NNS (version 11.1)

NNS.VAR: NNS VAR

Description

Nonparametric vector autoregressive model incorporating NNS.ARMA estimates of variables into NNS.reg for a multi-variate time-series forecast.

Usage

NNS.VAR(
  variables,
  h,
  tau = 1,
  dim.red.method = "cor",
  naive.weights = TRUE,
  obj.fn = expression(mean((predicted - actual)^2)/(NNS::Co.LPM(1, predicted, actual,
    target_x = mean(predicted), target_y = mean(actual)) + NNS::Co.UPM(1, predicted,
    actual, target_x = mean(predicted), target_y = mean(actual)))),
  objective = "min",
  status = TRUE,
  ncores = NULL,
  nowcast = FALSE
)

Value

Returns the following matrices of forecasted variables:

• "interpolated_and_extrapolated" Returns a data.frame of the linear interpolated and NNS.ARMA extrapolated values to replace NA values in the original variables argument. This is required for working with variables containing different frequencies, e.g. where NA would be reported for intra-quarterly data when indexed with monthly periods.

• "relevant_variables" Returns the relevant variables from the dimension reduction step.

• "univariate" Returns the univariate NNS.ARMA forecasts.

• "multivariate" Returns the multi-variate NNS.reg forecasts.

• "ensemble" Returns the ensemble of both "univariate" and "multivariate" forecasts.

Arguments

variables

a numeric matrix or data.frame of contemporaneous time-series to forecast.

h

integer; 1 (default) Number of periods to forecast. (h = 0) will return just the interpolated and extrapolated values.

tau

positive integer [ > 0]; 1 (default) Number of lagged observations to consider for the time-series data. Vector for single lag for each respective variable or list for multiple lags per each variable.

dim.red.method

options: ("cor", "NNS.dep", "NNS.caus", "all") method for reducing regressors via NNS.stack. (dim.red.method = "cor") (default) uses standard linear correlation for dimension reduction in the lagged variable matrix. (dim.red.method = "NNS.dep") uses NNS.dep for nonlinear dependence weights, while (dim.red.method = "NNS.caus") uses NNS.caus for causal weights. (dim.red.method = "all") averages all methods for further feature engineering.

naive.weights

logical; TRUE (default) Equal weights applied to univariate and multivariate outputs in ensemble. FALSE will apply weights based on the number of relevant variables detected.

obj.fn

expression; expression(mean((predicted - actual)^2)) / (Sum of NNS Co-partial moments) (default) MSE / co-movements is the default objective function. Any expression(...) using the specific terms predicted and actual can be used.

objective

options: ("min", "max") "min" (default) Select whether to minimize or maximize the objective function obj.fn.

status

logical; TRUE (default) Prints status update message in console.

ncores

integer; value specifying the number of cores to be used in the parallelized subroutine NNS.ARMA.optim. If NULL (default), the number of cores to be used is equal to the number of cores of the machine - 1.

nowcast

logical; FALSE (default) internal call for NNS.nowcast.

Author

Fred Viole, OVVO Financial Systems

References

Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" (ISBN: 1490523995)

Viole, F. (2019) "Multi-variate Time-Series Forecasting: Nonparametric Vector Autoregression Using NNS" tools:::Rd_expr_doi("10.2139/ssrn.3489550")

Viole, F. (2020) "NOWCASTING with NNS" tools:::Rd_expr_doi("10.2139/ssrn.3589816")

Viole, F. (2019) "Forecasting Using NNS" tools:::Rd_expr_doi("10.2139/ssrn.3382300")

Vinod, H. and Viole, F. (2017) "Nonparametric Regression Using Clusters" tools:::Rd_expr_doi("10.1007/s10614-017-9713-5")

Vinod, H. and Viole, F. (2018) "Clustering and Curve Fitting by Line Segments" tools:::Rd_expr_doi("10.20944/preprints201801.0090.v1")

Examples

 if (FALSE) {
 ####################################################
 ### Standard Nonparametric Vector Autoregression ###
 ####################################################

 set.seed(123)
 x <- rnorm(100) ; y <- rnorm(100) ; z <- rnorm(100)
 A <- cbind(x = x, y = y, z = z)

 ### Using lags 1:4 for each variable
 NNS.VAR(A, h = 12, tau = 4, status = TRUE)

 ### Using lag 1 for variable 1, lag 3 for variable 2 and lag 3 for variable 3
 NNS.VAR(A, h = 12, tau = c(1,3,3), status = TRUE)

 ### Using lags c(1,2,3) for variables 1 and 3, while using lags c(4,5,6) for variable 2
 NNS.VAR(A, h = 12, tau = list(c(1,2,3), c(4,5,6), c(1,2,3)), status = TRUE)

 ### PREDICTION INTERVALS
 # Store NNS.VAR output
 nns_estimate <- NNS.VAR(A, h = 12, tau = 4, status = TRUE)

 # Create bootstrap replicates using NNS.meboot
 replicates <- NNS.meboot(nns_estimate$ensemble[,1], rho = seq(-1,1,.25))["replicates",]
 replicates <- do.call(cbind, replicates)

 # Apply UPM.VaR and LPM.VaR for desired prediction interval...95 percent illustrated
 # Tail percentage used in first argument per {LPM.VaR} and {UPM.VaR} functions
 lower_CIs <- apply(replicates, 1, function(z) LPM.VaR(0.025, 0, z))
 upper_CIs <- apply(replicates, 1, function(z) UPM.VaR(0.025, 0, z))

 # View results
 cbind(nns_estimate$ensemble[,1], lower_CIs, upper_CIs)


 #########################################
 ### NOWCASTING with Mixed Frequencies ###
 #########################################

 library(Quandl)
 econ_variables <- Quandl(c("FRED/GDPC1", "FRED/UNRATE", "FRED/CPIAUCSL"),type = 'ts',
                          order = "asc", collapse = "monthly", start_date = "2000-01-01")

 ### Note the missing values that need to be imputed
 head(econ_variables)
 tail(econ_variables)


 NNS.VAR(econ_variables, h = 12, tau = 12, status = TRUE)
 }