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.
3
votes
1answer
126 views
How to determine ratios for mean-reverting basket
Suppose I have a basket of 3 securities A, B, and C. I believe that the basket is cointegrated and I want to create a mean-reverting trade. I fit the model:
...
1
vote
1answer
324 views
Predict Quadratic Trend in Time Series
Can anyone kindly point out if I made any mistakes in making predictions using quadratic regression model in time series? I called the predict() function with the appropriate data vector and model, ...
0
votes
1answer
126 views
help me compare methods to compute one instrument price from another instrument price
Assume we have two instruments A and B. Also time is increasing from 1 to n. Let's say that ...
-3
votes
0answers
80 views
Holt Winters Double Exponential Smoothing [closed]
I am looking out for Holt Winters Double Exponential Smoothing implementation using VBA Code.
I have searched everywhere but all I can observe, It comes with Excel Add-In. I am looking out for actual ...
1
vote
2answers
120 views
Statistics of difference between two GBMs
if I have two asset prices modeled separately as geometric brownian motions. How do i go about calculating the expected statistics of their difference? Like given the sigmas and mus of both processes, ...
1
vote
1answer
128 views
Testing Significance of Correlation
Lets say I have the returns of two stocks(stock1 and stock2). Now without running a regression, I lag one of the variables, calculate the correlation between the two stocks and repeat this process as ...
2
votes
0answers
143 views
Does the geometric Ornstein-Uhlenbeck process have stationary variance?
I know that the long run variance of the standard OU process is
$\lim_{s\rightarrow \infty}\mbox{Var}(P_{t+s}|P_t) = \frac{\sigma^2}{2\theta}$
I'm using the geometric version of the process. I ...
1
vote
3answers
246 views
Kolmogorov-Smirnov test
Is Kolmogorov-Smirnov test self-sufficient to prove normal distribution of a time series? And then test efficiency of a market?
0
votes
1answer
204 views
main arbitrage & statistical arbitrage concepts
can we please summarise here some of the basic concepts, tools used in arbitrage and statistical arbitrage in real life?
ARB: benefit from price difference on same asset
ARB: difference between ...
3
votes
0answers
106 views
Fitting a non linear AR + GARCH(1,1)-M model
I want to fit the following model to a time series:
$$
y_{t}=\alpha_{0}+\alpha_{1}y_{t-1}+\alpha_{2}y_{t-1}^{2}+\lambda h_{t}+\varepsilon_{t}
$$
$$
...
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 ...
11
votes
3answers
537 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 ...
3
votes
0answers
171 views
how to represent financial data as a spatial process
Does any one have a good tutorial , introduction or overview on the web for different ways of representing financial data as a spatial process? Such as those spatial processes often used in ...
0
votes
2answers
142 views
Interpretation of PCs
I have computed PC1 and PC2 wts on future contracts derived from cumulative log differences. How can I use them to get back the theoretical price of each contract using those 2 pcs? Thanks in ...
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 ...
1
vote
2answers
105 views
What do the terms in-sample and out-of-sample estimates mean in MVO?
How do the in-sample estimates and out-of-sample estimates I so often hear authors refer to in emperical analysis of MVO differ?
3
votes
2answers
228 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 ...
10
votes
0answers
139 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 ...
7
votes
5answers
788 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 ...
2
votes
2answers
125 views
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 ...
4
votes
0answers
143 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, ...
2
votes
1answer
551 views
How to fit ARMA+GARCH Model In R?
I am currently working on ARMA+GARCH model using R. I am looking out for example which explain step by step explanation for fitting this model in R. I have time series which is stationary and I am ...
3
votes
3answers
139 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 ...
7
votes
3answers
518 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 ...
0
votes
2answers
889 views
Kalman Filter Equity Example
I am looking out for some material where I can study about Kalman Filter applied to Equity using Excel or R?
0
votes
3answers
199 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 ...
2
votes
3answers
458 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 ...
4
votes
2answers
384 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.
...
8
votes
1answer
745 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
1answer
717 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 ...
1
vote
1answer
409 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
votes
1answer
378 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 ...
5
votes
3answers
754 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?
2
votes
0answers
102 views
What are the proper metrics to look at for checking discrepancies in these two time series
I am obtaining bid/ask price and volume market data from two different sources for the same ticker and for the same day and checking to see that at time intervals X they are "roughly the same". The ...
1
vote
2answers
232 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 ...
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!
2
votes
2answers
310 views
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
votes
0answers
115 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 ...
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 ...
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?
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 ...
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 ...
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 ...
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 ...
7
votes
1answer
995 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 ...
5
votes
5answers
525 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
votes
0answers
278 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
votes
1answer
383 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
votes
1answer
463 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
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 ...
