predict.varlse {bvhar} | R Documentation |
Forecasting Multivariate Time Series
Description
Forecasts multivariate time series using given model.
Usage
## S3 method for class 'varlse'
predict(object, n_ahead, level = 0.05, ...)
## S3 method for class 'vharlse'
predict(object, n_ahead, level = 0.05, ...)
## S3 method for class 'bvarmn'
predict(object, n_ahead, n_iter = 100L, level = 0.05, ...)
## S3 method for class 'bvharmn'
predict(object, n_ahead, n_iter = 100L, level = 0.05, ...)
## S3 method for class 'bvarflat'
predict(object, n_ahead, n_iter = 100L, level = 0.05, ...)
## S3 method for class 'bvarssvs'
predict(object, n_ahead, level = 0.05, ...)
## S3 method for class 'bvharssvs'
predict(object, n_ahead, level = 0.05, ...)
## S3 method for class 'bvarhs'
predict(object, n_ahead, level = 0.05, ...)
## S3 method for class 'bvharhs'
predict(object, n_ahead, level = 0.05, ...)
## S3 method for class 'bvarsv'
predict(object, n_ahead, level = 0.05, ...)
## S3 method for class 'bvharsv'
predict(object, n_ahead, level = 0.05, ...)
## S3 method for class 'predbvhar'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
## S3 method for class 'predbvhar'
knit_print(x, ...)
Arguments
object |
Model object |
n_ahead |
step to forecast |
level |
Specify alpha of confidence interval level 100(1 - alpha) percentage. By default, .05. |
... |
not used |
n_iter |
Number to sample residual matrix from inverse-wishart distribution. By default, 100. |
x |
|
digits |
digit option to print |
Value
predbvhar
class with the following components:
- process
object$process
- forecast
forecast matrix
- se
standard error matrix
- lower
lower confidence interval
- upper
upper confidence interval
- lower_joint
lower CI adjusted (Bonferroni)
- upper_joint
upper CI adjusted (Bonferroni)
- y
object$y
n-step ahead forecasting VAR(p)
See pp35 of Lütkepohl (2007). Consider h-step ahead forecasting (e.g. n + 1, ... n + h).
Let .
Then one-step ahead (point) forecasting:
Recursively, let .
Then two-step ahead (point) forecasting:
Similarly, h-step ahead (point) forecasting:
How about confident region? Confidence interval at h-period is
Joint forecast region of % can be computed by
See the pp41 of Lütkepohl (2007).
To compute covariance matrix, it needs VMA representation:
Then
n-step ahead forecasting VHAR
Let is VHAR linear transformation matrix (See var_design_formulation).
Since VHAR is the linearly transformed VAR(22),
let
.
Then one-step ahead (point) forecasting:
Recursively, let .
Then two-step ahead (point) forecasting:
and h-step ahead (point) forecasting:
n-step ahead forecasting BVAR(p) with minnesota prior
Point forecasts are computed by posterior mean of the parameters. See Section 3 of Bańbura et al. (2010).
Let be the posterior MN mean
and let
be the posterior MN precision.
Then predictive posterior for each step
and recursively,
See bvar_predictive_density how to generate the predictive distribution.
n-step ahead forecasting BVHAR
Let be the posterior MN mean
and let
be the posterior MN precision.
Then predictive posterior for each step
and recursively,
See bvar_predictive_density how to generate the predictive distribution.
n-step ahead forecasting VAR(p) with SSVS and Horseshoe
The process of the computing point estimate is the same. However, predictive interval is achieved from each Gibbs sampler sample.
n-step ahead forecasting VHAR with SSVS and Horseshoe
The process of the computing point estimate is the same. However, predictive interval is achieved from each Gibbs sampler sample.
References
Lütkepohl, H. (2007). New Introduction to Multiple Time Series Analysis. Springer Publishing.
Corsi, F. (2008). A Simple Approximate Long-Memory Model of Realized Volatility. Journal of Financial Econometrics, 7(2), 174–196.
Baek, C. and Park, M. (2021). Sparse vector heterogeneous autoregressive modeling for realized volatility. J. Korean Stat. Soc. 50, 495–510.
Bańbura, M., Giannone, D., & Reichlin, L. (2010). Large Bayesian vector auto regressions. Journal of Applied Econometrics, 25(1).
Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2013). Bayesian data analysis. Chapman and Hall/CRC.
Karlsson, S. (2013). Chapter 15 Forecasting with Bayesian Vector Autoregression. Handbook of Economic Forecasting, 2, 791–897.
Litterman, R. B. (1986). Forecasting with Bayesian Vector Autoregressions: Five Years of Experience. Journal of Business & Economic Statistics, 4(1), 25.
Ghosh, S., Khare, K., & Michailidis, G. (2018). High-Dimensional Posterior Consistency in Bayesian Vector Autoregressive Models. Journal of the American Statistical Association, 114(526).
George, E. I., Sun, D., & Ni, S. (2008). Bayesian stochastic search for VAR model restrictions. Journal of Econometrics, 142(1), 553–580.
George, E. I., Sun, D., & Ni, S. (2008). Bayesian stochastic search for VAR model restrictions. Journal of Econometrics, 142(1), 553–580.