# How to measure statistical significance of a non-binary-position trading strategy for an irregular time series?

What are the different ways to identify/measure whether a trade strategy is statistically significant?

Specifically I have an irregular time series of individual trades between:

• other buyers and sellers
• myself and other buyers and sellers

There are attributes that make this analysis challenging:

• the timeseries is irregular (different amount of time between trade events)
• the positions which generate returns are not binary: the exposure changes in size and the average purchase price changes.
• the number of trades which increase a position is not always the same as the number of trades which reduce a position.

Thoughts are that the percentage returns can't be normalized using duration as some timestamps are identical which would results in a zero denominator value.

The below table is an example, showing datetime, price and volume of each trade. All rows where trade_size is non-zero are trades generated by the strategy. capital_allocation is the position size which has been built up. percentage_returns is the percentage difference between the selling price and the wighted average purchase price.

+-------------------------+----------+--------+-------------+--------------------+--------------------+
| datetime                | price    | volume | trade_sizes | capital_allocation | percentage_returns |
+-------------------------+----------+--------+-------------+--------------------+--------------------+
| 2018-06-22 20:31:55.552 | 132000   | 0.031  | 0           | 0                  |                    |
+-------------------------+----------+--------+-------------+--------------------+--------------------+
| 2018-06-22 20:31:55.552 | 132000   | 0.031  | 0           | 0                  |                    |
+-------------------------+----------+--------+-------------+--------------------+--------------------+
| 2018-06-22 20:31:55.560 | 132000   | 0.031  | 0           | 0                  |                    |
+-------------------------+----------+--------+-------------+--------------------+--------------------+
| 2018-06-22 20:31:55.658 | 132000   | 1.161  | 0           | 0                  |                    |
+-------------------------+----------+--------+-------------+--------------------+--------------------+
| 2018-06-22 20:31:55.712 | 128166   | 0.1469 | 0.1469      | 0.1469             |                    |
+-------------------------+----------+--------+-------------+--------------------+--------------------+
| 2018-06-22 20:31:55.712 | 128161.2 | 0.0172 | 0.0172      | 0.1641             |                    |
+-------------------------+----------+--------+-------------+--------------------+--------------------+
| 2018-06-22 20:31:55.712 | 128160   | 0.4343 | 0.4343      | 0.5984             |                    |
+-------------------------+----------+--------+-------------+--------------------+--------------------+
| 2018-06-22 20:31:55.712 | 127963.2 | 1.0391 | 1.0391      | 1.6375             |                    |
+-------------------------+----------+--------+-------------+--------------------+--------------------+
| 2018-06-22 20:31:55.846 | 132000   | 0.07   | -0.07       | 1.5675             | 0.030962690863481  |
+-------------------------+----------+--------+-------------+--------------------+--------------------+
| 2018-06-22 20:31:55.868 | 132000   | 0.0775 | -0.0775     | 1.49               | 0.030962690863481  |
+-------------------------+----------+--------+-------------+--------------------+--------------------+
| 2018-06-22 20:31:56.317 | 131996.4 | 0.1191 | -0.1191     | 1.3709             | 0.030934573699185  |
+-------------------------+----------+--------+-------------+--------------------+--------------------+
| 2018-06-22 20:31:56.317 | 132000   | 1.3709 | -1.3709     | 0                  | 0.030962690863481  |
+-------------------------+----------+--------+-------------+--------------------+--------------------+
| 2018-06-22 20:31:56.547 | 132000   | 0.063  | 0           | 0                  |                    |
+-------------------------+----------+--------+-------------+--------------------+--------------------+
| 2018-06-22 20:31:56.558 | 132000   | 0.063  | 0           | 0                  |                    |
+-------------------------+----------+--------+-------------+--------------------+--------------------+
| 2018-06-22 20:31:56.560 | 132000   | 0.063  | 0           | 0                  |                    |
+-------------------------+----------+--------+-------------+--------------------+--------------------+
| 2018-06-22 20:31:56.619 | 132000   | 0.031  | 0           | 0                  |                    |
+-------------------------+----------+--------+-------------+--------------------+--------------------+


What are some approaches to prove that the trading strategy is successful and statistically significant?