# Questions tagged [statistics]

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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579 views

### Value at Risk - What if an account has never suffered from a negative return

I want to implement an algorithm that calculates an account's 95% value at risk on a monthly return base. The case I want to describe in this question is rather academic and will probably never happen ...
11k 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 ...
23k views

### What value should the risk free monthly return rate be (Sharpe ratio calculation)?

In calculating an annualized Sharpe ratio using monthly returns, what is commonly used as the value for the risk free rate? I am using this formula: ...
170 views

### Statistical estimation vs Stochastic calibration of models

I have never been able to deduce the precise differences between model building from the statistical perspective and the stochastic processes/calibration perspective. I can only infer that these are ...
168 views

### Sample from aggregate portfolio distribution versus individual asset distributions

Suppose I have three assets $x_1,x_2,x_3$ in a portfolio with weights $W=\begin{bmatrix} w_1 \\ w_2 \\ w_3 \end{bmatrix}$, expected returns $R=\begin{bmatrix} \mu_1 \\ \mu_2 \\ \mu_3 \end{bmatrix}$, ...
539 views

### Filtering smallest eigenvalues

In Risk Budgeting and Diversification Based on Optimized Uncorrelated Factors [1], which introduces minimum torsion bets, Meucci gives an example involving the computation of covariance matrices on ...
191 views

### What are good papers on order book dynamics?

I want to simulate a limit order book. For this I want a statistical model to model arrival of orders in the exchange. I would be thankful if anyone can point me in direction of relevant literature.
388 views

### Convergence of the distribution of 0.05 quantiles through Monte-Carlo simulation

I am trying to get admitted to a masters in quantitative finance (I come from a computer science background), so next week I will have 3h to solve an exam in statistical computing using my favourite ...
967 views

### Stress Testing Methods

I'm working on the following task: Given quarterly data: a time series representing the 1-year realized (10 years of data) rates of default on a portfolio of mortgages a slew of realized (10 years ...
1k 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 ...
176 views

### Imperfect Competition among Informed Traders - Back, Chao and Willard

The following assumptions are part of the paper of Back, Chao and Willard and I can not solve for the statistic that is denoted as $\phi$ in the sequel. I would be glad if anyone could help me. Below ...
180 views

### Adjust calculation of Sharpe ratio when portfolio is subjected to cash outflows

I have a portfolio with cash and marketable securities, a benchmark, and a desire to calculate its Sharpe ratio. However, this portfolio has cash outflows. Sometimes securities are sold to produce the ...
136 views

### Do we need to assume underlying returns are normal in BSM model, given Central Limit Theorem?

I am trying to get a better understanding of Central Limit Theorem and how it can be used in life and in finance. From what I have read, the BSM model assumes the underlying asset's simple returns ...
635 views

### How to have an unbiased estimation of the standard deviation when using rolling returns?

I want to estimate the weekly standard deviation of a lognormal process in a usual setup. $$\frac{dS}{S} = (\dots) dt + \sigma dW$$ where $\sigma$ is a constant and $W$ a brownian motion. The ...
617 views

### CIR model - nth moment generation $E^*[r_T^n]$

I am analyzing the nth moment generation process for $r_t$ with dynamics defined by CIR model $r_t$ has following dynamics $$dr_t=a(b-r_t)dt+\sigma \sqrt{r_t} dW_t^* \quad \quad (1)$$ for some ...
2k views

478 views

### Monte Carlo Convergence

Let $\{X_i\}$ be an i.i.d. sample of $X$ with $E(X) = \mu$ and $Var(X) = \sigma^2$. We know a MC estimate converges to the true value almost surely by the SLLN. That is,  \bar{X}_n \to \mu, \...
395 views

### Compare events effect on stock prices from different time periods

I’m going to test for the effect corporate credit rating announcements have on stock prices through different economic climates (good times vs. bad times). I want to research whether or not the stock ...
104 views

### Properties of a Symmetric Copula

I am working with the following copula, and have a few questions about it: $C(x,y) = xy + \theta (1-x)(1-y)xy$ Here $\theta \in [-1,1]$ and $x,y \in [0,1]$ First, I am trying to show this copula is ...
1k views

### How to compare different volatility measures?

I read the Euan Sinclair's book (Volatility trading) in which he suggests different volatility estimators (Close-to-close, Parkinson, Garman-Klass, ...). I am inquiring about what is the best stock ...
77 views

### how to derive t-statistic for alpha (Eq. 15.29) in "quantitative equity portfolio management"?

I am reading "quantitative equity portfolio management: an active approach to portfolio construction and management" by Ludwig B. Chincarini, Daehwan Kim, and am confused by this derivation ...
145 views

### Contribution to Mahalanobis Distance

I am using Mahalanobis Distance to measure abnormal behavior within a portfolio consisting of a handful of general asset types, and am trying to figure out how to decompose this measurement into ...
141 views

### sub-Gaussian random variables in financial economics

Unlike financial time series that typically possess fat tails, sub-Gaussian random variables have strong decay in the tails of their distribution. do sub-Gaussian random variables or processes appear ...
186 views

### Large deviations theory in finance

In probability theory, the theory of large deviations concerns the asymptotic behavior of remote tails of sequences of probability distributions. A related post says: Large deviations theory is ...
171 views

### Are intraday volatility estimators useful for close-to-close predictions

I am interested in predicting the PnL of a gamma scalping strategy which trades only once per day. For simplicity, let's say we can always trade at the daily close. So, what I need to predict are the ...
135 views

### Cash flows regression on macroeconomic data

I'm looking into a research project and am struggling to find any existing work on this or whether I'm asking the right question. My question is to test the relationship between macroeconomic ...
117 views

### Which areas of statistical physics do not get enough attention in quantitative finance?

It seems that over the past few decades many ideas from statistical physics have been successfully incorporated into economics and finance to form the sub-discipline of econophysics. However, it is ...
440 views

### How do the units compare inside the (rate - 0.5*sigma-squared) correction?

Usually, I find the units of the mean and the standard deviation of a distribution to be (quite obviously) the same. Can anyone come up with a really simple explanation (for MBA students, some of ...
99 views

### what is the minimum capital necessary for quantitative/automated/algorithm trading? [closed]

I mean from my home for myself I have a degree in statistics so I know time series, predictions, R ... I would like to design statistical model for trading with R I don't ask for trading strategies, ...
84 views

### Test for difference in security returns before and after financial regulation

I'm going to study the effect of corporate credit rating changes (Moody's) on stock prices before and after a specific financial regulation. So far i have used an event study where i have divided the ...
188 views

### State Space models with Short Time Series

My problem is that I have a state space model that I estimate using the Berndt–Hall–Hall–Hausman (BHHH) algorithm. The state space model is relatively simple in that the hidden part follows a pure AR(...
360 views

### Correlation between idiosyncratic residuals and forward returns

The classic mean-reversion strategy is to calculate an "expected return" (alpha) by computing the raw return for each security and then remove the part which you think is market driven. Statistically ...
217 views

### Should I use Resampling or Expectation Maximization to compute a robust covariance matrix?

I have several assets, each with different return histories. Some of the assets have 75 days of return history, others have 40 or so days. In calculating a robust covariance matrix, should I be using ...
1k 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 ...
283 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 geo-...
881 views

### High values of skewness and kurtosis of realized protfolio returns

I am investigating some asset allocation strategies and I am wondering about the results I obtain. I am working on monthly and weekly data of the same stock indices (SP500, FTSE 100 etc). And when I ...
89 views

### What's the meaning of linearity in classical statistics in Prado's book?

I am reading Prado's new book, Machine Learning for Asset Managers. In the page1 of his book, there is this sentence. To a greater extent than other mathematical disciplines, statistics is a ...
221 views

### Why does computing correlation between index levels vs. percentage changes yield completely different results?

I am examining the relationship between the S&P 500 and the Industrial Production Index. Computing the correlation between these these variables yield vastly different results if expressed in ...
1k views

### How to combine Gaussian marginals with Gaussian copula to obtain multivariate normals?

in the book "Numerical Methods and Optimization in Finance" I red the following: "Combining the Gaussian copula with Gaussian marginal gives a fancy way of expressing multivariate normals. However, ...
2k views

### Partial Least Squares Discriminant Analysis

Could anyone point me to detailed literature about "Partial Least Squares Discriminant Analysis"? Intuition, methodology and examples.. Thanks,