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R

# Goal:
# A stock is traded on 2 exchanges.
# Price data is missing at random on both exchanges owing to non-trading.
# We want to make a single price time-series utilising information
# from both exchanges. I.e., missing data for exchange 1 will
# be replaced by information for exchange 2 (if observed).
# Let's create some example data for the problem.
e1 <- runif(15) # Prices on exchange 1
e2 <- e1 + 0.05*rnorm(15) # Prices on exchange 2.
cbind(e1, e2)
# Blow away 5 points from each at random.
e1[sample(1:15, 5)] <- NA
e2[sample(1:15, 5)] <- NA
cbind(e1, e2)
# Now how do we reconstruct a time-series that tries to utilise both?
combined <- e1 # Do use the more liquid exchange here.
missing <- is.na(combined)
combined[missing] <- e2[missing] # if it's also missing, I don't care.
cbind(e1, e2, combined)
# There you are.