# NNS VAR Nonparametric vector autoregressive model incorporating NNS.ARMA estimates of variables into NNS.reg for a multi-variate time-series forecast. ```r 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 ) ``` ## 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-partialmoments)` (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 . ## Returns 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. ## Note * `"Error in { : task xx failed -}"` should be re-run with `NNS.VAR(..., ncores = 1)`. * Not recommended for factor variables, even after transformed to numeric. NNS.reg is better suited for factor or binary regressor extrapolation. ## Examples ```r ## Not run: #################################################### ### 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) ## End(Not run) ``` ## 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") ## Author(s) Fred Viole, OVVO Financial Systems

NNS.VAR function