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

Construct forecasts from estimated model

paramsndarray, 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.

horizonint, 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’.

alignstr, 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’}, optional

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.

simulationsint, optional

Number of simulations to run when computing the forecast using either simulation or bootstrap.

rngcallable(), 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_stateRandomState, optional

NumPy RandomState instance to use when method is ‘bootstrap’

reindexbool, optional

Whether to reindex the forecasts to have the same dimension as the series being forecast. Prior to 4.18 this was the default. As of 4.19 this is now optional. If not provided, a warning is raised about the future change in the default which will occur after September 2021.

New in version 4.19.

x{dict[label, numpy:array_like], numpy:array_like}

Values to use for exogenous regressors if any are included in the model. Three formats are accepted:

  • 2-d array-like: This format can be used when there is a single exogenous variable. The input must have shape (nforecast, horizon) or (nobs, horzion) where nforecast is the number of forecasting periods and nobs is the original shape of y. For example, if a single series of forecasts are made from the end of the sample with a horizon of 10, then the input can be (1, 10). Alternatively, if the original data had 1000 observations, then the input can be (1000, 10), and only the final row is used to produce forecasts.

  • A dictionary of 2-d array-like: This format is identical to the previous except that the dictionary keys must match the names of the exog variables. Requires that the exog variables were pass as a pandas DataFrame.

  • A 3-d NumPy array (or equivalent). In this format, each panel (0th axis) is a 2-d array that must have shape (nforecast, horizon) or (nobs,horizon). The array x[j] corresponds to the j-th column of the exogenous variables.

Due to the complexity required to accommodate all scenarios, please see the example notebook that demonstrates the valid formats for x.

New in version 4.19.


Container for forecasts. Key properties are mean, variance and residual_variance.


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.

Return type