forecast.odpcs: Get Forecast From an odpcs Object

In odpc: One-Sided Dynamic Principal Components

Get Forecast From an odpcs Object

Description

Get forecasts from an odpcs object.

Usage

  ## S3 method for class 'odpcs'
forecast(object, h, Z = NULL, add_residuals = FALSE, ...)

Arguments

object	An object of class odpcs, usually the result of odpc.
h	Integer. Number of periods for forecasting.
Z	Original data. Only used if add_residuals = TRUE.
add_residuals	Logical. Should the forecasts of the reconstruction residuals be added to the final forecast? Default is FALSE.
...	Additional arguments to be passed to auto.arima.

Details

Suppose q dynamic principal components were fitted to the data, each with (k_{1}^{i},k_{2}^{i}) lags, i=1,…,q. Let \widehat{\mathbf{f}}_{T}% ^{i} be the vector with the estimated values for the i-th dynamic principal component and \widehat{\mathbf{B}}^{i}, \widehat{\boldsymbol{α}}^{i} be the corresponding loadings and intercepts. Forecasts of the series are built by first fitting a SARIMA model to the components using auto.arima and getting their forecasts using forecast.Arima. Let \widehat{f}_{T+h|T}^{i} for h>0 be the forecast of f_{T+h}^{i} with information until time T. Then the h-steps ahead forecast of \mathbf{z}_{T} is obtained as

\widehat{z}_{T+h|T,j}=∑\limits_{i=1}^{q}≤ft( \widehat{α}_{j}% ^{i}+∑\limits_{v=0}^{k_{2}^{i}}\widehat{b}_{v,j}^{i}\widehat{f}% _{T+h-v|T}^{i}\right) \quad j=1,…,m.

If add_residuals = TRUE, univariate SARIMA models are fitted to the residuals of the reconstruction, and their forecasts are added to the forecasts described above.

Value

A matrix that is the h-steps ahead forecast of the original series.

See Also

odpc, crit.odpc, cv.odpc, components_odpcs, auto.arima, forecast.Arima

Examples

  T <- 201 #length of series
  m <- 10 #number of series
  set.seed(1234)
  f <- matrix(0, 2 * T + 1, 1)
  v <- rnorm(2 * T + 1)
  f[1] <- rnorm(1)
  theta <- 0.7
  for (t in  2:(2 * T)){
    f[t] <- theta * f[t - 1] + v[t]
  }
  f <- f[T:(2 * T)]
  x <- matrix(0, T, m)
  u <- matrix(rnorm(T * m), T, m)
  for (i in 1:m) {
    x[, i] <- sin(2 * pi * (i/m)) * f[1:T] + cos(2 * pi * (i/m)) * f[2:(T + 1)] + u[, i]
  }
  fit <- odpc(x[1:(T - 1), ], ks = c(1))
  forecasts <- forecast.odpcs(fit, h = 1)
  mse <- mean((x[T, ] - forecasts)**2)
  mse

odpc documentation built on March 18, 2022, 7:32 p.m.