# Computes a Few Alternative Forecasts. It is necessary to compare a given forecast method with some alternative ones. This function computes selected forecast quality measures for a few selected forecast methods (which might be treated as alternative ones to Dynamic Model Averaging, Dynamic Model Selection, etc.). Naive forecast (naive) is computed in a way that all forecasts are set to be the value of the last observation. For rolling OLS forecast (roll. OLS) for the first periods (until the size of a `window` is obtained) are estimated through recursive OLS (rec. OLS). Autoregressive models (AR(1) and AR(2)) are computed by ordinary least squares method. Time-varying parameters models (TVP, TVP-AR(1) and TVP-AR(2)) are computed as `tvp` with `V=1` and `lambda=0.99`. Auto ARIMA (auto ARIMA) is computed as `auto.arima`. ME (Mean Error), RMSE (Root Mean Squared Error), MAE (Mean Absolute Error), MPE (Mean Percentage Errror) and MAPE (Mean Absolute Percentage Error) are computed as `accuracy`. HR (Hit Ratio) is computed as `hit.ratio`. ```r altf(y,x,window=NULL,initial.period=NULL,d=NULL,f=NULL,fmod=NULL,c=NULL) ``` ## Arguments - `y`: `numeric` or a column `matrix` of a dependent variable - `x`: `matrix` of independent variables, different columns correspond to different independent variables - `window`: optional, `numeric`, a size of a rolling regression window (a number of observations), if not specified 10% of all observations are taken - `initial.period`: optional, `numeric`, a number of observation since which forecast quality measures are computed, if not specified the whole sample is used, i.e., `initial.period=1`, this argument also divides the sample into in-sample and out-of-sample for non-recursive methods (OLS, AR(1), AR(2), auto ARIMA) - `d`: optional, `logical`, a parameter used for HR (Hit Ratio) calculation, should be `d=FALSE` for level time-series and `d=TRUE` if time-series represent changes, if not specified `d=FALSE` - `f`: optional, `logical` vector, indicating which of alternative forecasts -- naive, OLS, rec. OLS, roll. OLS, TVP, AR(1), AR(2), auto ARIMA, TVP-AR(1) and TVP-AR(2) -- should be computed, if not specified `f=c(rep(TRUE,10))`, i.e., all alternative forecasts are computed - `fmod`: optional, class `dma` object, a model to be compared with alternative forecast - `c`: optional, `logical`, a parameter indicating whether constant is included in models, if not specified `c=TRUE` is used, i.e., constant is included ## Returns class `altf` object, `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 - **$y**: `y`, forecasted time-series - **$coeff.**: `list` of coefficients from all forecasting methods which were applied (for naive forecast they are not computed) - **$p.val.**: `list` of p-values for t-test of statistical significance for coefficients from all forecasting methods which were applied (for naive and TVP models they are not computed, and for auto ARIMA z-test is used) ## Examples ```r wti <- crudeoil[-1,1] drivers <- (lag(crudeoil[,-1],k=1))[-1,] ld.wti <- (diff(log(wti)))[-1,] ld.drivers <- (diff(log(drivers)))[-1,] a1 <- altf(y=ld.wti,x=ld.drivers,d=TRUE,initial.period=60) # models where constant term is not included in modelled equations (if applicable) a2 <- altf(y=ld.wti,x=ld.drivers,d=TRUE,c=FALSE,initial.period=60) # compute just selected models fcomp <- c(TRUE,TRUE,TRUE,FALSE,FALSE,FALSE,TRUE,TRUE,TRUE,FALSE) a3 <- altf(y=ld.wti,x=ld.drivers,d=TRUE,f=fcomp,initial.period=60) m1 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.90,initvar=10) a4 <- altf(y=ld.wti,x=ld.drivers,d=TRUE,f=fcomp,fmod=m1,initial.period=60) ``` ## See Also `plot.altf`, `print.altf`, `summary.altf`, `rec.reg`, `roll.reg`, `altf2`, `altf3`, `altf4`.

altf function