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# Testing Summary Statistics On Stocks

When I am charting a stock, I am often left asking questions that typical charting tools don't answer. So I decided to work on a different way of looking at stock performance data.

Stock Selection:
I picked Axion for my first analysis because it's a classic start up company, and I am very interested in start up companies. I will be adding an analysis for Lynas (OTCPK:LYSDY) and several other types of companies as yet to be determined.

Cumulative Distribution:
The cumulative distribution of daily stock changes provides a way of putting stock movements into a statistical framework that lets you determine how unusual a DAILY stock change is in terms of typical variation for that stock over time. In other words, the focus of this type of analysis is not on price levels, but changes in price levels on a daily basis.

Crossing Point:
The crossing point of the cumulative distribution tells you what proportion of the time daily stock changes are positive or negative. The analysis also tells me what proportion of the time there are no stock changes.

Daily Stock Volume and Changes in Daily Stock Prices:
The second set of analyses will be looking at the association between daily stock volume and daily changes in stock price changes. I ran an initial analysis on Axion, but the results were not in line with my expectations. I believe I know the reason why, and will be conducting a more in-depth analysis on this issue.

Outliers:
Outliers are comparatively rare large changes. Outliers are removed from the generation of the general statistics. However, I will be adding a table that looks specifically at each outlier event, and the frequencies of those kinds of events. For Axion, several of the outlier events were stock offerings. I am very interested to see how these events effect trend data.

Looking at Axion Power:
Axion Power cumulative percent average daily price changes over four years 1/2/2009 through 8/23/2012. Data is from Yahoo financial.

Seven Outliers were removed.

The mean price change is -.004.
The Standard deviation is .0473.
Two standard deviations is .0946.

The price distribution is mostly symmetric. That means statements of the following kind may be made. Movements of plus or minus 1 standard deviation occur 68.2% of the time. Movements in excess of plus or minus 2 standard deviations occur less than 5 % of the time.

So a change of plus 4.7 cents would be expected to occur less than 34% of the time (68.2 divided by 2).

Note that the cumulative distribution does not cross the vertical axis at 50%. This means it's more likely for negative price movements than positive movements. In fact, negative price changes occur about 67.5% of the time. This means the trend over time is negative, which is no surprise.

With this data, there are statistical associations of delta share price with share volume. However, this needs to be looked at further because share volume back in the early days was very much smaller than recent share volumes. So the analysis will have to be performed within year.