Question

I have a long numerical time series data of approximately 200,000 rows (lets call it Z).

In a loop, I subset x (about 30) consecutive rows from Z at a time and treat them as the query point q.

I want to locate within Z the y (~300) most correlated time series segments of length x (most correlated with q).

What is an efficient way to accomplish this?

Answer 1

The code below finds the 300 segments you are looking for and runs in 8 seconds on my none too powerful Windows laptop, so it should be fast enough for your purposes.

First, it constructs a 30-by-199971 matrix (Zmat), whose columns contain all of the length-30 “time series segments” you want to examine. A single call to cor(), operating on the vector q and the matrix Zmat, then calculates all of the desired correlation coefficients. Finally, the resultant vector is examined to identify the 300 sequences having the highest correlation coefficients.

# Simulate data
nZ <- 200000
nq <- 30
Z <- rnorm(nZ)
q <- seq_len(nq)

# From Z, construct a 30 by 199971 matrix, in which each column is a
# "time series segment". Column 1 contains observations 1:30, column 2
# contains observations 2:31, and so on through the end of the series.
Zmat <- sapply(seq_len(nZ - nq + 1),  
               FUN = function(X) Z[seq(from = X, length.out = nq)])

# Calculate the correlation of q with every column/"time series segment.
Cors <- cor(q, Zmat)

# Extract the starting position of the 300 most highly correlated segments    
ids <- order(Cors, decreasing=TRUE)[1:300]

# Maybe try something like the following to confirm that you have
# selected the most highly correlated segments.
hist(Cors, breaks=100)
hist(Cors[ids], col="red", add=TRUE)