Exponential Smoothing Model

Proud Economy 0005

I'm looking at “Forecasting With Exponential Smoothing: The State Space Approach” by Hyndman etal. (2008) and “Forecasting: principles and practice” by Hyndman and Athanasopoulos (2013). Hyndman is the maintainer of the R forecast package. Lots of cool stuff to learn here.

I discovered them while researching the exponential smoothing “ets” function.

library(forecast)
library(Quandl)
# Quandl.auth('yourauthenticationtoken')

getts <- function(series) {
    y <- Quandl(series, collapse = "quarterly", type = "xts")
    layout(matrix(c(1, 1, 2, 3), 2, 2, byrow = TRUE))
    plot.ts(y, main = series, ylab = series)
    acf(y, main = "Autocorrelations", ylim = c(-1, 1))
    pacf(y, main = "Partial Autocorrelations", ylim = c(-1, 1))
    return(y)
}

data:

“Gross domestic product (GDP), the featured measure of U.S. output, is the market value of the goods and services produced by labor and property located in the United States.”

gdp <- getts("FRED/GDPC1")

We'll take all the defaults to see what happens automatically with the “ets” function and follow it with default “forecast”.

gdp_ets <- ets(gdp)
summary(gdp_ets)

## ETS(A,Ad,N) 
## 
## Call:
##  ets(y = gdp) 
## 
##   Smoothing parameters:
##     alpha = 0.9999 
##     beta  = 0.4832 
##     phi   = 0.8936 
## 
##   Initial states:
##     l = 1756.5772 
##     b = 13.5391 
## 
##   sigma:  53.14
## 
##  AIC AICc  BIC 
## 3594 3594 3612 
## 
## Training set error measures:
##                 ME  RMSE   MAE   MPE  MAPE   MASE     ACF1
## Training set 9.143 53.14 39.25 16.14 71.64 0.6679 -0.02005

gdp_fit <- forecast(gdp_ets)
summary(gdp_fit)

## 
## Forecast method: ETS(A,Ad,N)
## 
## Model Information:
## ETS(A,Ad,N) 
## 
## Call:
##  ets(y = gdp) 
## 
##   Smoothing parameters:
##     alpha = 0.9999 
##     beta  = 0.4832 
##     phi   = 0.8936 
## 
##   Initial states:
##     l = 1756.5772 
##     b = 13.5391 
## 
##   sigma:  53.14
## 
##  AIC AICc  BIC 
## 3594 3594 3612 
## 
## Error measures:
##                 ME  RMSE   MAE   MPE  MAPE   MASE     ACF1
## Training set 9.143 53.14 39.25 16.14 71.64 0.6679 -0.02005
## 
## Forecasts:
##     Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 266          13774 13706 13842 13670 13878
## 267          13817 13669 13964 13592 14042
## 268          13855 13640 14070 13526 14184
## 269          13889 13609 14170 13460 14318
## 270          13920 13575 14265 13392 14448
## 271          13947 13538 14356 13321 14573
## 272          13971 13499 14444 13248 14694
## 273          13993 13458 14529 13174 14812
## 274          14013 13415 14610 13099 14927
## 275          14030 13372 14689 13023 15038

plot(gdp_fit)

Here's another blog article on “Learning Time Series with R” by Joseph Rickert that I just discovered. He lists several of the books that I've been looking at. I'm having fun exploring this stuff so far.

Gary Young