The study of the collection, organization, analysis, and interpretation of data. Questions may deal with descriptive statistics, probability distributions, random variables, sampling, regression, density estimation, filtering, inference, estimation theory, or computational statistics.
22
votes
6answers
5k views
How are correlation and cointegration related?
In what ways (and under what circumstances) are correlation and cointegration related, if at all? One difference is that one usually thinks of correlation in terms of returns and cointegration in ...
17
votes
2answers
557 views
How do you correct Max Draw-Down for auto-correlation?
When returns are auto-correlated, calculating a Sharpe ratio := $\frac {mean(x)}{\sqrt{var(x)}}$, (where $x$ are the returns) is complicated, but basically solved (see, e.g. Lo (2005)). Without the ...
14
votes
6answers
1k views
How random are financial data series?
Pseudorandom number generators are often tested using e.g. a test suite like Diehard tests or Dieharder. If one would run these tests e.g. on stock market time series or other financial data, would ...
13
votes
3answers
3k views
What is the best way to “fix” a covariance matrix that is not positive semi-definite?
I have a sample covariance matrix of S&P 500 security returns where the smallest k-th eigenvalues are negative and quite small (reflecting noise and some high correlations in the matrix).
I am ...
12
votes
5answers
3k views
What is the intuition behind cointegration?
What is the intuition behind cointegration? What does the Dickey-Fuller test do to test for it? Ideally, a non-technical explanation would be appreciated.
Say you need to explain it to an investor ...
12
votes
4answers
1k views
Are two identical time series cointegrated?
I did cointegration test on two identical time series, and the result shows that they are not cointegrated, but intuitively, I think they are.
Can anyone share some thoughts on this? Thanks!
11
votes
2answers
609 views
What is the precision of standard deviation estimates with small samples?
I was asked today to "quantify" the precision of an estimated the standard deviation from a small sample, I was not sure how to answer.
The case is quite simple, I have a sample of $n=25$ measures ...
11
votes
3answers
538 views
What are some research articles on using principle components to generate alpha?
Here's an example by Marco Avellenada from NYU titled "Statistical Arbitrage in the U.S. Equities Market". The idea of this paper involves capturing mean reversion in the residual returns of a ...
11
votes
1answer
3k views
How to interpret the eigenmatrix from a Johansen cointegration test?
I ran a Johansen cointegration test on 3 instruments, A B and C.
The results that I got are:
R<=x | Test Stat | 90% | 95% | 99%
r=0 --> 36.7 | 18.9 | 21.1 | 25.8
r=1 --> ...
10
votes
2answers
278 views
How to group timeseries showing similar curve
I am trying to classify similar looking curves of a timeseries and was wondering what is the best algorithm to research. Reading R, it looks like k-means clustering could be applied - but I don't know ...
10
votes
4answers
1k views
How do you evaluate a covariance forecast?
Suppose you have two sources of covariance forecasts on a fixed set of $n$ assets, method A and method B (you can think of them as black box forecasts, from two vendors, say), which are known to be ...
10
votes
0answers
141 views
A non parametric study of VaR with kernel density
I'm working in order to compare the calculation of the VaR between the methodology of copulas and kernel density, all this by using the software r.
The process that I follow is:
Obtain a sample ...
9
votes
2answers
1k views
How do I calculate the skewness of a portfolio of assets?
I need to calculate the skewness of a portfolio consisting of 6 assets. I know that for that I would need the co-skewness matrix between the assets. Does anybody know the formula for co-skewness or ...
9
votes
1answer
385 views
How are Expected Shortfall and Variance related?
I would like to know how Expected Shortfall $SF_\alpha$ and variance $\sigma^2$ are related.
If I follow what Aaron Brown answered in this post, when the underlying distribution is Normal with ...
9
votes
1answer
359 views
Comparing backtesting returns with real trading returns
I have 10 years of backtested simulated performance of some trading strategy (using historical prices), and N months of actual trading performance. What statistical test can I do find out if I'm on ...
9
votes
1answer
341 views
How to estimate the covariance of an index with a basket of stocks?
What would be an ideal way to estimate the covariance of an index with a basket of stocks? For example, should I use one-tail ANOVA test or an individual stock & index F-test?
8
votes
5answers
1k views
What exactly is meant by “microstructure noise”?
I see that term tossed around a lot, in articles relating to HFT, and ultra high frequency data.
It says at higher frequencies, smaller intervals, microstructure noise is very dominant.
What is ...
8
votes
4answers
2k views
Should I use an arithmetic or a geometric calculation for the Sharpe Ratio?
What are the advantages/disadvantages of using the arithmetic Sharpe Ratio vs the geometric Sharpe Ratio? Is one more correct? Or is one better in certain circumstances?
8
votes
3answers
377 views
How to test for and how to simulate price rise/fall asymmetry in the stock market
One of the stylized facts of financial time series seems to be a fundamental asymmetry between smooth upward movements over longer periods of time followed by abrupt declines over relatively shorter ...
8
votes
2answers
2k views
How can I compare distributions using only mean and standard deviation?
I only have means and standard deviations of samples of two random variables. What technique can I use to determine how similar the distributions these describe are? Assume that the values are built ...
8
votes
1answer
309 views
Has any research used Bayesian networks to estimate risk factor betas?
Is there any published research on estimating the beta of a security with respect to one or more risk factors via Bayesian networks?
I'd like to see if this is a promising angle of research.
8
votes
3answers
845 views
How to generate synthetic FX data for backtesting?
I want to generate synthetic forex data for the purpose of backtesting my trading algorithms. I have some rough ideas in mind on how to do this:
Start with a curve representing a trend, then randomly ...
8
votes
1answer
746 views
What is the Sugihara Trading System?
I recently heard the term Sugihara Trading System. I guess it might be some trading strategy or a special model to predict trends in market data, but I couldn't find out anything about it. Does anyone ...
7
votes
3answers
523 views
Hidden Markov Model & Its Application
I have started reading about HMM it gives an intuitive idea about what HMM is all about. I am looking out for example where its applied to Equity model using R / Excel. The material which I read so ...
7
votes
1answer
999 views
Why is the first principal component a proxy for the market portfolio, and what other proxies exist?
Let's say that I have a universe of stocks from a certain sector. I want to compute the market portfolio of this sector. Beta is the covariance between each stock and the market. But how do you ...
7
votes
4answers
706 views
How to interpolate gaps in a time series using closely related time series?
I am trying to construct a daily time series of prices and returns for some large universe of securities. However, all I have available are a monthly time series of the prices/returns (as well as ...
7
votes
5answers
790 views
How can I quantitatively test the validity of momentum indicators?
I am learning about quantitative finance, and I am struck by how different it is from the techniques that make it into magazines and TV, particularly technical analysis. Specifically, if they say an ...
7
votes
1answer
723 views
Skewness and Kurtosis under aggregation
Returns possess non-zero skewness and excess kurtosis. If these assets are temporally aggregated both will disappear due to the law of large numbers. To be exact, if we assume IID returns skewness ...
7
votes
3answers
281 views
How to improve the consistency of explained variance statistics in a linear equity model?
I have an intraday equity returns linear model that, overall, shows good values in terms of $R^2$, p-value and other explained variance statistics. Around 70% of the stocks show consistent R-squared ...
7
votes
2answers
298 views
How to combine various equity measures into a single measure (vector magnitude)
I have several measures:
...
7
votes
1answer
563 views
Why does the following data fail my cointegration test?
I have some closing price data for two Australian banks which track each other very closely.
http://dl.dropbox.com/u/12337149/stat/CBA.csv
http://dl.dropbox.com/u/12337149/stat/WBC.csv
Code from ...
6
votes
1answer
1k views
How do I reproduce the cross-sectional regression in “Intraday Patterns in the Cross-section of Stock Returns”?
Recently I was trying to reproduce the results of "Intraday Patterns in the Cross-section of Stock Returns". The authors used cross-sectional regression to determine which intraday lags have ...
6
votes
1answer
464 views
What is the best way to forecast prepayment rate in an emerging market mortgage loan portfolio?
I constructed a model to forecast the prepayment rates for a mortgage loan portfolio (of mortgages in an emerging market) using probit regression on factors such as loan-to-value, PTI, time from ...
6
votes
2answers
191 views
Is it better to grade hedging strategies based on the sum of absolute or squared hedging errors?
Let's say I have one strategy that has a hedging error of:
2,
2,
-2,
-2
Let's say I have another strategy that has a hedging error of
.5,
.5,
3,
3
Would it be a better idea to grade the hedging ...
6
votes
1answer
361 views
Are shorter holding period strategies better?
Consider two statistically identical strategies (identical information ratios, sample size, ratio of transaction costs to total profit, etc.) except that one has a much shorter average holding period. ...
6
votes
1answer
130 views
What tradeoff is there to using an accurate estimate with a large confidence interval?
I am working on calibrating a Heston model from simulated historical stock data.
After obtaining an accurate estimate of the model parameters I found very large 95% confidence intervals for these ...
6
votes
2answers
302 views
Efficiency vs. Robustness - To use a constant or not in single factor time-series regression?
Arbitrage pricing theory states that expected returns for a security are linear combination of exposures to risk factors and the returns on these risk factors. Betas, or the exposures of the security ...
5
votes
5answers
1k views
How many explanatory variables is too many?
When researching any sort of predictive model, whether using ordinary linear regression or more sophisticated methods such as neural networks or classification and regression trees, there seems to ...
5
votes
5answers
529 views
How to fit probability density function from sample moments?
If I have calculated the sample mean, variance, skew and kurtosis of a set of data, how would I go about fitting a probability distribution to match these moments (i.e. choosing a probability ...
5
votes
1answer
2k views
Annualzing the log of daily returns riddle
Two popular ways to measure returns are Arithmetic returns and Log returns. Let's define arithmetic (simple period) returns as: P(t) - P(t-1) / P(t-1). Let's define log return as Ln( P(t)/P(t-1) ) or ...
5
votes
1answer
340 views
How to model time series of illiquid stocks - 400 observations (transactions) per 8 hours?
How to model time series which are illiquid - 400 observations (transactions) per 8 hours ? Are there models suitable for this situation which incorporate not only size of the transactions but also ...
5
votes
3answers
761 views
Can the Hurst exponent be greater than one?
Can the Hurst exponent be greater than one? Does it mean that the time series follows a random walk or that it's not stationary?
5
votes
6answers
524 views
Encyclopedia of Statistical Tests
I am aware of: Encyclopedia of Chart Patterns,
Encyclopedia of Technical Analysis.
Question
I'm wondering if there's something similar, but in the form of:
"Encyclopedia of Statistical Backtesting ...
4
votes
2answers
1k views
How can I estimate the degrees of freedom for a Student's T distribution?
I am doing research estimating the value at risk for non-normally distributed assets. I need help in the process of estimating the parameters of Student's t distribution and which method to use. I ...
4
votes
2answers
412 views
How to make the final Interpretation of PCA?
I have question regarding final loading of data back to original variables.
So for example:
I have 10 variable from a,b,c....j using returns for last 300 days i got return matrix of 300 X 10.
...
4
votes
1answer
380 views
Coin Toss System
Coin Toss Runs Calculator
The expected number of runs for two consecutive heads or tails is 3. Is there an edge if we place a progressive constant size bet(limited to 3 times)for consecutive ...
4
votes
0answers
147 views
Asymmetric Volatility Modeling (Interpretation)
I am currently writing a paper on asymmetric volatility modeling of brent, gold, silver, wheat, soybean and corn from 1986-2012 and divided them into 4 sub-sample periods (i.e. 1986-1991, 1991-1997, ...
4
votes
0answers
116 views
Is it more accurate to analyze returns on a calendar day basis than a trading day basis?
I'm rather new to the actual practice of this kind of analysis, but it just seems wrong to me to throw Mondays' returns in with the rest without accounting for the passage of time on the weekend when ...
4
votes
0answers
280 views
ATM volatility versus OTM volatility and directional standard deviation
The forward instrument vol curve is skewed to the downside (50 delta risk reversal, 25 put, 25 call) were trading several ticks to the put).
Is there a smaller standard deviation (in price terms) to ...
3
votes
2answers
229 views
Statistical significance of a pair trading strategy
How can I test the significance of a pair trading strategy, i.e. that the H0 is "The strategy has no predicting power".
I was considering to use the technique in Evidence Based Technical Analysis ...
