U mde@sddlZddlZddlmZddlmZmZm Z ddl m Z ddl m Z ddlmZddlmZmZmZGdd d eZGd d d eZeeedS) N) inv_boxcox)boxcox rv_continuous rv_discrete) rv_frozen) PandasData)Results)ResultsWrapperpopulate_wrapper union_dictscs$eZdZdZd1fdd ZeddZeddZed d Zed d Z ed dZ e j ddZ eddZ eddZ eddZeddZeddZeddZeddZeddZed d!Zed"d#Zed$d%Zej d&d%Zd2d'd(Zd3d*d+Zd,d-Zd4d/d0ZZS)5HoltWintersResultsa 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. Ncsz|j|_t||||_||_||_||_||_||_||_ | |_ | |_ | |_ ||_ ||_||_| |_| |_||_dSN)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__\/home/sam/Atlas/atlas_env/lib/python3.8/site-packages/statsmodels/tsa/holtwinters/results.pyrBs$zHoltWintersResults.__init__cCs|jS)z3 The Akaike information criterion. )rr!r5r5r6r%iszHoltWintersResults.aiccCs|jS)z@ AIC with a correction for finite sample sizes. )rr7r5r5r6r&pszHoltWintersResults.aicccCs|jS)z5 The Bayesian information criterion. )rr7r5r5r6r'wszHoltWintersResults.biccCs|jS)zS The sum of squared errors between the data and the fittted value. )rr7r5r5r6r$~szHoltWintersResults.ssecCs|jS)zA The model used to produce the results instance. rr7r5r5r6r"szHoltWintersResults.modelcCs ||_dSr r8r!valuer5r5r6r"scCs|jS)zO An array of the levels values that make up the fitted values. )rr7r5r5r6r)szHoltWintersResults.levelcCs|jS)zU Flag indicating if model parameters were optimized to fit the data. )rr7r5r5r6r(szHoltWintersResults.optimizedcCs|jS)zN An array of the trend values that make up the fitted values. )rr7r5r5r6r*szHoltWintersResults.trendcCs|jS)zQ An array of the seasonal values that make up the fitted values. )rr7r5r5r6r+szHoltWintersResults.seasoncCs|jS)z DataFrame containing all parameters Contains short names and a flag indicating whether the parameter's value was optimized to fit the data. )rr7r5r5r6r,sz#HoltWintersResults.params_formattedcCs|jS)z/ An array of the fitted values )rr7r5r5r6r/szHoltWintersResults.fittedvaluescCs|jS)zI An array of both the fitted values and forecast values. )rr7r5r5r6r0szHoltWintersResults.fittedfcastcCs|jS)z1 An array of the forecast values )rr7r5r5r6r1szHoltWintersResults.fcastvaluescCs|jS)zR An array of the residuals of the fittedvalues and actual values. )rr7r5r5r6r-szHoltWintersResults.residcCs|jS)zJ The k parameter used to remove the bias in AIC, BIC etc. )rr7r5r5r6r.szHoltWintersResults.kcCs|jS)zX Optimization results if the parameters were optimized to fit the data. r r7r5r5r6r2szHoltWintersResults.mle_retvalscCs ||_dSr r;r9r5r5r6r2scCs|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 : ndarray Array of out of sample forecasts. )r"predictr#)r!startendr5r5r6r<szHoltWintersResults.predictcCszt|jjdd}t|tsXt|jjtjtjfrX|jjd|}|jjd||}n|jjjd}||d}|jj |j ||dWSt k r|jj fd|i|j j YSXdS)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?r)r=r>hN)getattrr"_index isinstanceintpdZ DatetimeIndexZ PeriodIndexshaper<r#AttributeErrorZ_predictr1)r!Zstepsr@r=r>r5r5r6forecasts   zHoltWintersResults.forecastc Cs<ddlm}ddlm}|j}|jjd}d}|jjj}t |t j rP|j d}nt |t j rb|j}|jjdkrrdn|jj}ddddd d }|jd } | rd nd } t | tr| n|jd} t | trd| } d|gfd|jjgfdtt|jgfd||jjgfd||jjgfdt|gfdt| gfdt| gfg} dtt|jjgfdd|jgfdd|jgfdd|jgfdd|jgfddg} |}|j|| | |d |j }d!d"}g}|!D]D\}}|"||j#d#d$|j#dd$tt$|j#d%gq||d&d'd(gd)t%|j&d*}|j'"||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 ResultsendogNZAdditiveZMultiplicativeNone)addadditivemulmultiplicativeN use_boxcoxTFlamdaz {:>10.5f}zDep. 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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. 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