B Z@sHdZddlZddlmZddlmZmZmZddl m Z ddl m Z m Z mZddlmZyddlmZWnek rd d ZYnXdd lmZd d ZddZddZddZddZddZddZddZddZddZd d!Z Gd"d#d#eZ!Gd$d%d%eZ"ee"e!Gd&d'd'e Z#Gd(d)d)e#Z$Gd*d+d+e#Z%dS),a1 Created on Wed Jul 12 09:35:35 2017 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 N)Results)populate_wrapper union_dictsResultsWrapper)TimeSeriesModel) basinhoppingbruteminimize) sqeuclidean) inv_boxcoxcCs*|dkr tt|||St|S)Nr)npZexpZlog1p)xZlmbdar:lib/python3.7/site-packages/statsmodels/tsa/holtwinters.pyr sr )boxcoxcCsp|||<|dd\}}}} } } d|} d|} ||}d|dd<d|dd<| |d<| |d<||| | | |fS)z"Initialization for the Holt ModelsNrr)r xipylbalphabeta_l0b0phialphacbetacy_alpharrr _holt_inits  r!c Cs\t||||||\} } } } }}x2td|D]$}||d| ||d||<q*Wt||S)zH Simple Exponential Smoothing Minimization Function (,) r)r!ranger )r rrrrrsmnmax_seenrrrrrr irrr_holt__-s$r(c Cst||||||\} } } } }}| dkr*| S| | kr6| Sxrtd|D]d}||d| ||d||d| ||<| ||||d|||d| ||<qBWt||| |S)z^ Multiplicative and Multiplicative Damped Minimization Function (M,) & (Md,) gr)r!r"r )r rrrrrr#r$r%r&rrrrrr r'rrr _holt_mul_dam9s04r)c Cst||||||\} } } } }}| dkr*| S| | kr6| Sxrtd|D]d}||d| ||d| ||d||<| ||||d|| ||d||<qBWt|| ||S)zR Additive and Additive Damped Minimization Function (A,) & (Ad,) gr)r!r"r )r rrrrrr#r$r%r&rrrrrr r'rrr _holt_add_damJs04r*c Cs|||<|dd\}} } } } } |dd}d|}d| }d| }||}| |}d|dd<d|dd<d|dd<| |d<| |d<||d|<|| | | |||||f S)z3Initialization for the Holt Winters Seasonal ModelsNrrrr)r rrrrrr#r$rrgammarrrs0rrgammacr y_gammarrr_holt_win_init[s     r/c  Cst||||||||\ } } } } }}}}}| dkr4| S| d| krD| Sxrtd|D]d}||d||d|||d||<||d||d|||d|||d<qPWt||d|d |S)zE Multiplicative Seasonal Minimization Function (,M) grN)r/r"r )r rrrrrr#r$r%r&rrr+rrrr-r r.r'rrr_holt_win__mulns& ,8r0c  Cst||||||||\ } } } } }}}}}| dkr4| S| d| krD| Sxztd|D]l}||d| ||d|||d||<||d| ||d|||d|||d<qPWt||d|d |S)z? Additive Seasonal Minimization Function (,A) grN)r/r"r )r rrrrrr#r$r%r&rrr+rrrr-r r.r'rrr_holt_win__adds& 0<r1c  Cs8t||||||||\ } } } } }}}}}| | dkr8| S| | ksL| d| krP| Sxtd|D]}||d||d|||d| ||d||<| ||||d|| ||d||<||d||d| ||d|||d|||d<q\Wt|| ||d|d |S)zq Additive and Additive Damped with Multiplicative Seasonal Minimization Function (A,M) & (Ad,M) grN)r/r"r )r rrrrrr#r$r%r&rrr+rrrr-r r.r'rrr_holt_win_add_mul_dams& &02r2c  Cs8t||||||||\ } } } } }}}}}| | dkr8| S| | ksL| d| krP| Sxtd|D]}||d||d|||d||d| ||<| ||||d|||d| ||<||d||d||d| |||d|||d<q\Wt||| |d|d |S)z} Multiplicative and Multiplicative Damped with Multiplicative Seasonal Minimization Function (M,M) & (Md,M) grN)r/r"r )r rrrrrr#r$r%r&rrr+rrrr-r r.r'rrr_holt_win_mul_mul_dams& &04r3c  Cs@t||||||||\ } } } } }}}}}| | dkr8| S| | ksL| d| krP| Sxtd|D]}||d| ||d|||d| ||d||<| ||||d|| ||d||<||d| ||d| ||d|||d|||d<q\Wt|| ||d|d |S)zk Additive and Additive Damped with Additive Seasonal Minimization Function (A,A) & (Ad,A) grN)r/r"r )r rrrrrr#r$r%r&rrr+rrrr-r r.r'rrr_holt_win_add_add_dams& &0Lr4c  Cs@t||||||||\ } } } } }}}}}| | dkr8| S| | ksL| d| krP| Sxtd|D]}||d| ||d|||d||d| ||<| ||||d|||d| ||<||d| ||d||d| |||d|||d<q\Wt|| ||d|d |S)zw Multiplicative and Multiplicative Damped with Additive Seasonal Minimization Function (M,A) & (M,Ad) grN)r/r"r )r rrrrrr#r$r%r&rrr+rrrr-r r.r'rrr_holt_win_mul_add_dams& &0Lr5cs4eZdZdZfddZd ddZd dd ZZS) HoltWintersResultsa Holt Winter's Exponential Smoothing Results Parameters ---------- model : ExponentialSmoothing instance The fitted model instance params : dictionary All the parameters for the Exponential Smoothing model. Attributes ---------- specification : dictionary Dictionary including all attributes from the VARMAX model instance. params: dictionary All the parameters for the Exponential Smoothing model. fittedfcast: array An array of both the fitted values and forecast values. fittedvalues: array An array of the fitted values. Fitted by the Exponential Smoothing model. fcast: array An array of the forecast values forecast by the Exponential Smoothing model. sse: float The sum of squared errors level: array An array of the levels values that make up the fitted values. slope: array An array of the slope values that make up the fitted values. season: array An array of the seaonal values that make up the fitted values. aic: float The Akaike information criterion. bic: float The Bayesian information criterion. aicc: float AIC with a correction for finite sample sizes. resid: array An array of the residuals of the fittedvalues and actual values. k: int the k parameter used to remove the bias in AIC, BIC etc. c s"|j|_tt|j||f|dS)N)datasuperr6__init__)selfmodelparamskwds) __class__rrr9szHoltWintersResults.__init__NcCs|j|j||S)a In-sample prediction and out-of-sample forecasting Parameters ---------- start : int, str, or datetime, optional 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. Default is the the zeroth observation. end : int, str, or datetime, optional 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. However, if the dates index does not have a fixed frequency, end must be an integer index if you want out of sample prediction. Default is the last observation in the sample. Returns ------- forecast : array Array of out of sample forecasts. )r;predictr<)r:startendrrrr?szHoltWintersResults.predictrcCsdy4|jjdd}|jjd|}|jj|j||dStk r^|jjfd|i|jjSXdS)a% 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 r)r@rAhN)r;_indexr?r< ValueError_predict fcastvalues)r:Zstepsr@rArrrforecast2s zHoltWintersResults.forecast)NN)r)__name__ __module__ __qualname____doc__r9r?rH __classcell__rr)r>rr6s,  r6c@s>eZdZddddddZeejeZdddZeejeZdS)HoltWintersResultsWrapperZrows) fittedvalueslevelresidseasonslopedates)r?rHN) rIrJrKZ_attrsrrZ _wrap_attrsZ_methodsZ _wrap_methodsrrrrrNJs rNc s@eZdZdZdfdd ZdddZdd d Zdd d ZZS)ExponentialSmoothinga 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 seasons to consider for the holt winters. 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. NFnonec stt|j|d|||d|dkr0ddd|}||_||_|dkrRddd|}||_|dk|_|dk|_|jdks|jdkr|dkrt d|jr|jst d|jr|dks|d krt d ||_ nd |_ t |j |_ dS) N)missing)ZadditiveZmultiplicativeaddmul)rYrXgz-Unable to correct for negative or zero valuesz#Can only dampen the trend componentrz%Unable to detect season automatically)r8rUr9trenddampedseasonaltrending seasoninganyNotImplementedErrorseasonal_periodslenendognobs) r:rcrZr[r\rarTZfreqrW)r>rrr9zs.     zExponentialSmoothing.__init__cCst|dkr|jdd}|j||d\}}}}|dkrJ|jfd|i|}n|jfddi|}|j|||dS)a 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 NrBr)r@rArrC)rDZ_get_prediction_indexrF fittedfcast)r:r<r@rAZ out_of_sampleZprediction_indexresrrrr?szExponentialSmoothing.predictTc , Cs|} |} |} |} |j} |j}|j}|j}|j}|j}|j}d}|rF| nd} |dkrbd}t| |}n8t|t r||}t| |}n|rt| \}}n d}| }t |dkrt dt |jf}t |jf}t |j|df}t d|}t t jj}|r|t |j|dk}|rJ|||||d||nd}|d krlt|d||nt|d||}nN|r|d}|d kr|d|dn|d|d}g}n|d}d}g}|rn| dk r| n d t|d}| dk r| n|rd |n| } d}!| dk r$| nd }"tttttttttd }#|r| dk rT| n dd|}!t | dk| dk| dkd|| dko|gdg|}$|#||f}%nr|rt | dk| dkddd| dko|gdg|}$|#d|f}%n,t | dkdddddgdg|}$|#d}%|| |!|||"g||dd<|$t ddddddgdg|@}&t ddddddgdg|}'t |%|'|&|&|||||||j|f dddd}(|(\||&<}})}*|dd\} } } }}} |dd}|rt!|%||$|$|||||||j|f |'|$ddd}(n,t"|%||$|$|||||||j|f |'|$d}(|(j#||$<|dd\} } } }}} |dd}|(}|j$d| | | | ||||||d }+||+j%_&|+S)aY fit Holt Winter's Exponential Smoothing 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 holts trend method, if the value is set then this value will be used as the value. smoothing_seasonal : float, optional The gamma value of the holt winters seasonal 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 Should the values that have not been set above be optimized automatically? use_boxcox : {True, False, 'log', float}, optional Should the boxcox tranform be applied to the data first? If 'log' then apply the log. If float then use lambda equal to float. remove_bias : bool, optional Should the bias be removed from the forecast values and fitted values before being returned? Does this by enforcing average residuals equal to zero. use_basinhopping : bool, optional Should the opptimser try harder using basinhopping to find optimal values? Returns ------- results : HoltWintersResults class See statsmodels.tsa.holtwinters.HoltWintersResults 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. Ng?loggrz!Only 1 dimensional data supportedrrrYg?g?gGz?) )rYrX)rYrY)rYN)rXrX)rXrY)rXN)NrX)NrY)NNg?TF)NN)gg?)gN)ZNsZ full_outputZfinish)argsboundsg{Gz?)Zminimizer_kwargsZstepsize) rCsmoothing_levelsmoothing_slopesmoothing_seasonal damping_slope initial_level initial_slopeinitial_seasons use_boxcoxlamda remove_bias)'rcr[r^r]rZr\rar isinstancefloatsqueezer ndimr`zerosrdZfinfoZdoublemaxarangemeanlistr2r3r0r4r5r1r*r)r(Zarrayrrr r rFZ_resultsZ mle_retvals),r:rkrlrmrn optimizedrrrtZuse_basinhoppingrrr+rr7r[r^r]rZr\r$Zoptrsrrrr#rr&rrr,Z init_alphaZ init_betaZ init_gammaZinit_phiZ func_dictrfuncZtxirjrfZgridZJouthwfitrrrfits4    .4*         * "    zExponentialSmoothing.fitc -s8|} |} |}|}|j}|j}|j}|j}|j}|j}|j|rB|nd}| dkr^d} t|d}nNt| t rx| } t|| }n4| rt|\}} n"d} | }t |dkrt dt |jf}t |jf}d| }| ||dd<|rd| }|r d|}|||dd<t |j|df}t |j|df}t |j|df||d<||d<|d<|rt t ||dt d|ddnt d|dd}t jt jdd d |}t jt jd d d |} t jt jd d d |}!|d krxtd|jdD]ȉ|dd|||d|!|d||<|r| | ||d||!|d||<|d||d|!|d||dd<qW|dd}"}#||d<|rN|!|d||d<|!|||d<|||}fddt|ddDdd<|d }$n|dkrPxtd|jdD]Љ|d| d|||d|!|d||<|r>| | ||d||!|d||<|d|||d|!|d||dd<qW|dd}"}#||d<|r|!|d||d<|!|||d<|||}fddt|ddDdd<|d }$nxtd|jdD]t|d|||d|!|d||<|rb| | ||d||!|d||<qbW|dd}"}#||d<|rH|!|d||d<|!|||d<|||}|}$|dd}%| s| dkst| t rt|$| }$t|%| }%| |d|%}"|dkr|$t|| d}#n"|d kr|$t|| d}#nt|$d| d|}&|d|dd|}'|jt |&|j|'d}(|(d|'d|'d|j|'d})|jt |&|j|'t |j}*||$d| d}+| r|$|+7}$|st j}| | |||d|dd| | | d |_t ||j|$|$d| d|$| dd|&|%|"|#|(|*|)|+|'d},t!|,S)z Helper prediction function Parameters ---------- h : int, optional The number of time steps to forecast ahead. g?rggNrz!Only 1 dimensional data supportedrcSs|S)Nr)rrrrrsz/ExponentialSmoothing._predict..)rYrXNcSsdS)Nrr)rrrrrrscSsdS)Nrr)rrrrrrsrYcs g|]}d|qS)rr).0j)r'r$r#rr sz1ExponentialSmoothing._predict..rXcs g|]}d|qS)rr)rr)r'r$r#rrrs) rkrlrmrnrorprqrrrsrt) rerOrGsserPrSrRaicbicaiccrQk)"rcr[r^r]rZr\rarrurvrwr rxr`ryrdZcumsumrepeatr{ZmultiplyrXZdividesubtractZpowerr"copyr r rgr|ZNaNr<r6rN)-r:rCrkrlrmrorprnrqrrrsrtrrr+rr7r[r^r]rZr\rr r.rrr-rrZphi_hZtrendedZdetrendZdampenrSrRZfittedrPrrrrrrQrr)r'r$r#rrFVs      D    *  $ 2 *R 2 *"     &&    zExponentialSmoothing._predict)NFNNNNrV)NN)NNNNTFFF) NNNNNNNNNNN) rIrJrKrLr9r?rrFrMrr)r>rrUYs  !rUcs.eZdZdZfddZdfdd ZZS) SimpleExpSmoothinga Simple Exponential Smoothing wrapper(...) Parameters ---------- endog : array-like Time series Returns ------- results : SimpleExpSmoothing class Notes ----- This is a full implementation of the simple exponential smoothing as per [1]. See Also --------- Exponential Smoothing Holt References ---------- [1] Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2014. cstt||dS)N)r8rr9)r:rc)r>rrr9szSimpleExpSmoothing.__init__NTcstt|j||dS)a/ fit Simple Exponential Smoothing wrapper(...) 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 Should the values that have not been set above be optimized automatically? 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. )rkr~)r8rr)r:rkr~)r>rrrszSimpleExpSmoothing.fit)NT)rIrJrKrLr9rrMrr)r>rrs rcs0eZdZdZd fdd Zd fdd ZZS) Holta Holt's Exponential Smoothing wrapper(...) Parameters ---------- endog : array-like Time series expoential : 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 holts exponential smoothing as per [1]. See Also --------- Exponential Smoothing Simple Exponential Smoothing References ---------- [1] Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2014. Fcs&|rdnd}tt|j|||ddS)NrYrX)rZr[)r8rr9)r:rcZ exponentialr[rZ)r>rrr9Ss z Holt.__init__NTcstt|j||||dS)a} fit Holt's Exponential Smoothing wrapper(...) 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 holts 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 Should the values that have not been set above be optimized automatically? Returns ------- results : HoltWintersResults class See statsmodels.tsa.holtwinters.HoltWintersResults Notes ----- This is a full implementation of the holts exponential smoothing as per [1]. References ---------- [1] Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2014. )rkrlrnr~)r8rr)r:rkrlrnr~)r>rrrWs zHolt.fit)FF)NNNT)rIrJrKrLr9rrMrr)r>rr3sr)&rLZnumpyr Zstatsmodels.base.modelrZstatsmodels.base.wrapperrrrZstatsmodels.tsa.base.tsa_modelrZscipy.optimizerrr Zscipy.spatial.distancer Z scipy.specialr ImportErrorZ scipy.statsrr!r(r)r*r/r0r1r2r3r4r5r6rNrUrrrrrrs>     c !<