dLagM (version 1.0.19)

forecast: Compute forecasts for distributed lag models

Description

Computes forecasts for the finite distributed lag models, autoregressive distributed lag models, Koyck transformation of distributed lag models, and polynomial distributed lag models.

Usage

forecast(model , x , h = 1 , interval = FALSE, level = 0.95 , nSim = 500)

Arguments

model

A fitted model by one of dlm(), koyckDlm(), ployDlm() or ardlDlm functions.

x

A vector or matrix including the new observations of independent time series. This is not restricted to ts objects. Please see the details for construction of this argument.

h

The number of ahead forecasts.

interval

If TRUE, \((1-\alpha)\%\) prediction intervals for forecasts are displayed along with forecasts.

level

Confidence level of prediction interval.

nSim

An integer showing the number of Monte Carlo simulations used to compute prediction intervals for forecasts.

Value

forecasts

A vector including forecasts.

Details

This function directly uses the model formula and estimates of model coefficients to find forecast one-by-one starting from the one-step ahead forecast.

Prediction intervals are found by the Monte Carlo approach using a Gaussian error distribution with zero mean and empirical variance of the dependent series.

When the model argument includes multiple independent series, x must be entered as a matrix including the new observations of each independent series in its rows. The number of columns of x must be equal to the forecast horizon h and the rows of x must match with the independent series in the order they appear in the data.

This function can still be used when some of the lags of independent series are removed from the model.

Examples

# NOT RUN {
# Only one independent series
data(warming)
#--- ARDL dlm ---
model.ardl = ardlDlm(x = warming$NoMotorVehicles, 
              y = warming$Warming, p = 1 , q = 1 )
forecast(model = model.ardl , x = c(95, 98) , 
                h = 2 , interval = FALSE)
forecast(model = model.ardl , x = c(95, 98, 87) , 
                h = 3 , interval = FALSE)
             
# Multiple independent series
data(M1Germany)
data = M1Germany[1:144,]
model.ardlDlm1  = ardlDlm(formula = logprice ~ interest + logm1, 
       data = data.frame(data) , p = 2 , q = 1 )
x.new =  matrix(c(0.07 , 9.06 , 0.071 , 9.09), ncol = 2, 
                nrow = 2)
forecast(model = model.ardlDlm1 , x = x.new , h = 2 , 
                interval = TRUE, nSim = 100)       
       
rem.p = list(interest = c(1,2))
rem.q = c(1)
remove = list(p = rem.p , q = rem.q)
model.ardlDlm2  = ardlDlm(formula = logprice ~ interest + logm1, 
       data = data.frame(data) , p = 2 , q = 2 , 
       remove = remove)

forecast(model = model.ardlDlm2 , x = x.new , h = 2 , 
                interval = FALSE)  
                
#--- Finite dlm ---                
model.dlm = dlm(x = warming$NoMotorVehicles , 
                y = warming$Warming , q = 2)
forecast(model = model.dlm , x = c(95 , 98, 101) , h = 3)


# Multiple independent series
model.dlm  = dlm(formula = logprice ~ interest + logm1, 
          data = data.frame(data) , q = 4)

x.new =  matrix(c(0.07 , 9.06 , 0.071 , 9.09), 
                ncol = 2, nrow = 2)
forecast(model = model.dlm , x = x.new , h = 2 , 
            interval = FALSE)

# Some lags are removed:
# Remove lags 0 and 2 from "interest" and 
# lags 1 and 3 from "logm1"
removed = list(interest = c(0,2), logm1 = c(1,3))
removed
model.dlm  = dlm(formula = logprice ~ interest + logm1 -1, 
              data = data.frame(data) , q = 4 , remove = removed)

x.new =  matrix(c(0.07 , 9.06 , 0.071 , 9.09 , 0.079 , 9.19 , 
                  0.069 , 9.21) , ncol = 4, nrow = 2)
forecast(model = model.dlm , x = x.new , h = 4 , 
         interval = FALSE)
forecast(model = model.dlm , x = x.new , h = 4 , 
            interval = FALSE)
  
x.new =  matrix(c(0.07 , 9.06 , 0.071 , 9.09, 0.08 , 9.12), ncol = 3, 
                nrow = 2)
forecast(model = model.dlm , x = x.new , h = 3,  interval = FALSE)

#--- Koyck dlm --- 
model.koyck = koyckDlm(x = warming$NoMotorVehicles , 
                       y = warming$Warming)
forecast(model = model.koyck  , x = c(95, 98, 101), h = 3 , 
                interval = FALSE)

#--- Polynomial dlm ---         
model.poly = polyDlm(x = warming$NoMotorVehicles , y = warming$Warming , 
                q = 2 , k = 2 , show.beta = TRUE)
forecast(model = model.poly , x = c(95, 98) , h = 1 , 
                interval = FALSE)

# }

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