python时间序列分析代码_时间序列分析VAR实验报告

# Note: The information criteria add 1 to the number of parameters # whenever the model has an AR or MA term since, in principle, # the variance could be treated as a free parameter and restricted # This code does not allow this, but it adds consistency with other # packages such as gretl and X12-ARIMA from __future__ import absolute_import from statsmodels.compat.python import string_types, range # for 2to3 with extensions from datetime import datetime import numpy as np from scipy import optimize from scipy.stats import t, norm from scipy.signal import lfilter from numpy import dot, log, zeros, pi from numpy.linalg import inv from statsmodels.tools.decorators import (cache_readonly, resettable_cache) import statsmodels.tsa.base.tsa_model as tsbase import statsmodels.base.wrapper as wrap from statsmodels.regression.linear_model import yule_walker, GLS from statsmodels.tsa.tsatools import (lagmat, add_trend, _ar_transparams, _ar_invtransparams, _ma_transparams, _ma_invtransparams, unintegrate, unintegrate_levels) from statsmodels.tsa.vector_ar import util from statsmodels.tsa.ar_model import AR from statsmodels.tsa.arima_process import arma2ma from statsmodels.tools.numdiff import approx_hess_cs, approx_fprime_cs from statsmodels.tsa.base.datetools import _index_date from statsmodels.tsa.kalmanf import KalmanFilter _armax_notes = """ Notes ----- If exogenous variables are given, then the model that is fit is .. math:: \\phi(L)(y_t - X_t\\beta) = \\theta(L)\epsilon_t where :math:`\\phi` and :math:`\\theta` are polynomials in the lag operator, :math:`L`. This is the regression model with ARMA errors, or ARMAX model. This specification is used, whether or not the model is fit using conditional sum of square or maximum-likelihood, using the `method` argument in :meth:`statsmodels.tsa.arima_model.%(Model)s.fit`. Therefore, for now, `css` and `mle` refer to estimation methods only. This may change for the case of the `css` model in future versions. """ _arma_params = """\ endog : array-like The endogenous variable. order : iterable The (p,q) order of the model for the number of AR parameters, differences, and MA parameters to use. exog : array-like, optional An optional arry of exogenous variables. This should *not* include a constant or trend. You can specify this in the `fit` method.""" _arma_model = "Autoregressive Moving Average ARMA(p,q) Model" _arima_model = "Autoregressive Integrated Moving Average ARIMA(p,d,q) Model" _arima_params = """\ endog : array-like The endogenous variable. order : iterable The (p,d,q) order of the model for the number of AR parameters, differences, and MA parameters to use. exog : array-like, optional An optional arry of exogenous variables. This should *not* include a constant or trend. You can specify this in the `fit` method.""" _predict_notes = """ Notes ----- Use the results predict method instead. """ _results_notes = """ Notes ----- It is recommended to use dates with the time-series models, as the below will probably make clear. However, if ARIMA is used without dates and/or `start` and `end` are given as indices, then these indices are in terms of the *original*, undifferenced series. Ie., given some undifferenced observations:: 1970Q1, 1 1970Q2, 1.5 1970Q3, 1.25 1970Q4, 2.25 1971Q1, 1.2 1971Q2, 4.1 1970Q1 is observation 0 in the original series. However, if we fit an ARIMA(p,1,q) model then we lose this first observation through differencing. Therefore, the first observation we can forecast (if using exact MLE) is index 1. In the differenced series this is index 0, but we refer to it as 1 from the original series. """ _predict = """ %(Model)s model in-sample and out-of-sample prediction Parameters ---------- %(params)s 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. However, if the dates index does not have a fixed frequency, end must be an integer index if you want out of sample prediction. exog : array-like, optional If the model is an ARMAX and out-of-sample forecasting is requested, exog must be given. Note that you'll need to pass `k_ar` additional lags for any exogenous variables. E.g., if you fit an ARMAX(2, q) model and want to predict 5 steps, you need 7 observations to do this. dynamic : bool, optional The `dynamic` keyword affects in-sample prediction. If dynamic is False, then the in-sample lagged values are used for prediction. If `dynamic` is True, then in-sample forecasts are used in place of lagged dependent variables. The first forecasted value is `start`. %(extra_params)s Returns ------- %(returns)s %(extra_section)s """ _predict_returns = """predict : array The predicted values. """ _arma_predict = _predict % {"Model" : "ARMA", "params" : """ params : array-like The fitted parameters of the model.""", "extra_params" : "", "returns" : _predict_returns, "extra_section" : _predict_notes} _arma_results_predict = _predict % {"Model" : "ARMA", "params" : "", "extra_params" : "", "returns" : _predict_returns, "extra_section" : _results_notes} _arima_predict = _predict % {"Model" : "ARIMA", "params" : """params : array-like The fitted parameters of the model.""", "extra_params" : """typ : str {'linear', 'levels'} - 'linear' : Linear prediction in terms of the differenced endogenous variables. - 'levels' : Predict the levels of the original endogenous variables.\n""", "returns" : _predict_returns, "extra_section" : _predict_notes} _arima_results_predict = _predict % {"Model" : "ARIMA", "params" : "", "extra_params" : """typ : str {'linear', 'levels'} - 'linear' : Linear prediction in terms of the differenced endogenous variables. - 'levels' : Predict the levels of the original endogenous variables.\n""", "returns" : _predict_returns, "extra_section" : _results_notes} _arima_plot_predict_example = """ Examples -------- >>> import statsmodels.api as sm >>> import matplotlib.pyplot as plt >>> import pandas as pd >>> >>> dta = sm.datasets.sunspots.load_pandas().data[['SUNACTIVITY']] >>> dta.index = pd.DatetimeIndex(start='1700', end='2009', freq='A') >>> res = sm.tsa.ARMA(dta, (3, 0)).fit() >>> fig, ax = plt.subplots() >>> ax = dta.ix['1950':].plot(ax=ax) >>> fig = res.plot_predict('1990', '2012', dynamic=True, ax=ax, ... plot_insample=False) >>> plt.show() .. plot:: plots/arma_predict_plot.py """ _plot_predict = (""" Plot forecasts """ + '\n'.join(_predict.split('\n')[2:])) % { "params" : "", "extra_params" : """alpha : float, optional The confidence intervals for the forecasts are (1 - alpha)% plot_insample : bool, optional Whether to plot the in-sample series. Default is True. ax : matplotlib.Axes, optional Existing axes to plot with.""", "returns" : """fig : matplotlib.Figure The plotted Figure instance""", "extra_section" : ('\n' + _arima_plot_predict_example + '\n' + _results_notes) } _arima_plot_predict = (""" Plot forecasts """ + '\n'.join(_predict.split('\n')[2:])) % { "params" : "", "extra_params" : """alpha : float, optional The confidence intervals for the forecasts are (1 - alpha)% plot_insample : bool, optional Whether to plot the in-sample series. Default is True. ax : matplotlib.Axes, optional Existing axes to plot with.""", "returns" : """fig : matplotlib.Figure The plotted Figure instance""", "extra_section" : ('\n' + _arima_plot_predict_example + '\n' + '\n'.join(_results_notes.split('\n')[:3]) + (""" This is hard-coded to only allow plotting of the forecasts in levels. """) + '\n'.join(_results_notes.split('\n')[3:])) } def cumsum_n(x, n): if n: n -= 1 x = np.cumsum(x) return cumsum_n(x, n) else: return x def _check_arima_start(start, k_ar, k_diff, method, dynamic): if start < 0: raise ValueError("The start index %d of the original series " "has been differenced away" % start) elif (dynamic or 'mle' not in method) and start < k_ar: raise ValueError("Start must be >= k_ar for conditional MLE " "or dynamic forecast. Got %d" % start) def _get_predict_out_of_sample(endog, p, q, k_trend, k_exog, start, errors, trendparam, exparams, arparams, maparams, steps, method, exog=None): """ Returns endog, resid, mu of appropriate length for out of sample prediction. """ if q: resid = np.zeros(q) if start and 'mle' in method or (start == p and not start == 0): resid[:q] = errors[start-q:start] elif start: resid[:q] = errors[start-q-p:start-p] else: resid[:q] = errors[-q:] else: resid = None y = endog if k_trend == 1: # use expectation not constant if k_exog > 0: #TODO: technically should only hold for MLE not # conditional model. See #274. # ensure 2-d for conformability if np.ndim(exog) == 1 and k_exog == 1: # have a 1d series of observations -> 2d exog = exog[:, None] elif np.ndim(exog) == 1: # should have a 1d row of exog -> 2d if len(exog) != k_exog: raise ValueError("1d exog given and len(exog) != k_exog") exog = exog[None, :] X = lagmat(np.dot(exog, exparams), p, original='in', trim='both') mu = trendparam * (1 - arparams.sum()) # arparams were reversed in unpack for ease later mu = mu + (np.r_[1, -arparams[::-1]] * X).sum(1)[:, None] else: mu = trendparam * (1 - arparams.sum()) mu = np.array([mu]*steps) elif k_exog > 0: X = np.dot(exog, exparams) #NOTE: you shouldn't have to give in-sample exog! X = lagmat(X, p, original='in', trim='both') mu = (np.r_[1, -arparams[::-1]] * X).sum(1)[:, None] else: mu = np.zeros(steps) endog = np.zeros(p + steps - 1) if p and start: endog[:p] = y[start-p:start] elif p: endog[:p] = y[-p:] return endog, resid, mu def _arma_predict_out_of_sample(params, steps, errors, p, q, k_trend, k_exog, endog, exog=None, start=0, method='mle'): (trendparam, exparams, arparams, maparams) = _unpack_params(params, (p, q), k_trend, k_exog, reverse=True) # print 'params:',params # print 'arparams:',arparams,'maparams:',maparams endog, resid, mu = _get_predict_out_of_sample(endog, p, q, k_trend, k_exog, start, errors, trendparam, exparams, arparams, maparams, steps, method, exog) # print 'mu[-1]:',mu[-1], 'mu[0]:',mu[0] forecast = np.zeros(steps) if steps == 1: if q: return mu[0] + np.dot(arparams, endog[:p]) + np.dot(maparams, resid[:q]), mu[0] else: return mu[0] + np.dot(arparams, endog[:p]), mu[0] if q: i = 0 # if q == 1 else: i = -1 for i in range(min(q, steps - 1)): fcast = (mu[i] + np.dot(arparams, endog[i:i + p]) + np.dot(maparams[:q - i], resid[i:i + q])) forecast[i] = fcast endog[i+p] = fcast for i in range(i + 1, steps - 1): fcast = mu[i] + np.dot(arparams, endog[i:i+p]) forecast[i] = fcast endog[i+p] = fcast #need to do one more without updating endog forecast[-1] = mu[-1] + np.dot(arparams, endog[steps - 1:]) return forecast, mu[-1] #Modified by me, the former is return forecast def _arma_predict_in_sample(start, end, endog, resid, k_ar, method): """ Pre- and in-sample fitting for ARMA. """ if 'mle' in method: fittedvalues = endog - resid # get them all then trim else: fittedvalues = endog[k_ar:] - resid fv_start = start if 'mle' not in method: fv_start -= k_ar # start is in terms of endog index fv_end = min(len(fittedvalues), end + 1) return fittedvalues[fv_start:fv_end] def _validate(start, k_ar, k_diff, dates, method): if isinstance(start, (string_types, datetime)): start = _index_date(start, dates) start -= k_diff if 'mle' not in method and start < k_ar - k_diff: raise ValueError("Start must be >= k_ar for conditional " "MLE or dynamic forecast. Got %s" % start) return start def _unpack_params(params, order, k_trend, k_exog, reverse=False): p, q = order k = k_trend + k_exog maparams = params[k+p:] arparams = params[k:k+p] trend = params[:k_trend] exparams = params[k_trend:k] if reverse: return trend, exparams, arparams[::-1], maparams[::-1] return trend, exparams, arparams, maparams def _unpack_order(order): k_ar, k_ma, k = order k_lags = max(k_ar, k_ma+1) return k_ar, k_ma, order, k_lags def _make_arma_names(data, k_trend, order, exog_names): k_ar, k_ma = order exog_names = exog_names or [] ar_lag_names = util.make_lag_names([data.ynames], k_ar, 0) ar_lag_names = [''.join(('ar.', i)) for i in ar_lag_names] ma_lag_names = util.make_lag_names([data.ynames], k_ma, 0) ma_lag_names = [''.join(('ma.', i)) for i in ma_lag_names] trend_name = util.make_lag_names('', 0, k_trend) exog_names = trend_name + exog_names + ar_lag_names + ma_lag_names return exog_names def _make_arma_exog(endog, exog, trend): k_trend = 1 # overwritten if no constant if exog is None and trend == 'c': # constant only exog = np.ones((len(endog), 1)) elif exog is not None and trend == 'c': # constant plus exogenous exog = add_trend(exog, trend='c', prepend=True) elif exog is not None and trend == 'nc': # make sure it's not holding constant from last run if exog.var() == 0: exog = None k_trend = 0 if trend == 'nc': k_trend = 0 return k_trend, exog def _check_estimable(nobs, n_params): if nobs <= n_params: raise ValueError("Insufficient degrees of freedom to estimate") class ARMA(tsbase.TimeSeriesModel): __doc__ = tsbase._tsa_doc % {"model" : _arma_model, "params" : _arma_params, "extra_params" : "", "extra_sections" : _armax_notes % {"Model" : "ARMA"}} def __init__(self, endog, order, exog=None, dates=None, freq=None, missing='none'): super(ARMA, self).__init__(endog, exog, dates, freq, missing=missing) exog = self.data.exog # get it after it's gone through processing _check_estimable(len(self.endog), sum(order)) self.k_ar = k_ar = order[0] self.k_ma = k_ma = order[1] self.k_lags = max(k_ar, k_ma+1) self.constant = 0 #Added by me if exog is not None: if exog.ndim == 1: exog = exog[:, None] k_exog = exog.shape[1] # number of exog. variables excl. const else: k_exog = 0 self.k_exog = k_exog def _fit_start_params_hr(self, order): """ Get starting parameters for fit. Parameters ---------- order : iterable (p,q,k) - AR lags, MA lags, and number of exogenous variables including the constant. Returns ------- start_params : array A first guess at the starting parameters. Notes ----- If necessary, fits an AR process with the laglength selected according to best BIC. Obtain the residuals. Then fit an ARMA(p,q) model via OLS using these residuals for a first approximation. Uses a separate OLS regression to find the coefficients of exogenous variables. References ---------- Hannan, E.J. and Rissanen, J. 1982. "Recursive estimation of mixed autoregressive-moving average order." `Biometrika`. 69.1. """ p, q, k = order start_params = zeros((p+q+k)) endog = self.endog.copy() # copy because overwritten exog = self.exog if k != 0: ols_params = GLS(endog, exog).fit().params start_params[:k] = ols_params endog -= np.dot(exog, ols_params).squeeze() if q != 0: if p != 0: # make sure we don't run into small data problems in AR fit nobs = len(endog) maxlag = int(round(12*(nobs/100.)**(1/4.))) if maxlag >= nobs: maxlag = nobs - 1 armod = AR(endog).fit(ic='bic', trend='nc', maxlag=maxlag) arcoefs_tmp = armod.params p_tmp = armod.k_ar # it's possible in small samples that optimal lag-order # doesn't leave enough obs. No consistent way to fix. if p_tmp + q >= len(endog): raise ValueError("Proper starting parameters cannot" " be found for this order with this " "number of observations. Use the " "start_params argument.") resid = endog[p_tmp:] - np.dot(lagmat(endog, p_tmp, trim='both'), arcoefs_tmp) if p < p_tmp + q: endog_start = p_tmp + q - p resid_start = 0 else: endog_start = 0 resid_start = p - p_tmp - q lag_endog = lagmat(endog, p, 'both')[endog_start:] lag_resid = lagmat(resid, q, 'both')[resid_start:] # stack ar lags and resids X = np.column_stack((lag_endog, lag_resid)) coefs = GLS(endog[max(p_tmp + q, p):], X).fit().params start_params[k:k+p+q] = coefs else: start_params[k+p:k+p+q] = yule_walker(endog, order=q)[0] if q == 0 and p != 0: arcoefs = yule_walker(endog, order=p)[0] start_params[k:k+p] = arcoefs # check AR coefficients if p and not np.all(np.abs(np.roots(np.r_[1, -start_params[k:k + p]] )) < 1): raise ValueError("The computed initial AR coefficients are not " "stationary\nYou should induce stationarity, " "choose a different model order, or you can\n" "pass your own start_params.") # check MA coefficients elif q and not np.all(np.abs(np.roots(np.r_[1, start_params[k + p:]] )) < 1): return np.zeros(len(start_params)) #modified by me raise ValueError("The computed initial MA coefficients are not " "invertible\nYou should induce invertibility, " "choose a different model order, or you can\n" "pass your own start_params.") # check MA coefficients # print start_params return start_params def _fit_start_params(self, order, method): if method != 'css-mle': # use Hannan-Rissanen to get start params start_params = self._fit_start_params_hr(order) else: # use CSS to get start params func = lambda params: -self.loglike_css(params) #start_params = [.1]*(k_ar+k_ma+k_exog) # different one for k? start_params = self._fit_start_params_hr(order) if self.transparams: start_params = self._invtransparams(start_params) bounds = [(None,)*2]*sum(order) mlefit = optimize.fmin_l_bfgs_b(func, start_params, approx_grad=True, m=12, pgtol=1e-7, factr=1e3, bounds=bounds, iprint=-1) start_params = self._transparams(mlefit[0]) return start_params def score(self, params): """ Compute the score function at params. Notes ----- This is a numerical approximation. """ return approx_fprime_cs(params, self.loglike, args=(False,)) def hessian(self, params): """ Compute the Hessian at params, Notes ----- This is a numerical approximation. """ return approx_hess_cs(params, self.loglike, args=(False,)) def _transparams(self, params): """ Transforms params to induce stationarity/invertability. Reference --------- Jones(1980) """ k_ar, k_ma = self.k_ar, self.k_ma k = self.k_exog + self.k_trend newparams = np.zeros_like(params) # just copy exogenous parameters if k != 0: newparams[:k] = params[:k] # AR Coeffs if k_ar != 0: newparams[k:k+k_ar] = _ar_transparams(params[k:k+k_ar].copy()) # MA Coeffs if k_ma != 0: newparams[k+k_ar:] = _ma_transparams(params[k+k_ar:].copy()) return newparams def _invtransparams(self, start_params): """ Inverse of the Jones reparameterization """ k_ar, k_ma = self.k_ar, self.k_ma k = self.k_exog + self.k_trend newparams = start_params.copy() arcoefs = newparams[k:k+k_ar] macoefs = newparams[k+k_ar:] # AR coeffs if k_ar != 0: newparams[k:k+k_ar] = _ar_invtransparams(arcoefs) # MA coeffs if k_ma != 0: newparams[k+k_ar:k+k_ar+k_ma] = _ma_invtransparams(macoefs) return newparams def _get_predict_start(self, start, dynamic): # do some defaults method = getattr(self, 'method', 'mle') k_ar = getattr(self, 'k_ar', 0) k_diff = getattr(self, 'k_diff', 0) if start is None: if 'mle' in method and not dynamic: start = 0 else: start = k_ar self._set_predict_start_date(start) # else it's done in super elif isinstance(start, int): start = super(ARMA, self)._get_predict_start(start) else: # should be on a date #elif 'mle' not in method or dynamic: # should be on a date start = _validate(start, k_ar, k_diff, self.data.dates, method) start = super(ARMA, self)._get_predict_start(start) _check_arima_start(start, k_ar, k_diff, method, dynamic) return start def _get_predict_end(self, end, dynamic=False): # pass through so predict works for ARIMA and ARMA return super(ARMA, self)._get_predict_end(end) def geterrors(self, params): """ Get the errors of the ARMA process. Parameters ---------- params : array-like The fitted ARMA parameters order : array-like 3 item iterable, with the number of AR, MA, and exogenous parameters, including the trend """ #start = self._get_predict_start(start) # will be an index of a date #end, out_of_sample = self._get_predict_end(end) params = np.asarray(params) k_ar, k_ma = self.k_ar, self.k_ma k = self.k_exog + self.k_trend method = getattr(self, 'method', 'mle') if 'mle' in method: # use KalmanFilter to get errors (y, k, nobs, k_ar, k_ma, k_lags, newparams, Z_mat, m, R_mat, T_mat, paramsdtype) = KalmanFilter._init_kalman_state(params, self) errors = KalmanFilter.geterrors(y, k, k_ar, k_ma, k_lags, nobs, Z_mat, m, R_mat, T_mat, paramsdtype) if isinstance(errors, tuple): errors = errors[0] # non-cython version returns a tuple else: # use scipy.signal.lfilter y = self.endog.copy() k = self.k_exog + self.k_trend if k > 0: y -= dot(self.exog, params[:k]) k_ar = self.k_ar k_ma = self.k_ma (trendparams, exparams, arparams, maparams) = _unpack_params(params, (k_ar, k_ma), self.k_trend, self.k_exog, reverse=False) b, a = np.r_[1, -arparams], np.r_[1, maparams] zi = zeros((max(k_ar, k_ma))) for i in range(k_ar): zi[i] = sum(-b[:i+1][::-1]*y[:i+1]) e = lfilter(b, a, y, zi=zi) errors = e[0][k_ar:] return errors.squeeze() def predict(self, params, start=None, end=None, exog=None, dynamic=False): method = getattr(self, 'method', 'mle') # don't assume fit #params = np.asarray(params) # will return an index of a date start = self._get_predict_start(start, dynamic) end, out_of_sample = self._get_predict_end(end, dynamic) if out_of_sample and (exog is None and self.k_exog > 0): raise ValueError("You must provide exog for ARMAX") endog = self.endog resid = self.geterrors(params) k_ar = self.k_ar if out_of_sample != 0 and self.k_exog > 0: if self.k_exog == 1 and exog.ndim == 1: exog = exog[:, None] # we need the last k_ar exog for the lag-polynomial if self.k_exog > 0 and k_ar > 0: # need the last k_ar exog for the lag-polynomial exog = np.vstack((self.exog[-k_ar:, self.k_trend:], exog)) if dynamic: #TODO: now that predict does dynamic in-sample it should # also return error estimates and confidence intervals # but how? len(endog) is not tot_obs out_of_sample += end - start + 1 pr, ct = _arma_predict_out_of_sample(params, out_of_sample, resid, k_ar, self.k_ma, self.k_trend, self.k_exog, endog, exog, start, method) self.constant = ct return pr predictedvalues = _arma_predict_in_sample(start, end, endog, resid, k_ar, method) if out_of_sample: forecastvalues, ct = _arma_predict_out_of_sample(params, out_of_sample, resid, k_ar, self.k_ma, self.k_trend, self.k_exog, endog, exog, method=method) self.constant = ct predictedvalues = np.r_[predictedvalues, forecastvalues] return predictedvalues predict.__doc__ = _arma_predict def loglike(self, params, set_sigma2=True): """ Compute the log-likelihood for ARMA(p,q) model Notes ----- Likelihood used depends on the method set in fit """ method = self.method if method in ['mle', 'css-mle']: return self.loglike_kalman(params, set_sigma2) elif method == 'css': return self.loglike_css(params, set_sigma2) else: raise ValueError("Method %s not understood" % method) def loglike_kalman(self, params, set_sigma2=True): """ Compute exact loglikelihood for ARMA(p,q) model by the Kalman Filter. """ return KalmanFilter.loglike(params, self, set_sigma2) def loglike_css(self, params, set_sigma2=True): """ Conditional Sum of Squares likelihood function. """ k_ar = self.k_ar k_ma = self.k_ma k = self.k_exog + self.k_trend y = self.endog.copy().astype(params.dtype) nobs = self.nobs # how to handle if empty? if self.transparams: newparams = self._transparams(params) else: newparams = params if k > 0: y -= dot(self.exog, newparams[:k]) # the order of p determines how many zeros errors to set for lfilter b, a = np.r_[1, -newparams[k:k + k_ar]], np.r_[1, newparams[k + k_ar:]] zi = np.zeros((max(k_ar, k_ma)), dtype=params.dtype) for i in range(k_ar): zi[i] = sum(-b[:i + 1][::-1] * y[:i + 1]) errors = lfilter(b, a, y, zi=zi)[0][k_ar:] ssr = np.dot(errors, errors) sigma2 = ssr/nobs if set_sigma2: self.sigma2 = sigma2 llf = -nobs/2.*(log(2*pi) + log(sigma2)) - ssr/(2*sigma2) return llf def fit(self, start_params=None, trend='c', method="css-mle", transparams=True, solver='lbfgs', maxiter=50, full_output=1, disp=5, callback=None, **kwargs): """ Fits ARMA(p,q) model using exact maximum likelihood via Kalman filter. Parameters ---------- start_params : array-like, optional Starting parameters for ARMA(p,q). If None, the default is given by ARMA._fit_start_params. See there for more information. transparams : bool, optional Whehter or not to transform the parameters to ensure stationarity. Uses the transformation suggested in Jones (1980). If False, no checking for stationarity or invertibility is done. method : str {'css-mle','mle','css'} This is the loglikelihood to maximize. If "css-mle", the conditional sum of squares likelihood is maximized and its values are used as starting values for the computation of the exact likelihood via the Kalman filter. If "mle", the exact likelihood is maximized via the Kalman Filter. If "css" the conditional sum of squares likelihood is maximized. All three methods use `start_params` as starting parameters. See above for more information. trend : str {'c','nc'} Whether to include a constant or not. 'c' includes constant, 'nc' no constant. solver : str or None, optional Solver to be used. The default is 'lbfgs' (limited memory Broyden-Fletcher-Goldfarb-Shanno). Other choices are 'bfgs', 'newton' (Newton-Raphson), 'nm' (Nelder-Mead), 'cg' - (conjugate gradient), 'ncg' (non-conjugate gradient), and 'powell'. By default, the limited memory BFGS uses m=12 to approximate the Hessian, projected gradient tolerance of 1e-8 and factr = 1e2. You can change these by using kwargs. maxiter : int, optional The maximum number of function evaluations. Default is 50. tol : float The convergence tolerance. Default is 1e-08. full_output : bool, optional If True, all output from solver will be available in the Results object's mle_retvals attribute. Output is dependent on the solver. See Notes for more information. disp : bool, optional If True, convergence information is printed. For the default l_bfgs_b solver, disp controls the frequency of the output during the iterations. disp < 0 means no output in this case. callback : function, optional Called after each iteration as callback(xk) where xk is the current parameter vector. kwargs See Notes for keyword arguments that can be passed to fit. Returns ------- statsmodels.tsa.arima_model.ARMAResults class See also -------- statsmodels.base.model.LikelihoodModel.fit : for more information on using the solvers. ARMAResults : results class returned by fit Notes ------ If fit by 'mle', it is assumed for the Kalman Filter that the initial unkown state is zero, and that the inital variance is P = dot(inv(identity(m**2)-kron(T,T)),dot(R,R.T).ravel('F')).reshape(r, r, order = 'F') """ k_ar = self.k_ar k_ma = self.k_ma # enforce invertibility self.transparams = transparams endog, exog = self.endog, self.exog k_exog = self.k_exog self.nobs = len(endog) # this is overwritten if method is 'css' # (re)set trend and handle exogenous variables # always pass original exog k_trend, exog = _make_arma_exog(endog, self.exog, trend) # Check has something to estimate if k_ar == 0 and k_ma == 0 and k_trend == 0 and k_exog == 0: raise ValueError("Estimation requires the inclusion of least one " "AR term, MA term, a constant or an exogenous " "variable.") # check again now that we know the trend _check_estimable(len(endog), k_ar + k_ma + k_exog + k_trend) self.k_trend = k_trend self.exog = exog # overwrites original exog from __init__ # (re)set names for this model self.exog_names = _make_arma_names(self.data, k_trend, (k_ar, k_ma), self.exog_names) k = k_trend + k_exog # choose objective function if k_ma == 0 and k_ar == 0: method = "css" # Always CSS when no AR or MA terms self.method = method = method.lower() # adjust nobs for css if method == 'css': self.nobs = len(self.endog) - k_ar if start_params is not None: start_params = np.asarray(start_params) else: # estimate starting parameters start_params = self._fit_start_params((k_ar, k_ma, k), method) if transparams: # transform initial parameters to ensure invertibility start_params = self._invtransparams(start_params) if solver == 'lbfgs': kwargs.setdefault('pgtol', 1e-8) kwargs.setdefault('factr', 1e2) kwargs.setdefault('m', 12) kwargs.setdefault('approx_grad', True) mlefit = super(ARMA, self).fit(start_params, method=solver, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, **kwargs) params = mlefit.params if transparams: # transform parameters back params = self._transparams(params) self.transparams = False # so methods don't expect transf. normalized_cov_params = None # TODO: fix this armafit = ARMAResults(self, params, normalized_cov_params) armafit.mle_retvals = mlefit.mle_retvals armafit.mle_settings = mlefit.mle_settings armafit.mlefit = mlefit return ARMAResultsWrapper(armafit) #NOTE: the length of endog changes when we give a difference to fit #so model methods are not the same on unfit models as fit ones #starting to think that order of model should be put in instantiation... class ARIMA(ARMA): __doc__ = tsbase._tsa_doc % {"model" : _arima_model, "params" : _arima_params, "extra_params" : "", "extra_sections" : _armax_notes % {"Model" : "ARIMA"}} def __new__(cls, endog, order, exog=None, dates=None, freq=None, missing='none'): p, d, q = order if d == 0: # then we just use an ARMA model return ARMA(endog, (p, q), exog, dates, freq, missing) else: mod = super(ARIMA, cls).__new__(cls) mod.__init__(endog, order, exog, dates, freq, missing) return mod def __init__(self, endog, order, exog=None, dates=None, freq=None, missing='none'): p, d, q = order if d > 2: #NOTE: to make more general, need to address the d == 2 stuff # in the predict method raise ValueError("d > 2 is not supported") super(ARIMA, self).__init__(endog, (p, q), exog, dates, freq, missing) self.k_diff = d self._first_unintegrate = unintegrate_levels(self.endog[:d], d) self.endog = np.diff(self.endog, n=d) #NOTE: will check in ARMA but check again since differenced now _check_estimable(len(self.endog), p+q) if exog is not None: self.exog = self.exog[d:] if d == 1: self.data.ynames = 'D.' + self.endog_names else: self.data.ynames = 'D{0:d}.'.format(d) + self.endog_names # what about exog, should we difference it automatically before # super call? def _get_predict_start(self, start, dynamic): """ """ #TODO: remove all these getattr and move order specification to # class constructor k_diff = getattr(self, 'k_diff', 0) method = getattr(self, 'method', 'mle') k_ar = getattr(self, 'k_ar', 0) if start is None: if 'mle' in method and not dynamic: start = 0 else: start = k_ar elif isinstance(start, int): start -= k_diff try: # catch when given an integer outside of dates index start = super(ARIMA, self)._get_predict_start(start, dynamic) except IndexError: raise ValueError("start must be in series. " "got %d" % (start + k_diff)) else: # received a date start = _validate(start, k_ar, k_diff, self.data.dates, method) start = super(ARIMA, self)._get_predict_start(start, dynamic) # reset date for k_diff adjustment self._set_predict_start_date(start + k_diff) return start def _get_predict_end(self, end, dynamic=False): """ Returns last index to be forecast of the differenced array. Handling of inclusiveness should be done in the predict function. """ end, out_of_sample = super(ARIMA, self)._get_predict_end(end, dynamic) if 'mle' not in self.method and not dynamic: end -= self.k_ar return end - self.k_diff, out_of_sample def fit(self, start_params=None, trend='c', method="css-mle", transparams=True, solver='lbfgs', maxiter=50, full_output=1, disp=5, callback=None, **kwargs): """ Fits ARIMA(p,d,q) model by exact maximum likelihood via Kalman filter. Parameters ---------- start_params : array-like, optional Starting parameters for ARMA(p,q). If None, the default is given by ARMA._fit_start_params. See there for more information. transparams : bool, optional Whehter or not to transform the parameters to ensure stationarity. Uses the transformation suggested in Jones (1980). If False, no checking for stationarity or invertibility is done. method : str {'css-mle','mle','css'} This is the loglikelihood to maximize. If "css-mle", the conditional sum of squares likelihood is maximized and its values are used as starting values for the computation of the exact likelihood via the Kalman filter. If "mle", the exact likelihood is maximized via the Kalman Filter. If "css" the conditional sum of squares likelihood is maximized. All three methods use `start_params` as starting parameters. See above for more information. trend : str {'c','nc'} Whether to include a constant or not. 'c' includes constant, 'nc' no constant. solver : str or None, optional Solver to be used. The default is 'lbfgs' (limited memory Broyden-Fletcher-Goldfarb-Shanno). Other choices are 'bfgs', 'newton' (Newton-Raphson), 'nm' (Nelder-Mead), 'cg' - (conjugate gradient), 'ncg' (non-conjugate gradient), and 'powell'. By default, the limited memory BFGS uses m=12 to approximate the Hessian, projected gradient tolerance of 1e-8 and factr = 1e2. You can change these by using kwargs. maxiter : int, optional The maximum number of function evaluations. Default is 50. tol : float The convergence tolerance. Default is 1e-08. full_output : bool, optional If True, all output from solver will be available in the Results object's mle_retvals attribute. Output is dependent on the solver. See Notes for more information. disp : bool, optional If True, convergence information is printed. For the default l_bfgs_b solver, disp controls the frequency of the output during the iterations. disp < 0 means no output in this case. callback : function, optional Called after each iteration as callback(xk) where xk is the current parameter vector. kwargs See Notes for keyword arguments that can be passed to fit. Returns ------- `statsmodels.tsa.arima.ARIMAResults` class See also -------- statsmodels.base.model.LikelihoodModel.fit : for more information on using the solvers. ARIMAResults : results class returned by fit Notes ------ If fit by 'mle', it is assumed for the Kalman Filter that the initial unkown state is zero, and that the inital variance is P = dot(inv(identity(m**2)-kron(T,T)),dot(R,R.T).ravel('F')).reshape(r, r, order = 'F') """ arima_fit = super(ARIMA, self).fit(start_params, trend, method, transparams, solver, maxiter, full_output, disp, callback, **kwargs) normalized_cov_params = None # TODO: fix this? arima_fit = ARIMAResults(self, arima_fit._results.params, normalized_cov_params) arima_fit.k_diff = self.k_diff return ARIMAResultsWrapper(arima_fit) def predict(self, params, start=None, end=None, exog=None, typ='linear', dynamic=False): # go ahead and convert to an index for easier checking if isinstance(start, (string_types, datetime)): start = _index_date(start, self.data.dates) if typ == 'linear': if not dynamic or (start != self.k_ar + self.k_diff and start is not None): return super(ARIMA, self).predict(params, start, end, exog, dynamic) else: # need to assume pre-sample residuals are zero # do this by a hack q = self.k_ma self.k_ma = 0 predictedvalues = super(ARIMA, self).predict(params, start, end, exog, dynamic) self.k_ma = q return predictedvalues elif typ == 'levels': endog = self.data.endog if not dynamic: predict = super(ARIMA, self).predict(params, start, end, dynamic) start = self._get_predict_start(start, dynamic) end, out_of_sample = self._get_predict_end(end) d = self.k_diff if 'mle' in self.method: start += d - 1 # for case where d == 2 end += d - 1 # add each predicted diff to lagged endog if out_of_sample: fv = predict[:-out_of_sample] + endog[start:end+1] if d == 2: #TODO: make a general solution to this fv += np.diff(endog[start - 1:end + 1]) levels = unintegrate_levels(endog[-d:], d) fv = np.r_[fv, unintegrate(predict[-out_of_sample:], levels)[d:]] else: fv = predict + endog[start:end + 1] if d == 2: fv += np.diff(endog[start - 1:end + 1]) else: k_ar = self.k_ar if out_of_sample: fv = (predict[:-out_of_sample] + endog[max(start, self.k_ar-1):end+k_ar+1]) if d == 2: fv += np.diff(endog[start - 1:end + 1]) levels = unintegrate_levels(endog[-d:], d) fv = np.r_[fv, unintegrate(predict[-out_of_sample:], levels)[d:]] else: fv = predict + endog[max(start, k_ar):end+k_ar+1] if d == 2: fv += np.diff(endog[start - 1:end + 1]) else: #IFF we need to use pre-sample values assume pre-sample # residuals are zero, do this by a hack if start == self.k_ar + self.k_diff or start is None: # do the first k_diff+1 separately p = self.k_ar q = self.k_ma k_exog = self.k_exog k_trend = self.k_trend k_diff = self.k_diff (trendparam, exparams, arparams, maparams) = _unpack_params(params, (p, q), k_trend, k_exog, reverse=True) # this is the hack self.k_ma = 0 predict = super(ARIMA, self).predict(params, start, end, exog, dynamic) if not start: start = self._get_predict_start(start, dynamic) start += k_diff self.k_ma = q return endog[start-1] + np.cumsum(predict) else: predict = super(ARIMA, self).predict(params, start, end, exog, dynamic) return endog[start-1] + np.cumsum(predict) return fv else: # pragma : no cover raise ValueError("typ %s not understood" % typ) predict.__doc__ = _arima_predict class ARMAResults(tsbase.TimeSeriesModelResults): """ Class to hold results from fitting an ARMA model. Parameters ---------- model : ARMA instance The fitted model instance params : array Fitted parameters normalized_cov_params : array, optional The normalized variance covariance matrix scale : float, optional Optional argument to scale the variance covariance matrix. Returns -------- **Attributes** aic : float Akaike Information Criterion :math:`-2*llf+2* df_model` where `df_model` includes all AR parameters, MA parameters, constant terms parameters on constant terms and the variance. arparams : array The parameters associated with the AR coefficients in the model. arroots : array The roots of the AR coefficients are the solution to (1 - arparams[0]*z - arparams[1]*z**2 -...- arparams[p-1]*z**k_ar) = 0 Stability requires that the roots in modulus lie outside the unit circle. bic : float Bayes Information Criterion -2*llf + log(nobs)*df_model Where if the model is fit using conditional sum of squares, the number of observations `nobs` does not include the `p` pre-sample observations. bse : array The standard errors of the parameters. These are computed using the numerical Hessian. df_model : array The model degrees of freedom = `k_exog` + `k_trend` + `k_ar` + `k_ma` df_resid : array The residual degrees of freedom = `nobs` - `df_model` fittedvalues : array The predicted values of the model. hqic : float Hannan-Quinn Information Criterion -2*llf + 2*(`df_model`)*log(log(nobs)) Like `bic` if the model is fit using conditional sum of squares then the `k_ar` pre-sample observations are not counted in `nobs`. k_ar : int The number of AR coefficients in the model. k_exog : int The number of exogenous variables included in the model. Does not include the constant. k_ma : int The number of MA coefficients. k_trend : int This is 0 for no constant or 1 if a constant is included. llf : float The value of the log-likelihood function evaluated at `params`. maparams : array The value of the moving average coefficients. maroots : array The roots of the MA coefficients are the solution to (1 + maparams[0]*z + maparams[1]*z**2 + ... + maparams[q-1]*z**q) = 0 Stability requires that the roots in modules lie outside the unit circle. model : ARMA instance A reference to the model that was fit. nobs : float The number of observations used to fit the model. If the model is fit using exact maximum likelihood this is equal to the total number of observations, `n_totobs`. If the model is fit using conditional maximum likelihood this is equal to `n_totobs` - `k_ar`. n_totobs : float The total number of observations for `endog`. This includes all observations, even pre-sample values if the model is fit using `css`. params : array The parameters of the model. The order of variables is the trend coefficients and the `k_exog` exognous coefficients, then the `k_ar` AR coefficients, and finally the `k_ma` MA coefficients. pvalues : array The p-values associated with the t-values of the coefficients. Note that the coefficients are assumed to have a Student's T distribution. resid : array The model residuals. If the model is fit using 'mle' then the residuals are created via the Kalman Filter. If the model is fit using 'css' then the residuals are obtained via `scipy.signal.lfilter` adjusted such that the first `k_ma` residuals are zero. These zero residuals are not returned. scale : float This is currently set to 1.0 and not used by the model or its results. sigma2 : float The variance of the residuals. If the model is fit by 'css', sigma2 = ssr/nobs, where ssr is the sum of squared residuals. If the model is fit by 'mle', then sigma2 = 1/nobs * sum(v**2 / F) where v is the one-step forecast error and F is the forecast error variance. See `nobs` for the difference in definitions depending on the fit. """ _cache = {} #TODO: use this for docstring when we fix nobs issue def __init__(self, model, params, normalized_cov_params=None, scale=1.): super(ARMAResults, self).__init__(model, params, normalized_cov_params, scale) self.sigma2 = model.sigma2 nobs = model.nobs self.nobs = nobs k_exog = model.k_exog self.k_exog = k_exog k_trend = model.k_trend self.k_trend = k_trend k_ar = model.k_ar self.k_ar = k_ar self.n_totobs = len(model.endog) k_ma = model.k_ma self.k_ma = k_ma df_model = k_exog + k_trend + k_ar + k_ma self._ic_df_model = df_model + 1 self.df_model = df_model self.df_resid = self.nobs - df_model self._cache = resettable_cache() self.constant = 0 #Added by me @cache_readonly def arroots(self): return np.roots(np.r_[1, -self.arparams])**-1 @cache_readonly def maroots(self): return np.roots(np.r_[1, self.maparams])**-1 @cache_readonly def arfreq(self): r""" Returns the frequency of the AR roots. This is the solution, x, to z = abs(z)*exp(2j*np.pi*x) where z are the roots. """ z = self.arroots if not z.size: return return np.arctan2(z.imag, z.real) / (2*pi) @cache_readonly def mafreq(self): r""" Returns the frequency of the MA roots. This is the solution, x, to z = abs(z)*exp(2j*np.pi*x) where z are the roots. """ z = self.maroots if not z.size: return return np.arctan2(z.imag, z.real) / (2*pi) @cache_readonly def arparams(self): k = self.k_exog + self.k_trend return self.params[k:k+self.k_ar] @cache_readonly def maparams(self): k = self.k_exog + self.k_trend k_ar = self.k_ar return self.params[k+k_ar:] @cache_readonly def llf(self): return self.model.loglike(self.params) @cache_readonly def bse(self): params = self.params hess = self.model.hessian(params) if len(params) == 1: # can't take an inverse, ensure 1d return np.sqrt(-1./hess[0]) return np.sqrt(np.diag(-inv(hess))) def cov_params(self): # add scale argument? params = self.params hess = self.model.hessian(params) return -inv(hess) @cache_readonly def aic(self): return -2 * self.llf + 2 * self._ic_df_model @cache_readonly def bic(self): nobs = self.nobs return -2 * self.llf + np.log(nobs) * self._ic_df_model @cache_readonly def hqic(self): nobs = self.nobs return -2 * self.llf + 2 * np.log(np.log(nobs)) * self._ic_df_model @cache_readonly def fittedvalues(self): model = self.model endog = model.endog.copy() k_ar = self.k_ar exog = model.exog # this is a copy if exog is not None: if model.method == "css" and k_ar > 0: exog = exog[k_ar:] if model.method == "css" and k_ar > 0: endog = endog[k_ar:] fv = endog - self.resid # add deterministic part back in #k = self.k_exog + self.k_trend #TODO: this needs to be commented out for MLE with constant #if k != 0: # fv += dot(exog, self.params[:k]) return fv @cache_readonly def resid(self): return self.model.geterrors(self.params) @cache_readonly def pvalues(self): #TODO: same for conditional and unconditional? df_resid = self.df_resid return t.sf(np.abs(self.tvalues), df_resid) * 2 def predict(self, start=None, end=None, exog=None, dynamic=False): return self.model.predict(self.params, start, end, exog, dynamic) predict.__doc__ = _arma_results_predict def _forecast_error(self, steps): sigma2 = self.sigma2 ma_rep = arma2ma(np.r_[1, -self.arparams], np.r_[1, self.maparams], nobs=steps) fcasterr = np.sqrt(sigma2 * np.cumsum(ma_rep**2)) return fcasterr def _forecast_conf_int(self, forecast, fcasterr, alpha): const = norm.ppf(1 - alpha / 2.) conf_int = np.c_[forecast - const * fcasterr, forecast + const * fcasterr] return conf_int def forecast(self, steps=1, exog=None, alpha=.05): """ Out-of-sample forecasts Parameters ---------- steps : int The number of out of sample forecasts from the end of the sample. exog : array If the model is an ARMAX, you must provide out of sample values for the exogenous variables. This should not include the constant. alpha : float The confidence intervals for the forecasts are (1 - alpha) % Returns ------- forecast : array Array of out of sample forecasts stderr : array Array of the standard error of the forecasts. conf_int : array 2d array of the confidence interval for the forecast """ if exog is not None: #TODO: make a convenience function for this. we're using the # pattern elsewhere in the codebase exog = np.asarray(exog) if self.k_exog == 1 and exog.ndim == 1: exog = exog[:, None] elif exog.ndim == 1: if len(exog) != self.k_exog: raise ValueError("1d exog given and len(exog) != k_exog") exog = exog[None, :] if exog.shape[0] != steps: raise ValueError("new exog needed for each step") # prepend in-sample exog observations exog = np.vstack((self.model.exog[-self.k_ar:, self.k_trend:], exog)) forecast, ct = _arma_predict_out_of_sample(self.params, steps, self.resid, self.k_ar, self.k_ma, self.k_trend, self.k_exog, self.model.endog, exog, method=self.model.method) self.constant = ct # compute the standard errors fcasterr = self._forecast_error(steps) conf_int = self._forecast_conf_int(forecast, fcasterr, alpha) return forecast, fcasterr, conf_int def summary(self, alpha=.05): """Summarize the Model Parameters ---------- alpha : float, optional Significance level for the confidence intervals. 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 """ from statsmodels.iolib.summary import Summary model = self.model title = model.__class__.__name__ + ' Model Results' method = model.method # get sample TODO: make better sample machinery for estimation k_diff = getattr(self, 'k_diff', 0) if 'mle' in method: start = k_diff else: start = k_diff + self.k_ar if self.data.dates is not None: dates = self.data.dates sample = [dates[start].strftime('%m-%d-%Y')] sample += ['- ' + dates[-1].strftime('%m-%d-%Y')] else: sample = str(start) + ' - ' + str(len(self.data.orig_endog)) k_ar, k_ma = self.k_ar, self.k_ma if not k_diff: order = str((k_ar, k_ma)) else: order = str((k_ar, k_diff, k_ma)) top_left = [('Dep. Variable:', None), ('Model:', [model.__class__.__name__ + order]), ('Method:', [method]), ('Date:', None), ('Time:', None), ('Sample:', [sample[0]]), ('', [sample[1]]) ] top_right = [ ('No. Observations:', [str(len(self.model.endog))]), ('Log Likelihood', ["%#5.3f" % self.llf]), ('S.D. of innovations', ["%#5.3f" % self.sigma2**.5]), ('AIC', ["%#5.3f" % self.aic]), ('BIC', ["%#5.3f" % self.bic]), ('HQIC', ["%#5.3f" % self.hqic])] smry = Summary() smry.add_table_2cols(self, gleft=top_left, gright=top_right, title=title) smry.add_table_params(self, alpha=alpha, use_t=False) # Make the roots table from statsmodels.iolib.table import SimpleTable if k_ma and k_ar: arstubs = ["AR.%d" % i for i in range(1, k_ar + 1)] mastubs = ["MA.%d" % i for i in range(1, k_ma + 1)] stubs = arstubs + mastubs roots = np.r_[self.arroots, self.maroots] freq = np.r_[self.arfreq, self.mafreq] elif k_ma: mastubs = ["MA.%d" % i for i in range(1, k_ma + 1)] stubs = mastubs roots = self.maroots freq = self.mafreq elif k_ar: arstubs = ["AR.%d" % i for i in range(1, k_ar + 1)] stubs = arstubs roots = self.arroots freq = self.arfreq else: # 0,0 model stubs = [] if len(stubs): # not 0, 0 modulus = np.abs(roots) data = np.column_stack((roots.real, roots.imag, modulus, freq)) roots_table = SimpleTable(data, headers=[' Real', ' Imaginary', ' Modulus', ' Frequency'], title="Roots", stubs=stubs, data_fmts=["%17.4f", "%+17.4fj", "%17.4f", "%17.4f"]) smry.tables.append(roots_table) return smry def summary2(self, title=None, alpha=.05, float_format="%.4f"): """Experimental summary function for ARIMA Results Parameters ----------- title : string, optional Title for the top table. If not None, then this replaces the default title alpha : float significance level for the confidence intervals float_format: string print format for floats in parameters summary 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.summary2.Summary : class to hold summary results """ from pandas import DataFrame # get sample TODO: make better sample machinery for estimation k_diff = getattr(self, 'k_diff', 0) if 'mle' in self.model.method: start = k_diff else: start = k_diff + self.k_ar if self.data.dates is not None: dates = self.data.dates sample = [dates[start].strftime('%m-%d-%Y')] sample += [dates[-1].strftime('%m-%d-%Y')] else: sample = str(start) + ' - ' + str(len(self.data.orig_endog)) k_ar, k_ma = self.k_ar, self.k_ma # Roots table if k_ma and k_ar: arstubs = ["AR.%d" % i for i in range(1, k_ar + 1)] mastubs = ["MA.%d" % i for i in range(1, k_ma + 1)] stubs = arstubs + mastubs roots = np.r_[self.arroots, self.maroots] freq = np.r_[self.arfreq, self.mafreq] elif k_ma: mastubs = ["MA.%d" % i for i in range(1, k_ma + 1)] stubs = mastubs roots = self.maroots freq = self.mafreq elif k_ar: arstubs = ["AR.%d" % i for i in range(1, k_ar + 1)] stubs = arstubs roots = self.arroots freq = self.arfreq else: # 0, 0 order stubs = [] if len(stubs): modulus = np.abs(roots) data = np.column_stack((roots.real, roots.imag, modulus, freq)) data = DataFrame(data) data.columns = ['Real', 'Imaginary', 'Modulus', 'Frequency'] data.index = stubs # Summary from statsmodels.iolib import summary2 smry = summary2.Summary() # Model info model_info = summary2.summary_model(self) model_info['Method:'] = self.model.method model_info['Sample:'] = sample[0] model_info[' '] = sample[-1] model_info['S.D. of innovations:'] = "%#5.3f" % self.sigma2**.5 model_info['HQIC:'] = "%#5.3f" % self.hqic model_info['No. Observations:'] = str(len(self.model.endog)) # Parameters params = summary2.summary_params(self) smry.add_dict(model_info) smry.add_df(params, float_format=float_format) if len(stubs): smry.add_df(data, float_format="%17.4f") smry.add_title(results=self, title=title) return smry def plot_predict(self, start=None, end=None, exog=None, dynamic=False, alpha=.05, plot_insample=True, ax=None): from statsmodels.graphics.utils import _import_mpl, create_mpl_ax _ = _import_mpl() fig, ax = create_mpl_ax(ax) # use predict so you set dates forecast = self.predict(start, end, exog, dynamic) # doing this twice. just add a plot keyword to predict? start = self.model._get_predict_start(start, dynamic=False) end, out_of_sample = self.model._get_predict_end(end, dynamic=False) if out_of_sample: steps = out_of_sample fc_error = self._forecast_error(steps) conf_int = self._forecast_conf_int(forecast[-steps:], fc_error, alpha) if hasattr(self.data, "predict_dates"): from pandas import TimeSeries forecast = TimeSeries(forecast, index=self.data.predict_dates) ax = forecast.plot(ax=ax, label='forecast') else: ax.plot(forecast) x = ax.get_lines()[-1].get_xdata() if out_of_sample: label = "{0:.0%} confidence interval".format(1 - alpha) ax.fill_between(x[-out_of_sample:], conf_int[:, 0], conf_int[:, 1], color='gray', alpha=.5, label=label) if plot_insample: ax.plot(x[:end + 1 - start], self.model.endog[start:end+1], label=self.model.endog_names) ax.legend(loc='best') return fig plot_predict.__doc__ = _plot_predict class ARMAResultsWrapper(wrap.ResultsWrapper): _attrs = {} _wrap_attrs = wrap.union_dicts(tsbase.TimeSeriesResultsWrapper._wrap_attrs, _attrs) _methods = {} _wrap_methods = wrap.union_dicts(tsbase.TimeSeriesResultsWrapper._wrap_methods, _methods) wrap.populate_wrapper(ARMAResultsWrapper, ARMAResults) class ARIMAResults(ARMAResults): def predict(self, start=None, end=None, exog=None, typ='linear', dynamic=False): return self.model.predict(self.params, start, end, exog, typ, dynamic) predict.__doc__ = _arima_results_predict def _forecast_error(self, steps): sigma2 = self.sigma2 ma_rep = arma2ma(np.r_[1, -self.arparams], np.r_[1, self.maparams], nobs=steps) fcerr = np.sqrt(np.cumsum(cumsum_n(ma_rep, self.k_diff)**2)*sigma2) return fcerr def _forecast_conf_int(self, forecast, fcerr, alpha): const = norm.ppf(1 - alpha/2.) conf_int = np.c_[forecast - const*fcerr, forecast + const*fcerr] return conf_int def forecast(self, steps=1, exog=None, alpha=.05): """ Out-of-sample forecasts Parameters ---------- steps : int The number of out of sample forecasts from the end of the sample. exog : array If the model is an ARIMAX, you must provide out of sample values for the exogenous variables. This should not include the constant. alpha : float The confidence intervals for the forecasts are (1 - alpha) % Returns ------- forecast : array Array of out of sample forecasts stderr : array Array of the standard error of the forecasts. conf_int : array 2d array of the confidence interval for the forecast Notes ----- Prediction is done in the levels of the original endogenous variable. If you would like prediction of differences in levels use `predict`. """ if exog is not None: if self.k_exog == 1 and exog.ndim == 1: exog = exog[:, None] if exog.shape[0] != steps: raise ValueError("new exog needed for each step") # prepend in-sample exog observations exog = np.vstack((self.model.exog[-self.k_ar:, self.k_trend:], exog)) forecast, ct = _arma_predict_out_of_sample(self.params, steps, self.resid, self.k_ar, self.k_ma, self.k_trend, self.k_exog, self.model.endog, exog, method=self.model.method) #self.constant = ct d = self.k_diff endog = self.model.data.endog[-d:] forecast = unintegrate(forecast, unintegrate_levels(endog, d))[d:] # get forecast errors fcerr = self._forecast_error(steps) conf_int = self._forecast_conf_int(forecast, fcerr, alpha) return forecast, fcerr, conf_int def plot_predict(self, start=None, end=None, exog=None, dynamic=False, alpha=.05, plot_insample=True, ax=None): from statsmodels.graphics.utils import _import_mpl, create_mpl_ax _ = _import_mpl() fig, ax = create_mpl_ax(ax) # use predict so you set dates forecast = self.predict(start, end, exog, 'levels', dynamic) # doing this twice. just add a plot keyword to predict? start = self.model._get_predict_start(start, dynamic=dynamic) end, out_of_sample = self.model._get_predict_end(end, dynamic=dynamic) if out_of_sample: steps = out_of_sample fc_error = self._forecast_error(steps) conf_int = self._forecast_conf_int(forecast[-steps:], fc_error, alpha) if hasattr(self.data, "predict_dates"): from pandas import TimeSeries forecast = TimeSeries(forecast, index=self.data.predict_dates) ax = forecast.plot(ax=ax, label='forecast') else: ax.plot(forecast) x = ax.get_lines()[-1].get_xdata() if out_of_sample: label = "{0:.0%} confidence interval".format(1 - alpha) ax.fill_between(x[-out_of_sample:], conf_int[:, 0], conf_int[:, 1], color='gray', alpha=.5, label=label) if plot_insample: import re k_diff = self.k_diff label = re.sub("D\d*\.", "", self.model.endog_names) levels = unintegrate(self.model.endog, self.model._first_unintegrate) ax.plot(x[:end + 1 - start], levels[start + k_diff:end + k_diff + 1], label=label) ax.legend(loc='best') return fig plot_predict.__doc__ = _arima_plot_predict class ARIMAResultsWrapper(ARMAResultsWrapper): pass wrap.populate_wrapper(ARIMAResultsWrapper, ARIMAResults) if __name__ == "__main__": import statsmodels.api as sm # simulate arma process from statsmodels.tsa.arima_process import arma_generate_sample y = arma_generate_sample([1., -.75], [1., .25], nsample=1000) arma = ARMA(y) res = arma.fit(trend='nc', order=(1, 1)) np.random.seed(12345) y_arma22 = arma_generate_sample([1., -.85, .35], [1, .25, -.9], nsample=1000) arma22 = ARMA(y_arma22) res22 = arma22.fit(trend='nc', order=(2, 2)) # test CSS arma22_css = ARMA(y_arma22) res22css = arma22_css.fit(trend='nc', order=(2, 2), method='css') data = sm.datasets.sunspots.load() ar = ARMA(data.endog) resar = ar.fit(trend='nc', order=(9, 0)) y_arma31 = arma_generate_sample([1, -.75, -.35, .25], [.1], nsample=1000) arma31css = ARMA(y_arma31) res31css = arma31css.fit(order=(3, 1), method="css", trend="nc", transparams=True) y_arma13 = arma_generate_sample([1., -.75], [1, .25, -.5, .8], nsample=1000) arma13css = ARMA(y_arma13) res13css = arma13css.fit(order=(1, 3), method='css', trend='nc') # check css for p < q and q < p y_arma41 = arma_generate_sample([1., -.75, .35, .25, -.3], [1, -.35], nsample=1000) arma41css = ARMA(y_arma41) res41css = arma41css.fit(order=(4, 1), trend='nc', method='css') y_arma14 = arma_generate_sample([1, -.25], [1., -.75, .35, .25, -.3], nsample=1000) arma14css = ARMA(y_arma14) res14css = arma14css.fit(order=(4, 1), trend='nc', method='css') # ARIMA Model from statsmodels.datasets import webuse dta = webuse('wpi1') wpi = dta['wpi'] mod = ARIMA(wpi, (1, 1, 1)).fit()