Naive Weighted Inflation Forecast

inflation_survey_weight.R

library(Quandl)
p <- 100 * Quandl('FRED/GDPDEF', collapse = 'quarterly', start_date = '1960-01-01', end_date = '2012-01-01', type = 'ts', transformation = 'rdiff')

#Michigan Inflation Expectations aren't in Quandl yet
library(quantmod)
getSymbols("MICH",src="FRED")
#Median expected price change next 12 months, Survey of Consumers.

#Convert to ts object
MICH.start <- as.numeric(format.Date(start(MICH), '%Y'))
MICH.start <- c(MICH.start, as.numeric(format.Date(start(MICH), '%m')))
MICH <- ts(MICH, start = MICH.start, freq = 12)

#Aggregate to quarterly frequency
survey.mean <- aggregate(MICH, FUN = mean, nfrequency = 4)
survey.median <- aggregate(MICH, FUN = median, nfrequency = 4)

#Survey measures 12 month expected price change. Convert to implied quarterly price change
survey.mean <- 100 * ((survey.mean/100 + 1)^(1/4) - 1)
survey.median <- 100 * ((survey.median/100 + 1)^(1/4) - 1)

#Calculate MSFE for simple strategies that take a linear combination of inflation survey. Note that this changes the forecast period to be when we have values for the survey.
f.start <- c(1973,2)
f.end <- c(2012, 1)

naive <- function(w = 0, step = 1){
  
  survey.lag <- lag(survey.mean, -step)
  survey.lag <- window(survey.lag, start = f.start, end = f.end)
  
  p.lag <- lag(p, -step)
  p.lag <- window(p.lag, start = f.start, end = f.end)
  
  #Give the survey weight w
  pred <- w * survey.lag + (1 - w) * p.lag
  actual <- window(p, start = f.start, end = f.end)
  
  return(mean((pred - actual)^2))
  
}#end naive


w <- seq(from = 0, to = 1, by = 0.01)
step <- 1:8
w.vector <- rep(w, each = length(step))
step.vector <- rep(step, times = length(w))

MSFE.naive <- mapply(naive, w = w.vector, step = step.vector)
parameters <- cbind(w.vector, step.vector)
colnames(parameters) <- c('w', 'step')
MSFE.naive <- cbind(parameters, MSFE.naive)
MSFE.naive <- data.frame(MSFE.naive)
MSFE.naive$step <- as.factor(MSFE.naive$step)

library(ggplot2)
qplot(w, MSFE.naive, col = step, data = MSFE.naive, geom = 'line', size = I(2)) + theme_bw() + xlab('Weight Given to Survey') + ylab('MSFE') + labs(colour = "Steps Ahead")