## Forecasting using principal components from a large number of predictors.(English)Zbl 1041.62081

Summary: This article considers forecasting a single time series when there are many predictors ($$N$$) and time series observations ($$T$$). When the data follow an approximate factor model, the predictors can be summarized by a small number of indexes, which we estimate using principal components. Feasible forecasts are shown to be asymptotically efficient in the sense that the difference between the feasible forecasts and the infeasible forecasts constructed using the actual values of the factors converges in probability to 0 as both $$N$$ and $$T$$ grow large. The estimated factors are shown to be consistent, even in the presence of time variation in the factor model.

### MSC:

 62M20 Inference from stochastic processes and prediction 62H25 Factor analysis and principal components; correspondence analysis 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)

### Keywords:

factor models; principal components; prediction
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