wavdrcast-package: wavdrcast: Wavelet-based direct multistep forecast

In nelson16silva/wavdrcast: Wavelet-Based Direct Multistep Forecast

Description

This package provides forecasts of time series using a direct multistep model where regressors can be composed by AR components, exogenous variables and wavelet-based signal estimation.

Details

wavdrcast is a package for forecasting time series using a direct multistep model estimation. In particular, wavelet-based signal estimation of the time series is used as an additional regressor or even the only one. This is useful for evaluation of core inflation and outupt gap measures constructed from wavelet methods, for example. A functional available in wavdrcast package allows one to choose a good wavelet specification for sinal extraction considering the forecast criterion. The scope is not limited to wavelet regressors, however. In general, any other data set can be used as a regressor, including just AR components of the time series. This can be interesting when one is comparing the forecast property of candidates model to be a good estimator of the core inflation or output gap. If the data set are subjected to revisions, functions for vintages are also available.

Model

The most general OLS regression model is writting as:

x_{t + h} = α + \mathbf{{β}}'\mathbf{x}_t + \mathbf{{γ}}'\mathbf{z}_t + \mathbf{{θ}}'\mathbf{d}_t + ε_{t + h},

where:

• x_{t + h}, regressed x leaded h step-ahead;

• α, constant;

• \mathbf{{β}}' = (β_0, …, β_p), vector of p + 1 coefficients;

• \mathbf{x}_t = (x_t, …, x_{t - p})', variable x in t and its p lags;

• \mathbf{{γ}}' = (γ^1_0, …, γ^1_{q_1}, …, γ^n_0, …, γ^n_{q_n}, γ^w_0, …, γ^w_{q_w}), vector of coefficients on \mathbf{z}_t;

• \mathbf{z}_t = (z^1_t, …, z^1_{t - q_1}, …, z^n_t, …, z^n_{t - q_n}, z^w_t, …, z^w_{t - q_w})', vector of exogenous variables and its q_i, i = (1, …, n, w) lags. By convention, the exogenous variable from wavelet-based signal estimation (z^w_t), if included, is ordered last;

• \mathbf{{θ}}' = (θ_1, …, θ_m), coefficients;

• \mathbf{d}_t = (d_1, …, d_m)', exogenous variables not subjected to be lagged, possibly dummy variables;

• ε_{t + h}, white noise error term.

If x_{t + h} = y_{t + h} - y_t, then x_t = Δ x_t = y_t - y_{t - 1} and z^w_t = y_t - y^w_t, where y^w_t is a wavelet-based signal estimation of y_t. For example, if y_t is the logarithm of the output, then z^w_t = y_t - y^w_t is the wavelet-base estimation of the output gap. Other variables z^i_t, i = (1, …, n) are never automatically differentiated, so it is a user's decision to include them in level or difference.

From this specification, it is possible to estimate particular models like:

• y_{t + h} - y_t = α + \mathbf{{β}}Δ \mathbf{y}_t + ε_{t + h}, (AR case);

• y_{t + h} - y_t = α + γ_0^w z^w_t + ε_{t + h}, (evaluation of the wavelet-based output gap, for example);

• x_{t + h} = α + ∑^p_{i = 0}β_ix_{t - i} + ∑^q_{i = 0}γ^1_i z^1_{t - i} + ε_{t + h}, (evaluation of core inflation measure that exclude food and energy, for example).

In the last equation above, it was assumed that the variable z are not revised, as it is almost always the case for core inflation measures that exclude food and energy. If not, there is a function in the package that considers the case in which z can be revised in each point of time when new data are available. If z is the core inflation measure from HP filter, for example, then an evaluation of the forecast property should consider that the estimation of all element in z can be different for each out-of-sample observation included in the sample. If z includes z^w, as is the case of the second equation above, then for each point in time a new estimation of z^w is did automatically.

Author(s)

Maintainer: Nelson Silva [e-mail]

nelson16silva/wavdrcast documentation built on April 25, 2021, 7:03 a.m.