# Dynamic Model Averaging in Economics and Finance with fDMA: A Package for R
## 5 Information-Theoretic Averaging
OLS
- av. rec. OLS
- av. roll. OLS
- av. TVP
- averaging is done over time-varying parameters linear regressions (TVPs), i.e., models like the ones being averaged in Dynamic Model Averaging (DMA). In other words, the models computed by the function tvp, described already in this paper, are averaged. V = 1 and lambda = 0.99 are used inside the function as tvp arguments. * fmod is optional. This represents a class dma object. Then previously estimated DMA, DMS or Median Probability Model can be quickly compared with alternative forecast in a sense of forecast quality measures,
* parallel is optional. This logical indicates whether parallel computations should be used. By default parallel = FALSE is used. All weights, except the ones defined by av = \"ord\" and a situation that _av. OLS_ method is chosen, are recursively updated. In other words, in the initial period equal weights are ascribed to the models. Then, they are successively updated based on the chosen criterion. If gprob is used, then for _av. OLS_ mean values of Google searches from the in-sample period are taken, for _av. rec. OLS_ - mean values from periods up to the current one, for _av. roll. OLS_ - mean values from the last window periods, and for _av. TVP_ - values from the current period. In particular, it should be noticed that weights are computed basing on the past information; whereas gprob matrix is not lagged one period back automatically inside the function. The outcomes are an object of altf2 class, i.e., a list of:  
* $summary: matrix of forecast quality measures ordered by columns, forecast methods are ordered by rows,
* $y.hat: list of predicted values from all forecasting methods which were applied,
* $y: y, the dependent (forecasted) time-series,
* $coeff. : list of coefficients from all forecasting methods which were applied,
* $weights: list of weights of models used in averaging for all forecasting methods which were applied,
* $p.val. : list of \(p\)-values (averaged with respect to suitable weights) for \(t\)-test of statistical significance for coefficients from all forecasting methods which were applied (for _av. TVP_ they are not computed),
* $rel.var.imp.: list of relative variable importance from all forecasting methods which were applied, i.e., the sum of weights of exactly those models used in averaging which contain a given variable as the explanatory variable,
* $exp.var. : list of expected number of variables (including constant) from all forecasting methods which were applied, i.e., the weighted average of explanatory variables in the models. Recursive regressions and rolling window regressions are based on rec.reg and roll.reg functions described later in this paper. The outcomes can be easily and quickly presented with print.altf2, summary.altf2 and plot.altf2 functions. The first function prints forecast quality measures. The second, additionally provides  
* mean values of coefficients,
* minimum, maximum and mean relative variable importance reached during the analysed time period for each explanatory variable,
* frequency when relative variable importance is over 0.5 for each explanatory variable,
* how often \(p\)-values (averaged over used models) for \(t\)-test of statistical significance for each explanatory variable are below 1%, 5% and 10%, respectively.