SAMPLE SIZE AND REPRESENTATIVENESS in Software
SAMPLE SIZE AND REPRESENTATIVENESS UPCA Supplement 2 Scanner In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Printing UPCA Supplement 2 In None Using Barcode generator for Software Control to generate, create UPC A image in Software applications. Although, for statistical reasons, the system developer should seek the largest sam ple possible, there is a tradeoff between sample size and representativeness when dealing with the financial markets. Larger samples mean samples that go farther back in time, which is a problem because the market of years ago may be fundamentally different from the market of todayremember the S&P 500 in 1983 This means that a larger sample may sometimes be a less representative sample, or one that confounds several distinct populations of data! Therefore, keep in mind that, although the goal is to have the largest sample possible, it is equally important to try to make sure the period from which the sample is drawn is still representative of the market being predicted. GS1  12 Recognizer In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. UCC  12 Encoder In C# Using Barcode generation for .NET framework Control to generate, create UPCA image in .NET applications. EVALUATING A SYSTEM STATISTICALLY
Encoding Universal Product Code Version A In Visual Studio .NET Using Barcode generation for ASP.NET Control to generate, create UPCA Supplement 2 image in ASP.NET applications. Draw UPCA Supplement 2 In Visual Studio .NET Using Barcode generator for Visual Studio .NET Control to generate, create UPC A image in VS .NET applications. Now that some of the basics are out of the way, let us look at how statistics are used when developing and evaluating a trading system. The examples below employ a system that was optimized on one sample of data (the msample data) and then run (tested) on another sample of data (the outofsample data). The outofsample evaluation of this system will be discussed before the insample one because the statistical analysis was simpler for the former (which is equivalent to the evaluation of an unoptimized trading system) in that no corrections for multiple tests or optimization were required. The system is a lunar model that trades the S&P 500; it was published in an article we wrote (see Katz with McCormick, June 1997). The TradeStation code for this system is shown below: Making UPCA Supplement 5 In VB.NET Using Barcode creation for Visual Studio .NET Control to generate, create UPC Code image in .NET applications. Bar Code Encoder In None Using Barcode generation for Software Control to generate, create barcode image in Software applications. Example 1: Evaluating the OutofSample Test
Draw Data Matrix ECC200 In None Using Barcode maker for Software Control to generate, create Data Matrix 2d barcode image in Software applications. UPC  13 Drawer In None Using Barcode generator for Software Control to generate, create UPC  13 image in Software applications. Evaluating an optimized system on a set of outofsample data that was never used during the optimization process is identical to evaluating an unoptimized system. In both cases, one test is run without adjusting any parameters. Table 41 illustrates the use of statistics to evaluate an unoptimized system: It contains the outofsample or verification results together with a variety of statistics. Remember, in this test, a fresh set of data was used; this data was not used as the basis for adjustments in the system s parameters. 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, l/1/95 through l/1/97; this is the outofsample or verification data. The model was then run on this outofsample data, and it generated simulated trades. Fortyseven 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; i.e., it is a sample of trades taken from the universe or population of all trades for that system. At this point, some inference must be made regarding the average profit per trade in the population as a whole, based on the sample of trades. Could the performance obtained in the sample be due to chance alone To find the answer, the system must be statistically evaluated. To begin statistically evaluating this system, the sample mean (average) for n (the number of trades or sample size) must first be calculated. The mean is simply the sum of the profit/loss figures for the trades generated divided by n (in this case, 47). The sample mean was $974.47 per trade. The standard deviation (the variability in the trade profit/loss figures) is then computed by subtracting the sample mean from each of the profit/loss numbers for all 47 trades in the sample; this results in 47 (n) deviations. Each of the deviations is then squared, and then all squared deviations are added together. The sum of the squared deviations is divided hy n  I (in this case, 46). By taking the square root of the resultant number (the mean squared deviation), the sample standard deviation is obtained. Using the sample standard deviation, the expected standard deviation of the nean is computed: The sample standard deviation (in this case, $6,091.10) is divided by the square root of the sample size. For this example, the expected standard deviation of the mean was $888.48. To determine the likelihood that the observed profitability is due to chance alone, a simple ttest is calculated. Since the sample profitability is being compared with no profitability, zero is subtracted from the sample mean trade profit/loss (computed earlier). The resultant number is then divided by the sample standard deviation to obtain the value of the tstatistic, which in this case worked out to be 1.0968. Finally the probability of getting such a large tstatistic by chance alone (under the assumption that the system was not profitable in the population from which the sample was drawn) is calculated: The cumulative tdistribution for that tstatistic is cotnputed with the appropriate degrees of freedom, which in this case was n  1, or 46. Encode ANSI/AIM Code 39 In None Using Barcode creator for Software Control to generate, create Code39 image in Software applications. UPC Symbol Creation In None Using Barcode generator for Software Control to generate, create UPCA image in Software applications. Creating GS1  8 In None Using Barcode generation for Software Control to generate, create GTIN  8 image in Software applications. Generate DataMatrix In Java Using Barcode drawer for Java Control to generate, create Data Matrix image in Java applications. Create ECC200 In VB.NET Using Barcode drawer for .NET Control to generate, create Data Matrix ECC200 image in .NET framework applications. Make DataMatrix In ObjectiveC Using Barcode drawer for iPhone Control to generate, create Data Matrix 2d barcode image in iPhone applications. Scanning GTIN  12 In C#.NET Using Barcode decoder for .NET Control to read, scan read, scan image in .NET applications. Making Bar Code In Java Using Barcode encoder for BIRT Control to generate, create bar code image in BIRT reports applications. Draw UPC Symbol In .NET Using Barcode creation for VS .NET Control to generate, create UCC  12 image in VS .NET applications. Encode Bar Code In None Using Barcode generation for Font Control to generate, create bar code image in Font applications. 
