#### Evaluating the system: Part 1

Posted on January 6, 2011 at 5:00 AM |

Among the kinds of inferential statistics that are most useful to traders are t-tests. T-tests are useful for determining the probability that the mean or sum of any series of independent values (derived from a sampling process) is greater or less than some other such mean, is a fixed number, or falls within a certain band. For example, t-tests can reveal the probability that the total profits from a series of trades, each with its individual profit/loss figure, could be greater than some thr...

Read Full Post »#### Evaluating the system: Part 2

Posted on January 6, 2011 at 4:00 AM |

The parameters of the trading model have already been set. A sample of data was drawn from a period in the past, in this specific case, 1/2/1990 through 3/31/2000; this is the out-of-sample or verification data. The model was then run on this out of- sample data, and it generated simulated trades. Forty-five trades were taken. This set of trades can itself be considered a sample of trades, one drawn from the population of all trades that the system took in the past or will take in the future;...

Read Full Post »#### Evaluating the system: Part 3a

Posted on January 6, 2011 at 3:00 AM |

What if the distribution is not normal? An assumption in the t-test is that the underlying distribution of the data is normal. However, the distribution of profit/loss figures of a trading system is anything but normal, especially if there are stops and profit targets, which shows the distribution of profits and losses for trades taken by the Directional RSI system. Think of it for a moment. Rarely will a profit greater than the profit target occur. In fact, a lot of trades are going to bunch...

Read Full Post »#### Evaluating the system: Part 3b

Posted on January 6, 2011 at 2:00 AM |

**Normal Distribution test (Skewness-Kurtosis).**

**Serial Correlation test (Durbin-Watson).**

#### Evaluating the system: Part 4

Posted on January 6, 2011 at 1:00 AM |

Over the 10 years of data on which the system was optimized, there were 45 trades (n= 45). The mean or average trade yielded about $199.4936, and the trades were normally variable, with a sample standard deviation of around ±$150.7709. The expected standard deviation of the mean suggests that if samples of this kind were repeatedly taken, the mean would vary only about one-tenth as much as the individual trades, and that many of the samples would have mean profit abilities in the range o...

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