I believe there are 4 cases, conventionally called:

h(t) > h(t-1) and l(t) > l(t-1) an uptrend day

h(t) < h(t-1) and l(t) > l(t-1) an inside day

h(t) > h(t-1) and l(t) < l(t-1) an outside day

h(t) < h(t-1) and l(t) < l(t-1) a downtrend day

Victor Niederhoffer writes: 

Excuse me? 

Alex Castaldo replies: 

OK, OK, let's call then upshift day and downshift day then.


Kim Zussman adds: 

What about outie and innie?

Using SPY (2000-present), checked for outside days (today's high > yesterday's high, today's low < yesterday's low). Then checked the return for the next day.

Days after outies were also checked if the market was up-trending (20DMA > 100DMA), and, in addition to up-trending, if the intra-day return was up (C>O). Here are the c-c returns after (vs zero), for all days (c-c ret), all days after outside days outie+1), days after outside days and up-trending (and 20>100), days after outside days and up-trending, and the outside day was up intra-day (and C>O):

One-Sample T: c-c ret, outie+1, and 20>100, and C>O

Test of mu = 0 vs not = 0

Variable        N       Mean     StDev   SE Mean       95% CI             T
c-c ret         3550   0.00022  0.0131  0.0002  (-0.0002, 0.0006)   1.01
outie+1         353   0.00049  0.0118  0.0006  (-0.0007, 0.0017)   0.77
and 20>100  234   0.00061  0.0090  0.0005  (-0.0005, 0.0017)   1.03
and C>O       89    -0.00047  0.0090  0.0009  (-0.0023, 0.0014)  -0.49

Zeroish, with none significant, and days after outside days and up-trending winning the race at 0.06% per day avg.


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