Financial issues: loans, mortgage, investment

Prices often form patterns that can be evaluated using probability methods, or simply viewed in much the same way as a frequency distribution, or histogram. Because the concepts are sound, but the statistical analysis is often difficult because of limited amounts of data or changing conditions, analysts have taken a much more empirical approach toward studying price distributions. The following section will look at some innovative ways to look at price distributions and how they are interpreted into trading opportunities.

Applying any technique to a rolling time interval of the most recent N bars is a common method of keeping in tune with current market conditions. in the case of a simple moving average, we should be very familiar with the lag that is introduced. For trends, when prices are moving steadily higher, the lag causes the trendline to be much lower.There is a similar lag when using the most recent N bars to calculate a standard deviation, even when the data has been detrended. If we are measuring the volatility of the market, and prices rally quickly, the volatility rises. This will be seen in the larger value of 1 standard deviation measured over a fixed number of days, or bars. If we are looking for a confirmation of a buy signal based on an increase in volatility, we should get it.
However, the volatility represented by the standard deviation will not decline as fast as we expect because of the same lag. Once higher volatility has occurred on a single day. it will remain part of the standard deviation value until it passes completely out of the calculation window. That will prevent a new volatility event from being recognized soon after a short decline in volatility. It will also make it difficult, if not impossible, to get a timely exit signal on reduced volatility, because the lag keeps the volatility appearing high until at least part of this new, more active price movement begins to pass out of the end of the calculation window.