!geddlZddlZddlmZddlmZmZm Z ddl m Z ddl m Z ddlmZddlmZmZmZGdd eZGd d eZeeey) N) inv_boxcox)boxcox rv_continuous rv_discrete) rv_frozen) PandasData)Results)ResultsWrapperpopulate_wrapper union_dictsceZdZdZ dfd ZedZedZedZedZ edZ e jdZ ed Z ed Z ed Zed Zed ZedZedZedZedZedZedZejdZddZddZdZ ddZxZS)HoltWintersResultsa Results from fitting Exponential Smoothing models. Parameters ---------- model : ExponentialSmoothing instance The fitted model instance. params : dict All the parameters for the Exponential Smoothing model. sse : float The sum of squared errors. aic : float The Akaike information criterion. aicc : float AIC with a correction for finite sample sizes. bic : float The Bayesian information criterion. optimized : bool Flag indicating whether the model parameters were optimized to fit the data. level : ndarray An array of the levels values that make up the fitted values. trend : ndarray An array of the trend values that make up the fitted values. season : ndarray An array of the seasonal values that make up the fitted values. params_formatted : pd.DataFrame DataFrame containing all parameters, their short names and a flag indicating whether the parameter's value was optimized to fit the data. resid : ndarray 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. fittedvalues : ndarray An array of the fitted values. Fitted by the Exponential Smoothing model. fittedfcast : ndarray An array of both the fitted values and forecast values. fcastvalues : ndarray An array of the forecast values forecast by the Exponential Smoothing model. mle_retvals : {None, scipy.optimize.optimize.OptimizeResult} Optimization results if the parameters were optimized to fit the data. c(|j|_t| ||||_||_||_||_||_||_||_ | |_ | |_ | |_ ||_ ||_||_| |_| |_||_yN)datasuper__init___model_sse_aic_aicc_bic _optimized_level_trend_season_params_formatted _fittedvalues _fittedfcast _fcastvalues_resid_k _mle_retvals)selfmodelparamssseaicaiccbic optimizedleveltrendseasonparams_formattedresidk fittedvalues fittedfcast fcastvalues mle_retvals __class__s `/var/www/dash_apps/app1/venv/lib/python3.12/site-packages/statsmodels/tsa/holtwinters/results.pyrzHoltWintersResults.__init__Bs(JJ  '     #   !1)'' 'c|jS)z3 The Akaike information criterion. )rr$s r7r(zHoltWintersResults.aici yyr8c|jS)z@ AIC with a correction for finite sample sizes. )rr:s r7r)zHoltWintersResults.aiccps zzr8c|jS)z5 The Bayesian information criterion. )rr:s r7r*zHoltWintersResults.bicwr;r8c|jS)zS The sum of squared errors between the data and the fittted value. )rr:s r7r'zHoltWintersResults.sse~r;r8c|jS)zA The model used to produce the results instance. rr:s r7r%zHoltWintersResults.model {{r8c||_yrr@r$values r7r%zHoltWintersResults.models  r8c|jS)zO An array of the levels values that make up the fitted values. )rr:s r7r,zHoltWintersResults.levelrAr8c|jS)zU Flag indicating if model parameters were optimized to fit the data. )rr:s r7r+zHoltWintersResults.optimizeds r8c|jS)zN An array of the trend values that make up the fitted values. )rr:s r7r-zHoltWintersResults.trendrAr8c|jS)zQ An array of the seasonal values that make up the fitted values. )rr:s r7r.zHoltWintersResults.seasons ||r8c|jS)z DataFrame containing all parameters Contains short names and a flag indicating whether the parameter's value was optimized to fit the data. )rr:s r7r/z#HoltWintersResults.params_formatteds%%%r8c|jS)z/ An array of the fitted values )rr:s r7r2zHoltWintersResults.fittedvaluess !!!r8c|jS)zI An array of both the fitted values and forecast values. )rr:s r7r3zHoltWintersResults.fittedfcast    r8c|jS)z1 An array of the forecast values )r r:s r7r4zHoltWintersResults.fcastvaluesrLr8c|jS)zR An array of the residuals of the fittedvalues and actual values. )r!r:s r7r0zHoltWintersResults.residrAr8c|jS)zJ The k parameter used to remove the bias in AIC, BIC etc. )r"r:s r7r1zHoltWintersResults.ks wwr8c|jS)zX Optimization results if the parameters were optimized to fit the data. r#r:s r7r5zHoltWintersResults.mle_retvalsrLr8c||_yrrQrCs r7r5zHoltWintersResults.mle_retvalss !r8cP|jj|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 : ndarray Array of out of sample forecasts. )r%predictr&)r$startends r7rTzHoltWintersResults.predicts!.zz!!$++uc::r8c t|jjdd}t|tszt|jjt j t jfr<|jjd|z}|jjd||zz}n+|jjjd}||zdz }|jj|j||S#t$r5|jjdd|i|jjcYSwxYw)a' Out-of-sample forecasts Parameters ---------- steps : int The number of out of sample forecasts from the end of the sample. Returns ------- forecast : ndarray Array of out of sample forecasts freqr)rUrVh)getattrr%_index isinstanceintpd DatetimeIndex PeriodIndexshaperTr&AttributeError_predictr4)r$stepsrXrUrVs r7forecastzHoltWintersResults.forecasts  K4::,,fa8DdC(Z !!B$4$4bnn#E. ))"-4jj''+edl: ))//2ema'::%%dkkC%H H K&4::&&>>$++>JJ J KsC=D;D>=D>c "ddlm}ddlm}|j}|j j dz}d}|jjj}t|tjr|jd}n&t|tjr |j}|jjdn|jj }ddddd d }|j"d } | rd nd } t| t$r| n|j"d} t| t&r| d} d|gfd|j j gfdt%t)j*|j,gfd||jj.gfd||jjgfdt%|gfdt%| gfdt%| gfg} dt%t1|jj2gfd|j4dgfd|j6dgfd|j8dgfd|j:dgfddg} |}|j=|| | | |j>}d!}g}|jAD]\\}}|jC||jDd"|jDdd#t%tG|jDd$d#g^||gd%d&tI|jJ'}|jLjC||S)(a6 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 r)Summary) SimpleTablez Model ResultsendogNAdditiveMultiplicativeNone)addadditivemulmultiplicativeN use_boxcoxTFlamdaz>10.5fzDep. Variable:zModel:z Optimized:zTrend:z Seasonal:zSeasonal Periods:zBox-Cox:zBox-Cox Coeff.:zNo. Observations:SSEz5.3fAICBICAICC)zDate:N)zTime:N)gleftgrighttitlec"tj|}d}tj|r t|dS|dk7rt tj |}|dkDs|dkr|dSt d|z d}d|d }|j|S) NrY>20rz>20.5gz{:>20.zf})npabsisnanstrr`log10minformat)xabs_xscaledecfmts r7_fmtz(HoltWintersResults.summary.._fmtcsFF1IEExx{a&&zBHHUO,qyEBJF$a%i#CC5$C::a= r8rYr~)coeffcoder+)headersr|stubs)'statsmodels.iolib.summaryrjstatsmodels.iolib.tablerkr%r6__name__r orig_endogr_ra DataFramecolumnsSeriesnameseasonalseasonal_periodsr&rfloatranyr+r-lenrlr'r(r*r)add_table_2colsr/iterrowsappendilocboollistindextables)r$rjrkr%r| dep_variablerrlookup transformbox_cox_transform box_cox_coefftop_left top_rightsmry formattedrtab_vals params_tables r7summaryzHoltWintersResults.summarys 67 ((+;; ZZ__// j",, /%--a0L  BII .%??Lzz""* ,,  "#.  KK - $-D5#Is3IW9M  mU +,V4M  ~ . 001 2 Ct~~ 678 9 tzz//01 2 6$**"5"567 8 3'7#8"9 : #/01 2 ]!3 4 5  !3s4::+;+;'<#="> ? 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Parameters ---------- nsimulations : int The number of simulation steps. anchor : int, str, or datetime, optional First period for simulation. The simulation will be conditional on all existing datapoints prior to the `anchor`. Type depends on the index of the given `endog` in the model. Two special cases are the strings 'start' and 'end'. `start` refers to beginning the simulation at the first period of the sample, and `end` refers to beginning the simulation at the first period after the sample. Integer values can run from 0 to `nobs`, or can be negative to apply negative indexing. Finally, if a date/time index was provided to the model, then this argument can be a date string to parse or a datetime type. Default is 'end'. repetitions : int, optional Number of simulated paths to generate. Default is 1 simulated path. error : {"add", "mul", "additive", "multiplicative"}, optional Error model for state space formulation. Default is ``"add"``. random_errors : optional Specifies how the random errors should be obtained. Can be one of the following: * ``None``: Random normally distributed values with variance estimated from the fit errors drawn from numpy's standard RNG (can be seeded with the `random_state` argument). This is the default option. * A distribution function from ``scipy.stats``, e.g. ``scipy.stats.norm``: Fits the distribution function to the fit errors and draws from the fitted distribution. Note the difference between ``scipy.stats.norm`` and ``scipy.stats.norm()``, the latter one is a frozen distribution function. * A frozen distribution function from ``scipy.stats``, e.g. ``scipy.stats.norm(scale=2)``: Draws from the frozen distribution function. * A ``np.ndarray`` with shape (`nsimulations`, `repetitions`): Uses the given values as random errors. * ``"bootstrap"``: Samples the random errors from the fit errors. random_state : int or np.random.RandomState, optional A seed for the random number generator or a ``np.random.RandomState`` object. Only used if `random_errors` is ``None``. Default is ``None``. Returns ------- sim : pd.Series, pd.DataFrame or np.ndarray An ``np.ndarray``, ``pd.Series``, or ``pd.DataFrame`` of simulated values. If the original data was a ``pd.Series`` or ``pd.DataFrame``, `sim` will be a ``pd.Series`` if `repetitions` is 1, and a ``pd.DataFrame`` of shape (`nsimulations`, `repetitions`) else. Otherwise, if `repetitions` is 1, a ``np.ndarray`` of shape (`nsimulations`,) is returned, and if `repetitions` is not 1 a ``np.ndarray`` of shape (`nsimulations`, `repetitions`) is returned. Notes ----- The simulation is based on the state space model of the Holt-Winter's methods. The state space model assumes that the true value at time :math:`t` is randomly distributed around the prediction value. If using the additive error model, this means: .. math:: y_t &= \hat{y}_{t|t-1} + e_t\\ e_t &\sim \mathcal{N}(0, \sigma^2) Using the multiplicative error model: .. math:: y_t &= \hat{y}_{t|t-1} \cdot (1 + e_t)\\ e_t &\sim \mathcal{N}(0, \sigma^2) Inserting these equations into the smoothing equation formulation leads to the state space equations. The notation used here follows [1]_. Additionally, .. math:: B_t &= b_{t-1} \circ_d \phi\\ L_t &= l_{t-1} \circ_b B_t\\ S_t &= s_{t-m}\\ Y_t &= L_t \circ_s S_t, where :math:`\circ_d` is the operation linking trend and damping parameter (multiplication if the trend is additive, power if the trend is multiplicative), :math:`\circ_b` is the operation linking level and trend (addition if the trend is additive, multiplication if the trend is multiplicative), and :math:`\circ_s` is the operation linking seasonality to the rest. The state space equations can then be formulated as .. math:: y_t &= Y_t + \eta \cdot e_t\\ l_t &= L_t + \alpha \cdot (M_e \cdot L_t + \kappa_l) \cdot e_t\\ b_t &= B_t + \beta \cdot (M_e \cdot B_t + \kappa_b) \cdot e_t\\ s_t &= S_t + \gamma \cdot (M_e \cdot S_t + \kappa_s) \cdot e_t\\ with .. math:: \eta &= \begin{cases} Y_t\quad\text{if error is multiplicative}\\ 1\quad\text{else} \end{cases}\\ M_e &= \begin{cases} 1\quad\text{if error is multiplicative}\\ 0\quad\text{else} \end{cases}\\ and, when using the additive error model, .. math:: \kappa_l &= \begin{cases} \frac{1}{S_t}\quad \text{if seasonality is multiplicative}\\ 1\quad\text{else} \end{cases}\\ \kappa_b &= \begin{cases} \frac{\kappa_l}{l_{t-1}}\quad \text{if trend is multiplicative}\\ \kappa_l\quad\text{else} \end{cases}\\ \kappa_s &= \begin{cases} \frac{1}{L_t}\quad\text{if seasonality is multiplicative}\\ 1\quad\text{else} \end{cases} When using the multiplicative error model .. math:: \kappa_l &= \begin{cases} 0\quad \text{if seasonality is multiplicative}\\ S_t\quad\text{else} \end{cases}\\ \kappa_b &= \begin{cases} \frac{\kappa_l}{l_{t-1}}\quad \text{if trend is multiplicative}\\ \kappa_l + l_{t-1}\quad\text{else} \end{cases}\\ \kappa_s &= \begin{cases} 0\quad\text{if seasonality is multiplicative}\\ L_t\quad\text{else} \end{cases} References ---------- .. [1] Hyndman, R.J., & Athanasopoulos, G. (2018) *Forecasting: principles and practice*, 2nd edition, OTexts: Melbourne, Australia. OTexts.com/fpp2. Accessed on February 28th 2020. )rqrsrprr)rprrzerror must be 'add' or 'mul'!NrVrUrz/Cannot anchor simulation outside of the sample.rtrusmoothing_levelsmoothing_trendsmoothing_seasonal damping_trendrYr initial_levelrZ initial_trendinitial_seasonszNIf random_errors is an ndarray, it must have shape (nsimulations, repetitions) bootstrapT)sizereplacezWArgument random_state must be None, an integer, or an instance of np.random.RandomStater)rz,Argument random_errors has unexpected value!)rr)r)7 ValueErrorr%nobs_get_index_locr_slicerUr- damped_trendrr&maxr has_trend has_seasonalrmultiplypowerrpr,r.empty concatenatetileTrr2_ysqrtsumrndarrayrdrandomchoicerandnr` RandomStaterrfitrvsrranger atleast_1dsqueezerrr_get_prediction_indexrar endog_namesr)6r$ nsimulationsanchor repetitionserror random_errors random_state start_idxrr-dampedrrtrualphabetagammaphimn_params mul_seasonal mul_trend mul_errorop_bop_d neutral_bop_s neutral_sr,rr.ylvlbsr_sfittedr0sigmaepsrngr&tb0l0s0y0etakappa_lkappa_bkappa_ssimrs6 r7simulatezHoltWintersResults.simulates d 2 2!&%@GE  &<= = >Vu_ I w I"jj77?OIq!)U+%OO q=  (I tzz &NO O   ((::&&[[.  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