forecast
Forecast univariate autoregressive integrated moving average (ARIMA) model responses or conditional variances
Syntax
Description
[
returns Y
,YMSE
]
= forecast(Mdl
,numperiods
,Y0
)numperiods
consecutive forecasted responses Y
and corresponding mean square errors (MSE) YMSE
of the fully specified, univariate ARIMA model Mdl
. The presample response data Y0
initializes the model to generate forecasts.
[
uses additional options specified by one or more name-value arguments. For example, for a model with a regression component (that is, an ARIMAX model), Y
,YMSE
] = forecast(Mdl
,numperiods
,Y0
,Name,Value
)'X0',X0,'XF',XF
specifies the presample and forecasted predictor data X0
and XF
, respectively.
Examples
Input Arguments
Output Arguments
More About
Algorithms
The
forecast
function sets the number of sample paths (numpaths
) to the maximum number of columns among the presample data setsE0
,V0
, andY0
. All presample data sets must have either one column ornumpaths
> 1 columns. Otherwise,forecast
issues an error. For example, if you supplyY0
andE0
, andY0
has five columns representing five paths, thenE0
can each have one column or five columns. IfE0
has one column,forecast
appliesE0
to each path.NaN
values in presample and future data sets indicate missing data.forecast
removes missing data from the presample data sets following this procedure:forecast
horizontally concatenates the specified presample data setsY0
,E0
,V0
, andX0
so that the latest observations occur simultaneously. The result can be a jagged array because the presample data sets can have a different number of rows. In this case,forecast
prepads variables with an appropriate number of zeros to form a matrix.forecast
applies list-wise deletion to the combined presample matrix by removing all rows containing at least oneNaN
.forecast
extracts the processed presample data sets from the result of step 2, and removes all prepadded zeros.
forecast
applies a similar procedure to the forecasted predictor dataXF
. Afterforecast
applies list-wise deletion toXF
, the result must have at leastnumperiods
rows. Otherwise,forecast
issues an error.List-wise deletion reduces the sample size and can create irregular time series.
When
forecast
estimates the MSEsYMSE
of the conditional mean forecastsY
, the function treats the specified predictor data setsX0
andXF
as exogenous, nonstochastic, and statistically independent of the model innovations. Therefore,YMSE
reflects only the variance associated with the ARIMA component of the input modelMdl
.
References
[1] Baillie, Richard T., and Tim Bollerslev. “Prediction in Dynamic Models with Time-Dependent Conditional Variances.” Journal of Econometrics 52, (April 1992): 91–113. https://doi.org/10.1016/0304-4076(92)90066-Z.
[2] Bollerslev, Tim. “Generalized Autoregressive Conditional Heteroskedasticity.” Journal of Econometrics 31 (April 1986): 307–27. https://doi.org/10.1016/0304-4076(86)90063-1.
[3] Bollerslev, Tim. “A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return.” The Review of Economics and Statistics 69 (August 1987): 542–47. https://doi.org/10.2307/1925546.
[4] Box, George E. P., Gwilym M. Jenkins, and Gregory C. Reinsel. Time Series Analysis: Forecasting and Control. 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1994.
[5] Enders, Walter. Applied Econometric Time Series. Hoboken, NJ: John Wiley & Sons, Inc., 1995.
[6] Engle, Robert. F. “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation.” Econometrica 50 (July 1982): 987–1007. https://doi.org/10.2307/1912773.
[7] Hamilton, James D. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994.