Are the density graphs shown about the log returns

Posted 2022-07-01 clearc

1. Are the density graphs shown about the log returns? If so, can you test if it‘s a normal distribution test or not? You can use the Jacque-Bera test.
Based on your plot of the histogram/distributions of returns. Do you observed Heavy-tailedness in the data? (lots of extremely large or negatively large values)
b. Do you observed peakedness of the data? (sharpe peak of the distribution)

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2. One suggestion, don‘t just present the graphs to me. Write a report on what you see with them. You don‘t even need to send all the plots. Select some that are useful. For the random sampling, can you explain what you plot in a paragraph? I actually don‘t need to have a full histogram. I just want something like what attached in the email (gaps between observations.png)

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Here is what you want to do: Take 1 year or even just 6 months first, plot a graph counting the number of gaps for different seconds. ( Graph looks like the one attached). Say for example, on the graph (2,20) means there are 20 gaps between two consecutive trade arrivals of 2 second, (30,10) means there are 10 gaps between two consecutive trade arrivals of 30 seconds. In general you would like to see a decreasing trend: less gaps of long seconds between two trades. Don‘t include 0 and 1 in your graph because that will be too many!

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3.
Let‘s do the volatility signature plot:

This plot cares about whether there are too much noise in the data:

First, calculate daily realized volatility(RV) with different price sampling frequencies. Remember what I show you last time below?:

Create a 2014 by 234 matrix. we get volatility over each 100 seconds so we will have 234 volatility ( remember we have 23401 seconds in part 1, so you will have 23400 log returns and 23400/100 =234 for the number of 100 second intervals). Based on the return matrix you generated in part 1, you need to accumulate the squared log returns over each 100 second interval. This will be your volatility for that interval. Follow this you will then create a 2014 by 234 matrix.

The above is 100-RV of price sampled at 1 second frequency. We will use that later on. For now I want you to accumulate to 1-day (i.e., 23400 seconds) for prices sampled at 1 second, 5 seconds, 10 seconds, 20 seconds, 30s, 50, 1min, 100s, 300s, 1000s, 2000s...just do as many as you can. When you sample prices not of 1 second, you just simply skip some prices in between.

Next, plot the RV on the y-axis, (1 second, 5 seconds, 10 seconds, 20 seconds, 30s, 50, 1min, 100s, 300s, 1000s, 2000s) on the x-axis to see how they are related.

4. trade arrival:

Now you know the distribution of the gaps, what is the average waiting time for a trade to arrive? what is the average number of trades per second in a year? what is the average time length of no trade in a year? Can you see if the arrival distribution fits in a Poisson arrival process?

Thank and let me know

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