- Some basic forecasting methods
- Forecasting time series with complex seasonality
- Dealing with missing values and outliers

School of Economics and Management

Beihang University

http://yanfei.site

- Some basic forecasting methods
- Forecasting time series with complex seasonality
- Dealing with missing values and outliers

library(fpp2) library(ggplot2) library(forecast) autoplot(beer, main = 'Australian quarterly beer production')

autoplot(pigs, main = 'Number of pigs slaughtered in Victoria')

autoplot(dowjones, main = 'Dow−Jones index')

- Forecasting is estimating how the sequence of observations will continue into the future.
- We usually think probabilistically about future sample paths
- What range of values covers the possible sample paths with 80% probability?

beer <- window(ausbeer, start = 1992, end = c(2005,4)) beer.arima <- auto.arima(beer) autoplot(forecast(beer.arima))

Average method: forecast of all future values is equal to mean of historical data.

Naïve method: forecasts equal to last observed value.

Seasonal naïve method: forecasts equal to last value from same season.

## average method beerfit.mean <- meanf(beer, h = 11) ## naive method beerfit.naive <- naive(beer, h = 11) ## seasonal naive method beerfit.snaive <- snaive(beer, h = 11) cols <- c("mean" = "#0000ee","naive" = "#ee0000","snaive" = "green") ## plot autoplot(beerfit.mean, PI = FALSE, main ='Forecasts for quarterly beer production') + geom_line(aes(x=time(beerfit.mean$mean),y=beerfit.mean$mean,colour='mean')) + geom_line(aes(x=time(beerfit.naive$mean),y=beerfit.naive$mean,colour='naive')) + geom_line(aes(x=time(beerfit.snaive$mean),y=beerfit.snaive$mean,colour='snaive')) + guides(fill=FALSE) + scale_colour_manual(name="Forecasts",values=cols)