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.

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Squared and Absolute Returns

I've always wondered why do one use squared or absolute returns to determine if volatility modeling is required for the return series? We understand that there are various tests for its ...
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0answers
496 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, ...
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3answers
181 views

How to see if a set of asset returns corresponds to a known correlation matrix?

Let's say I have an arbitrary set of $n$ period returns for $k$ assets, and a given $k \times k$ correlation matrix (of asset returns), which is known a priori. Does it makes sense, or is it even ...
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3answers
259 views

Profit estimation with a dice: 10 dollars for 6, -1 dollar for anything else

I recently found the following question: What is your profit estimate throwing a dice in the long run if you get 10 dollars for each time you hit 6 and lose 1 dollar for any other number? I tried to ...
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3answers
2k views

What advanced statistical techniques are quant researchers using? [closed]

Some time ago I was talking to a representative of one of the leading quantitative hedge funds. We talked about recruitment and the following had me stunned: The representative explained that they ...
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2answers
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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. ...
9
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1answer
882 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 ...
9
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1answer
2k 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 ...
2
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1answer
3k views

Hurst Exponent Calculation

I am trying to calculate the Hurst Exponent using Excel. I am facing a problem where the exponent value sometime goes beyond 1. Can someone share a link / material so that it will help me to calculate ...
4
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1answer
508 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 ...
2
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2answers
643 views

.NET statistical packages recommendation

What open source or commercial .NET statistical package would you guys recommend? I am doing statistical arbitrage in options. The functions I need mainly are regressions, optimizations..etc. It would ...
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4answers
2k 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!
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2answers
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Detrending price data for analysis of signal returns

I'm looking to conduct hypothesis tests on some of my trading signals to see if the signal returns are statistically significant enough to falsify my null hypothesis that the signal has no predictive ...
4
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0answers
156 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 ...
28
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6answers
11k 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 ...
11
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2answers
938 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 ...
9
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1answer
2k 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 ...
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5answers
1k 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 ...
4
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0answers
468 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 ...
9
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1answer
728 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 ...
6
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1answer
1k 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 ...
7
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3answers
319 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 ...
8
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3answers
526 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 ...
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6answers
2k 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 ...
2
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2answers
3k 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
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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 ...
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5answers
3k 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 ...
9
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1answer
511 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
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1answer
437 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
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1answer
859 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 ...
14
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1answer
6k 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
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2answers
212 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
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1answer
2k 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
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2answers
706 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
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1answer
497 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
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1answer
181 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
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1answer
129 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
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3answers
2k 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 ...
5
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2answers
3k 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 ...
5
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1answer
4k 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 ...
10
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1answer
443 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 ...
12
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4answers
2k 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 ...