You can see that if the correlation is in State 1 or 2 (Vertical) then the probability that the next sequence of correlations on 7 candles will increase, is very high.
State 1: Probability next 7 in higher state = (1 - (0.3)) x 100 = 70%
State 2: Probability next 7 in higher state = (1 - (0.0448) + (0.2239)) x 100 = 73.13%
Using the transition probabilities as a predictor is straight forward.
If I consider the sequence (1,-1,1,-1,1,-1,1,-1) as a showing how the last 8 bars closed (up = 1, down = -1).
Then I can create an duplicate sequence lag 1 bar to look at the auto correlation as so:
- Original Sequence (1st 7 Bars): (1,-1,1,-1,1,-1,1)
- Copy Sequence (Last 7 Bars): (-1,1,-1,1,-1,1,-1)
The 'auto correlation' in this case is -1 (State 1). If we introduce a 9th Bar with Value -1 and now look at the auto correlation in the last 7 Bars.
The Correlation value is -0.75. So the correlation value has increased from -1 to -0.75 due to the introduction of the 9th bar which was in the same direction as the 8th bar. In the previous case, all the bars in successive time were in opposite directions, with the introduction of the 9th bar, this time in the same direction as the 8th bar, the correlation in the last 7 has increased.
So going back to the transition matrix, we know that if the correlation state in the last 7 bars is very low ( 1 or 2) there is a circa 70% probability that the incoming bar will increase the correlation value (therefore correlation state) which can only happen if the incoming bar is in the same direction as the last bar observed.
i.e. there is a 70% chance that the 9th bar will be in the same direction as the 8th bar given that the correlation of the previous 8 bars was in state 1 (Correlation value -1).
The general principle is that if you observe the auto correlations of any market feature, you can calculate the transition probabilities between the auto correlation states. If the auto correlation is in a very low state, then there is a very high probability that the incoming bars will have a higher auto correlation, that implies that the incoming bar is more likely than at any other time to have similar characteristics to the bar just closed.
So if the market feature being looked at was the True Range. If the true range in the last bar is above the ATR for a period and rising, where the auto correlation of true range is in a very low state, then it is very likely that the incoming and future bars will also have a higher and rising True Range.