Solved – Asynchronous (irregular) Time Series Analysis

cross correlationrtime seriesunevenly-spaced-time-series

I am trying to analyze the lead-lag between time series of two stock prices.
In regular time series analysis, we can do Cross Correlaton, VECM (Granger Causality). However how does one handle the same in irregularly spaced time series.

The hypothesis is that one of the instruments leads the other.

I have data for both symbols to the microseconds.

I have looked at RTAQ package and also tried applying VECM.
RTAQ is more on a univariate time series while VECM is not significant on
these timescales.

> dput(STOCKS[,]))
structure(c(29979, 29980, 29980, 29980, 29981, 29981, 29991, 
29992, 29993, 29991, 29990, 29992), .Dim = c(6L, 2L), .Dimnames = list(NULL, c("Pair_Bid", "Calc_Bid" )), index = structure(c(1340686178.55163, 1340686181.40801, 1340686187.2642, 
1340686187.52668, 1340686187.78777, 1340686189.36693), class = c("POSIXct", "POSIXt"), tzone = ""), class = "zoo")

Best Answer

I know of one possible solution, but it is sufficiently complicated that I'm going to take the easy option and link you to the relevant academic paper (a critically under-rated paper in my opinion):

Frank de Jong, Theo Nijman (1997) "High Frequency Analysis of Lead-Lag Relationships Between Financial Markets"

I'm sure more work must have been done on this problem since then. A good way to find it is to use the "citations" page on ideas.repec. A link to the relevant page for the above-mentioned paper is here. A few titles look quite relevant.

Related Solutions

Solved – Highly irregular time series

I have spent quite some time building a general framework for unevenly-spaced time series: http://www.eckner.com/research.html

In addition, I have written a paper is about trend and seasonality estimation for unevenly-spaced time series.

I hope you will find the results helpful!

Solved – Moving average of irregular time series data using R

If the problem is just plotting the data (i.e., if you have already identified the faults), you can simply write a function that counts the events in the past hour, as follows.

# Sample data, with two peaks
library(zoo)
seconds <- 60*60*24 # One day
lambda <- function(x) ( 1 + sin(2*pi*x/seconds) ^ 2 ) / 2
n <- 100
x <- seconds*sort(runif(n))
x <- x[runif(n) < lambda(x)]
x <- zoo( 0*x+1, x )
plot( index(x), x, type="h" ) 

# Moving average over the past hour
f <- function(u) sum(u - 3600 < index(x) & index(x) <= u )
f <- Vectorize(f)
curve(f(x), xlim=c(0,seconds))

# Exponentially-weighted average, half-life = 1 hour
tau <- 3600
f <- function(u) sum( ifelse(index(x)<=u,exp((index(x)-u)/tau),0) )
f <- Vectorize(f)
curve(f(x), xlim=c(0,seconds))

But this will be inefficient if there is a lot of data. Instead, you can consider two types of events: "a fault occurred" (i.e., enters our window of observation) and "a fault occurred one hour ago" (i.e., leaves our window of observation). Associate the values +1 and -1 to those events, and compute the cumulated sum: that is the number of faults in the previous hour.

# More efficient moving average
y <- merge(x, zoo(-x, index(x) + 3600), fill=0)
plot( cumsum(y[,1] + y[,2]) )

Best Answer

Related Solutions

Solved – Highly irregular time series

Solved – Moving average of irregular time series data using R

Related Question