Forecasting financial and macroeconomic variables using data reduction methods: New empirical evidence
Journal of Econometrics, (2014): 352-367
In this paper, we empirically assess the predictive accuracy of a large group of models that are specified using principle components and other shrinkage techniques, including Bayesian model averaging and various bagging, boosting, least angle regression and related methods. Our results suggest that model averaging does not dominate other...更多
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- Technological advances over the last ...ve decades have led to impressive gains in computational power, and in the quantity of available ...nancial and macroeconomic data.
- There has been something of a race going on in recent years, as technology, both computational and theoretical, has been hard pressed to keep up with the ever increasing mountain of data available for empirical use.
- Di¤usion index techniques o¤er a simple and sensible approach for extracting common factors that underlie the dynamic evolution of large numbers of variables.
- Technological advances over the last ...ve decades have led to impressive gains in computational power, and in the quantity of available ...nancial and macroeconomic data
- To be more speci...c, let Y be a time series vector of dimension (T 1) and let X be a time-series predictor matrix of dimension (T N ) ; and de...ne the following dynamic factor model, where Ft denotes a 1 r vector of unobserved common factors that can be extracted from Xt: Namely, let Xt = Ft 0 + et; where et is an 1 N vector of disturbances and is an N r coe¢ cient matrix
- The purpose of this paper is to empirically assess the predictive accuracy of various linear models; pure principal component type models; principal components models constructed using subsets of variables selected based on the elastic net and other shrinkage techniques; principle components models where the factors to be used in prediction are directly selected using shrinkage methods such as ridge regression and bagging; models constructed by directly applying shrinkage methods to the data; and a number of model averaging methods
- The variable mnemonics are given in Table 1, and forecasting models used are summarized in Table 2
- For the case where models are estimated using recursive data windows, our results are gathered in Tables 3 to 6 and some summary results are presented in Tables 7 and 8
- For the majority of the target variables that we forecast, we ...nd that various of these shrinkage methods, when combined with factor analysis, perform better than all other models. This suggests that di¤usion index methodology is useful when combined with other shrinkage methods, adding to the extant evidence of this ...nding (see Bai and Ng (2008a,b) and Stock and Watson (2005a)
- Using the transformed data set, denoted above by X, the factors are estimated by the method of principal components.
- Speci...cation Type 2: Principal component models of the type given in (3) are constructed using subsets of variables from the largescale dataset that are ...rst selected via application of the shrinkage methods of Section 3.
- This is di¤erent from the above approach of estimating factors using all of the variables
- The authors discuss the results of the prediction experiments.
- The variable mnemonics are given in Table 1, and forecasting models used are summarized in Table 2.
- Details of the data and estimation procedures used to construct the sequences of recursive and rolling ex-ante h-step ahead forecasts reported on are outlined in Section 4.
- For the case where models are estimated using recursive data windows, the results are gathered in Tables 3 to 6 and some summary results are presented in Tables 7 and 8
- Concluding Remarks
This paper surveys factor models and shrinkage techniques, and presents the results of a “horse-race”in which mean-square-forecast-error (MSFE) “best”models are selected, in the context of a variety of forecast horizons, estimation schemes and sample periods.
- For the majority of the target variables that the authors forecast, we ...nd that various of these shrinkage methods, when combined with factor analysis, perform better than all other models.
- This suggests that di¤usion index methodology is useful when combined with other shrinkage methods, adding to the extant evidence of this ...nding (see Bai and Ng (2008a,b) and Stock and Watson (2005a).
- Given the rather extensive empirical evidence to the contrary, when specifying linear prediction models, this is taken as further evidence of the usefulness of the more sophisticated nonlinear modelling approach
- Table1: Target Variables For Which Forecasts Are Constructed*
- Table2: Models and Methods Used In Real-Time Forecasting Experiments*
- Table3: Relative Mean Square Forecast Errors: Recursive Estimation, Specification Type 1 (no lags)*
- Table4: Relative Mean Square Forecast Errors: Recursive Estimation, Specification Type 1 (with lags)*
- Table5: Relative Mean Square Forecast Errors: Recursive Estimation, Specification Type 2*
- Table6: Relative Mean Square Forecast Errors: Recursive Estimation, Specification Type 3*
- Table7: Forecast Experiment Summary Results*
- Table8: Forecast Experiment Summary Results: Various Subsamples*
Selection of the number of lagged variable to include is done using the SIC. Out-ofsample forecasts begin after 13 years (e.g. the initial in-sample estimation period is R =156 observations, and the out-of-sample period consists of P observations, for h = 1). For example, when forecasting the unemployment rate, when h = 12, the ...rst forecast will be Y^168 = ^W W156 + ^F F~156: In our rolling estimation scheme, the in-sample estimation period used to calibrate our prediction models is ...xed at length 10 years
4.1 Data. The data that we use are monthly observations on 146 U.S macroeconomic time series for the period 1960:01 - 2009:5 (N = 144; T = 593)3. Forecasts are constructed for eleven variables, including: the unemployment rate, personal income less transfer payments, the 10 year Treasury-bond yield, the consumer price index, the producer price index, non-farm payroll employment, housing starts, industrial production, M2, the S&P 500 index, and gross domestic product.4
degree line denotes cases: 45
This is done in Figure 1, where we report the ten most frequently selected variables for a variety of MSFE-best models and forecast horizons. Keeping in mind that factors are re-estimated at each point in time, prior to each new prediction being constructed, a 45 degree line denotes cases for which a particular variables is selected every time. For example, in Panels A and B, the BAA Bond Yield - Federal Funds Rate spread is the most frequently selected predictor when constructing factors to forecast the Producer Price Index and Housing Starts, respectively
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