Ten-bar patterns for SPY

If I toss nine unbiased coins simultaneously there are 2^9 = 512 unique patterns of heads and tails possible. If I now toss another coin, the outcome is unaffected by the pattern of the nine coins.

The question is: does the same apply to traded instruments?

A trade is not a coin flip but is the result of a buyer and seller agreeing to do the trade. Each has their reasons. The next day (bar) one is in profit, the other is in loss. The latter is anxious to cut his loss. This, I think, gives bias to the next trade, which a coin does not have.

To try and answer this question I have analysed 5,693 daily bars of the SPY index for the period 29 January 1993 to 4 September 2015. Here is a count of up-days within a moving 10-bar window. There is clearly a bias to the upside.

0 0
1 15
2 93
3 494
4 1093
5 1477
6 1356
7 782
8 309
9 66
10 8

I also harvested by hand 1,536 5-minute bars from four forex pairs. Here is the data, expressed in percent. Series 1 is the FX, series 2 is the result of 10-coin flips, and series 3 is the SPY. Note that the x-axis should read 0 to 10, not 1 to 11. Note how close FX and SPY are to each other, and their difference with the unbiased coin flips.

I am curious to know if the direction of the tenth bar can be predicted from the pattern of the preceding nine bars. For example, in 5,396 bars there are only three occasions of nine consecutive down bars (0). In every case, this was followed by an up bar (1). My notation for these three occurrences is 3×0/3. In another data base of 21,297 bars there are only 13 occasions of nine consecutive down bars, all of which were followed by an up bar, i.e. 13×0/13.

I have written a little program that holds all the patterns that have appeared in the past. As new patterns are formed, they are added to the data base.

The program tells me how many times the same pattern has appeared with a 0 and with a 1 at the end (i.e. 14×3/11). If this is today’s pattern, I can see tomorrow’s pattern by sliding the binary number one notch to the left. In other words, today’s pattern was available yesterday.

From the numbers, is it reasonable to assume the day is more likely to an up-day? Does the data indicate that the tenth bar is influenced by the preceding nine bars, or is the tenth bar a 50/50 coin flip?

Thank you for addressing this question, Helmut