Abstract
The discussion of forecasting with VAR models proceeds in two steps. First, we assume that the parameters of the model are known. Although this assumption is unrealistic, it will nevertheless allow us to introduce and analyze important concepts and ideas. In a second step, we then investigate how the results established in the first step have to be amended if the parameters are estimated. The analysis will focus on stationary and causal VAR(1) processes. Processes of higher order can be accommodated by rewriting them in companion form.
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- 1.
If the mean is non-zero, a constant A 0 must be added to the forecast function.
- 2.
A stationary stochastic process is called deterministic if it can be perfectly forecasted from its infinite past. It is called purely non-deterministic if there is no deterministic component (see Sect. 3.2).
- 3.
Thus, \(\Delta \log P_{t}\) equals the inflation rate.
- 4.
Although the unit root test indicate that R t is integrated of order one, we do not difference this variable. This specification will not affect the consistency of the estimates nor the choice of the lag-length (Sims et al. 1990), but has the advantage that each component of X t is expressed in percentage points which facilitates the interpretation.
- 5.
Such tests would include an analysis of the autocorrelation properties of the residuals and tests of structural breaks.
- 6.
Alternatively one could use the mean-absolute-percentage-error (MAPE). However, as all variables are already in percentages, the MAE is to be preferred.
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Neusser, K. (2016). Forecasting with VAR Models. In: Time Series Econometrics. Springer Texts in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-319-32862-1_14
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