Gabriel E. Cabrera Guzman: Forecasting Methods using Multiple Variables

Gabriel E. Cabrera

Kitchen Sink

Schwarz Information Criterion (SIC)

Pooled Average (POOL-AVG)

\[ \hat{r}^{POOL}_{t+1} = \sum^{K}_{i=1} w_{i,t}\hat{r}_{i,t+1} \]

Pooled DMSFE (POOL-DMSFE)

\[ w_{i,t} = \phi^{-1}_{i,t} / \sum^{K}_{k=1} \phi^{-1}_{k,t} \] where

\[ \phi_{i,t} = \sum^{t-1}_{s=m} \theta^{t-1-s}(r_{s+1} - \hat{r}_{i,s+1})^2 \]

Diffusion Index

Sum-of-the-Parts

Compare Out-Of-Sample Forecast

\[ R^{2}_{OS} = 1 -\frac{(1/ n_2) \sum^{n_2}_{s=1}(r_{n_1+s} - \hat{r}_{i,n_1 + s})^2}{(1/ n_2) \sum^{n_2}_{s=1}(r_{n_1+s} - \bar{r}_{n_1 + s})^2} \]

Monthly U.S. Equity Premium Out-of-Sample Forecasting Results
Multiple Economic Variables, 1957:01–2010:12
Method	Overall	Expansion	Recession
Method	$R^2_{OS}(\%)$	$R^2_{OS}(\%)$	$R^2_{OS}(\%)$
Panel A: Unrestricted forecasts
Kitchen Sink	−8.43 [0.42]	−9.41 [0.68]	−6.38 [0.28]
SIC	−5.61 [0.99]	−5.80 [1.00]	−5.21 [0.79]
POOL-AVG	0.44 [0.03]	0.12 [0.21]	1.10 [0.01]
POOL-DMSFE	0.51 [0.02]	0.08 [0.25]	1.39 [0.01]
Diffusion index	0.68 [0.01]	−1.00 [0.27]	4.15 [0.00]
Sum-of-the-parts	0.93 [0.01]	0.29 [0.13]	2.24 [0.01]
Panel B: Forecasts with nonnegativity restrictions
Kitchen Sink	−2.57 [0.59]	−3.38 [0.64]	−0.89 [0.45]
SIC	−4.47 [0.99]	−4.73 [0.99]	−3.93 [0.85]
POOL-AVG	0.44 [0.03]	0.12 [0.21]	1.10 [0.01]
POOL-DMSFE	0.51 [0.02]	0.08 [0.25]	1.39 [0.01]
Diffusion index	0.70 [0.01]	−0.68 [0.24]	3.57 [0.00]
Sum-of-the-parts	0.99 [0.00]	0.31 [0.12]	2.40 [0.00]

\[ \text{CDSFE}_{i,\tau} = \sum^{\tau}_{s=1} (r_{n_1 + s} - \bar{r}_{n_1 + s})^2 - \sum^{\tau}_{s=1} (r_{n_1 + s} - \hat{r}_{i,n_1 + s})^2 \]

Reuse

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Citation

For attribution, please cite this work as

Cabrera (2021, April 24). Gabriel E. Cabrera Guzman: Forecasting Methods using Multiple Variables. Retrieved from http://gcabrerag.rbind.io/blog/site/posts/2021-04-24-forecasting-methods-using-multiple-variables/

BibTeX citation

@misc{cabrera2021forecasting,
  author = {Cabrera, Gabriel E.},
  title = {Gabriel E. Cabrera Guzman: Forecasting Methods using Multiple Variables},
  url = {http://gcabrerag.rbind.io/blog/site/posts/2021-04-24-forecasting-methods-using-multiple-variables/},
  year = {2021}
}