pretest (version 0.2)

recursive_hstep_fast: Forecasting h-steps ahead using Recursive Least Squares Fast

Description

Consider the following LS-fitted Model with intercept: y_(t+h) = beta_0 + x_t * beta + u_(t+h) which is used to generate out-of-sample forecasts of y, h-steps ahead (h=1,2,3,. . . ). It calculates the recursive residuals starting from the first (n * pi0) data points, where n is the total number of data points.

Usage

recursive_hstep_fast(y, x, pi0, h)

Value

Series of residuals estimated

Arguments

y

n x 1 Outcome series, which should be numeric and one dimensional.

x

n x p Predictor matrix (intercept would be added automatically).

pi0

Fraction of the sample, which should be within 0 and 1.

h

Number of steps ahead to predict, which should be a positive integer.

Author

Rong Peng,

Details

recursive_hstep_fast is the fast version that avoids the recursive calculation of inverse of the matrix using Sherman-Morrison formula. recursive_hstep_slow is the slow version that calculates the standard OLS recursively.

Examples

x<- rnorm(15);
y<- x+rnorm(15);
temp1 <- recursive_hstep_fast(y,x,pi0=0.5,h=1);