Case 1 review : Change in the closing price of one day is not a sigificant indicator of next day's more.
Case II:
Objective: To determine if the direction of open and close (C > O or C < O) of one day acts as an indication for the direction of price movement the next day.
Data used:
Dow Jones Industrial Average from 1970 - Daily data. Total bars = 8,241 bars of data.
Condition:
If Yesterday's Close > Yesterday's Open and Today's close > Today's open (or) if yesterday's close < yesterday's open and today's close < today's open, plot 1, otherwise plot 0.
The sum of the above is added and divided by the total sample size (bars used).
Probable inferences:
a: If the probability is significantly higher than 50%, then, today's price direction can be used as a tool for tomorrow's price in the same direction as today (with open and close as the base).
b: If the probability is significantly lower than 50%, then, today's price direction can be used as a tool for tomorrow's price in the opposite direction as today. (with open and close as the base).
c: If the calculated probability is neither significantly higher than 50% or significantly lower than 50%, indifference exists.
I use 50% mark here because that is the probability through coin toss that C > O or C < O.
Inference:
From 1970-2002, there existed a probability of 51.1467% that price will move in the same direction it did the previous day. Putting it in other terms, 48.8853% of the time, it moved in the opposite direction.
I have once again not validated this statement by using statistical hypothesis testing but by view of the eye, the conclusion that can be reached is that historically, today's relationship (direction wise) between open and close does not serve as a sufficient information as to tomorrow's price movement.
I have attached the test result.
I request members to comment on this.
Obliged.