Financial Econometrics and Empirical Market Microstructure
Time-Warped Longest Common Subsequence (T-WLCS)
The basic idea is to unite both DTW and LCSS approaches (Guo and Siegelmann 2004)
f 0, _if _i = 0 _or_j = 0
cij = max {a-i, j, ci, j_i, c,-_ij_i + 1 ,_if_i, j >0, Qt = Cj (5)
: max Ci_i, j, cij_i} , _if_i, j > 0, Qi ф Cj
Example 1.C = 41516171, Q = 4567, LCS(C, Q) = 4, T-WLCS(C, Q) = 4 Example 2. C = 44556677, Q = 4567, LCS(C, Q) = 4, T-WLCS(C, Q) = 8 Example 3. C = 4455661111177, Q = 4567, LCS(C, Q) = 4, T-WLCS(C, Q) = 8
A time series X is said to Granger-cause Y if it can be shown, usually through a series of t-tests and F-tests on lagged values of X (and with lagged values of Y also included), that those X-values provide statistically significant information about future values of Y (Granger 1969).
