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.
8
votes
3answers
376 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 ...
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 ...
7
votes
4answers
697 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 ...
10
votes
2answers
277 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 ...
2
votes
2answers
2k views
Calculating Portfolio Skewness & Kurtosis
I need to calculate the skewness and kurtosis of 2 asset portfolio, can someone please help me with the formulas and definition of terms? Thank you.
I have been using the matrices method and I am not ...
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 ...
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 ...
8
votes
1answer
306 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.
9
votes
1answer
339 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?
7
votes
1answer
558 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 ...
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 --> ...
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
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 ...
17
votes
2answers
554 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 ...
6
votes
1answer
360 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
129 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 ...
2
votes
1answer
99 views
How to reconstruct a discontinued economic time series such as the Fed's CP rate?
The old 3-Month Commercial Paper Rate (CP3M) on FRED was discontinued in 1997. I would like to reconstruct this series in a reasonable fashion, so I can use it to analyze more recent events.
I was ...
8
votes
3answers
837 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 ...
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 ...
6
votes
2answers
297 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
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 ...
9
votes
1answer
358 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 ...
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 ...
7
votes
2answers
298 views
How to combine various equity measures into a single measure (vector magnitude)
I have several measures:
...
