Time Series and Forecasting

R has extensive facilities for analyzing time series data. This section describes the creation of a time series, seasonal decompostion, modeling with exponential and ARIMA models, and forecasting with the forecast package.

library(forecast)

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

Creating a time series

The ts() function will convert a numeric vector into an R time series object. The format is ts(vector, start=, end=, frequency=) where start and end are the times of the first and last observation and frequency is the number of observations per unit time (1=annual, 4=quartly, 12=monthly, etc.).

# save a numeric vector containing 72 monthly observations
# from Jan 2009 to Dec 2014 as a time series object
myvector <- sort(rnorm(72,100,4)) + rnorm(72,5,1)
myts <- ts(myvector, start=c(2009, 1), end=c(2014, 12), frequency=12) 

# subset the time series (June 2014 to December 2014)
myts2 <- window(myts, start=c(2014, 6), end=c(2014, 12)) 

# plot series
plot(myts)

Seasonal Decomposition

A time series with additive trend, seasonal, and irregular components can be decomposed using the stl() function. Note that a series with multiplicative effects can often by transformed into series with additive effects through a log transformation (i.e., newts <- log(myts)).

# Seasonal decomposition
fit <- stl(myts, s.window="period")
plot(fit)

# additional plots
monthplot(myts)

library(forecast)
seasonplot(myts)

png

Exponential Models

Both the HoltWinters() function in the base installation, and the ets() function in the forecast package, can be used to fit exponential models.

# simple exponential - models level
fit <- HoltWinters(myts, beta=FALSE, gamma=FALSE)
# double exponential - models level and trend
fit <- HoltWinters(myts, gamma=FALSE)
# triple exponential - models level, trend, and seasonal components
fit <- HoltWinters(myts)

## Warning in HoltWinters(myts): optimization difficulties: ERROR:
## ABNORMAL_TERMINATION_IN_LNSRCH

# predictive accuracy
library(forecast)
accuracy(fit)

# predict next three future values
library(forecast)
forecast(fit, 3)
plot(forecast(fit, 3))