also -------- ExponentialSmoothing SimpleExpSmoothing References ---------- .. [1] Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2014. cCs8|r dnd}tt|j|d|d|dS(NR4R5R}R(R8RR9(R:RMt exponentialRR}((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pyR9<sc CsCtt|jd|d|d|d|d|d|d|d|S( s Fit the model Parameters ---------- smoothing_level : float, optional The alpha value of the simple exponential smoothing, if the value is set then this value will be used as the value. smoothing_slope : float, optional The beta value of the Holt's trend method, if the value is set then this value will be used as the value. damping_slope : float, optional The phi value of the damped method, if the value is set then this value will be used as the value. optimized : bool, optional Estimate model parameters by maximizing the log-likelihood start_params: array, optional Starting values to used when optimizing the fit. If not provided, starting values are determined using a combination of grid search and reasonable values based on the initial values of the data initial_level: float, optional Value to use when initializing the fitted level. initial_slope: float, optional Value to use when initializing the fitted slope. use_brute: bool, optional Search for good starting values using a brute force (grid) optimizer. If False, a naive set of starting values is used. Returns ------- results : HoltWintersResults class See statsmodels.tsa.holtwinters.HoltWintersResults Notes ----- This is a full implementation of the Holt's exponential smoothing as per [1]. References ---------- [1] Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2014. RRRRiRRRR(R8RR( R:RRRRiRRRR((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pyR@s.  N(RoRRRyR9RRRxR(((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pyRs   (2Rtstatsmodels.compat.pythonRtnumpyRtpandasRqtscipy.optimizeRRRtscipy.spatial.distanceRt scipy.specialRt scipy.statsRtstatsmodels.base.modelRtstatsmodels.base.wrapperRR R tstatsmodels.tsa.base.tsa_modelR tstatsmodels.tsa.tsatoolsR t&statsmodels.tsa._exponential_smoothersttsat_exponential_smootherst smoothersRR&R'R(R-R.R/R0R1R2R3RRRt PY_SMOOTHERSR6RRRR(((s:lib/python2.7/site-packages/statsmodels/tsa/holtwinters.pyt sb                    L