predict.mtscp: Make predictions from a `"mtscp"` object

Description

This function makes predictions from a "mtscp" object.

Usage

# S3 method for mtscp
predict(
  object,
  newdata = NULL,
  n.ahead = 10,
  control_ARIMA = list(),
  control_VAR = list(),
  ...
)

Value

Y_pred: A list of length n.ahead, where each element is a \(p \times q\) matrix representing the predicted values at each time step.

Arguments

object: An object of class "mtscp" constructed by CP_MTS.
newdata: Optional. A new data matrix to predict from.
n.ahead: An integer specifying the number of steps ahead for prediction.
control_ARIMA: A list of arguments passed to the function auto.arima() of forecast. See 'Details' and the manual of auto.arima(). The default is list(ic = "aic").
control_VAR: A list of arguments passed to the function VAR() of vars. See 'Details' and the manual of VAR(). The default is list(type = "const", lag.max = 6, ic = "AIC").
...: Currently not used.

Details

Forecasting for \({\bf y}_t\) can be implemented in two steps:

Step 1. Get the \(h\)-step ahead forecast of the \(\hat{d} \times 1\) time series \(\hat{\bf x}_t=(\hat{x}_{t,1},\ldots,\hat{x}_{t,\hat{d}})'\) [See CP_MTS], denoted by \(\hat{\bf x}_{n+h}\), using a VAR model (if \(\hat{d} > 1\)) or an ARIMA model (if \(\hat{d} = 1\)). The orders of VAR and ARIMA models are determined by AIC by default. Otherwise, they can also be specified by users through the arguments control_VAR and control_ARIMA, respectively.

Step 2. The forecasted value for \({\bf Y}_t\) is obtained by \(\hat{\bf Y}_{n+h}= \hat{\bf A} \hat{\bf X}_{n+h} \hat{\bf B}'\) with \( \hat{\bf X}_{n+h} = {\rm diag}(\hat{\bf x}_{n+h})\).

Examples

Run this code

library(HDTSA)
data(FamaFrench, package = "HDTSA")

## Remove the market effects
reg <- lm(as.matrix(FamaFrench[, -c(1:2)]) ~ as.matrix(FamaFrench$MKT.RF))
Y_2d = reg$residuals

## Rearrange Y_2d into a 3-dimensional array Y
Y = array(NA, dim = c(NROW(Y_2d), 10, 10))
for (tt in 1:NROW(Y_2d)) {
  for (ii in 1:10) {
    Y[tt, ii, ] <- Y_2d[tt, (1 + 10*(ii - 1)):(10 * ii)]
  }
}

res_cp <- CP_MTS(Y, lag.k = 20, method = "CP.Refined")
pred_cp_Y <- predict(res_cp, n.ahead = 1)[[1]]