ConstantMean.forecast(params, horizon=1, start=None, align='origin', method='analytic', simulations=1000, rng=None, random_state=None)

Construct forecasts from estimated model

  • params ({ndarray, Series}, optional) – Alternative parameters to use. If not provided, the parameters estimated when fitting the model are used. Must be identical in shape to the parameters computed by fitting the model.

  • horizon (int, optional) – Number of steps to forecast

  • start ({int, datetime, Timestamp, str}, optional) – An integer, datetime or str indicating the first observation to produce the forecast for. Datetimes can only be used with pandas inputs that have a datetime index. Strings must be convertible to a date time, such as in ‘1945-01-01’.

  • align (str, optional) – Either ‘origin’ or ‘target’. When set of ‘origin’, the t-th row of forecasts contains the forecasts for t+1, t+2, …, t+h. When set to ‘target’, the t-th row contains the 1-step ahead forecast from time t-1, the 2 step from time t-2, …, and the h-step from time t-h. ‘target’ simplified computing forecast errors since the realization and h-step forecast are aligned.

  • method ({'analytic', 'simulation', 'bootstrap'}) – Method to use when producing the forecast. The default is analytic. The method only affects the variance forecast generation. Not all volatility models support all methods. In particular, volatility models that do not evolve in squares such as EGARCH or TARCH do not support the ‘analytic’ method for horizons > 1.

  • simulations (int) – Number of simulations to run when computing the forecast using either simulation or bootstrap.

  • rng (callable, optional) – Custom random number generator to use in simulation-based forecasts. Must produce random samples using the syntax rng(size) where size the 2-element tuple (simulations, horizon).

  • random_state (RandomState, optional) – NumPy RandomState instance to use when method is ‘bootstrap’


forecasts – t by h data frame containing the forecasts. The alignment of the forecasts is controlled by align.

Return type



>>> import pandas as pd
>>> from arch import arch_model
>>> am = arch_model(None,mean='HAR',lags=[1,5,22],vol='Constant')
>>> sim_data = am.simulate([0.1,0.4,0.3,0.2,1.0], 250)
>>> sim_data.index = pd.date_range('2000-01-01',periods=250)
>>> am = arch_model(sim_data['data'],mean='HAR',lags=[1,5,22],  vol='Constant')
>>> res =
>>> fig = res.hedgehog_plot()


The most basic 1-step ahead forecast will return a vector with the same length as the original data, where the t-th value will be the time-t forecast for time t + 1. When the horizon is > 1, and when using the default value for align, the forecast value in position [t, h] is the time-t, h+1 step ahead forecast.

If model contains exogenous variables (model.x is not None), then only 1-step ahead forecasts are available. Using horizon > 1 will produce a warning and all columns, except the first, will be nan-filled.

If align is ‘origin’, forecast[t,h] contains the forecast made using y[:t] (that is, up to but not including t) for horizon h + 1. For example, y[100,2] contains the 3-step ahead forecast using the first 100 data points, which will correspond to the realization y[100 + 2]. If align is ‘target’, then the same forecast is in location [102, 2], so that it is aligned with the observation to use when evaluating, but still in the same column.