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.

Filter by
Sorted by
Tagged with
3
votes
2answers
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 ...
3
votes
2answers
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 ...
3
votes
3answers
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: ...
3
votes
2answers
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 ...
3
votes
2answers
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 $R=\begin{bmatrix} \mu_1 \\ \mu_2 \\ \mu_3 \end{bmatrix}$, ...
3
votes
2answers
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 ...
3
votes
1answer
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.
3
votes
2answers
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 ...
3
votes
1answer
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 ...
3
votes
2answers
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 ...
3
votes
1answer
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 ...
3
votes
1answer
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 ...
3
votes
2answers
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 ...
3
votes
1answer
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 ...
3
votes
1answer
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 ...
3
votes
2answers
2k views

Degrees of freedom in calculating significance of GARCH coefficients

I am trying to determine the significance of coefficients of a GARCH model by calculate the p-values using the following Matlab formula: pvalues = 2*(1-tcdf(abs(t),n-v)), where $t$ is the t-stat, $...
3
votes
1answer
112 views

The use of $p$-value in finance after the recent statement of ASA (American Statistical Association)

The ASA (American Statistical Association) has just released a statement about the misuse of $p$-value. Will this action have much effect on the use of $p$-value in finance?
3
votes
1answer
626 views

Weights Blowing up in PCA

I'm using daily settlement data to get yield levels for a couple of products. From this data I am doing PCA on a rolling collection of the yield levels. I have been using sci-kit learn's PCA function, ...
3
votes
1answer
221 views

Summary statistic for the average probability of default?

I have the following scenario: Let $X_i$ denote the event where some institution $i$ 'defaults' (don't worry about the exact definition of a default here, it is not relevant to the question at hand). ...
3
votes
3answers
218 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 ...
3
votes
1answer
186 views

Help on interpreting the methods in a certain academic paper

Has anyone read the paper "Spread of risk across financial markets:better to invest in the peripheries" by F. Pozzi, T. Di Matteo & T. Aste? If so, how do you interpret equation (1) in ...
3
votes
2answers
293 views

How can momentum trading strategies work if returns are not serially correlated?

Returns are demonstrably not serially correlated in most financial time series (Day 1 returns are uncorrelated to Day 2 returns etc.) . Since this is the case, how can momentum trading strategies work?...
3
votes
1answer
658 views

Modeling tail data using Generalized Pareto distribution

I just estimated a ARMA(1,1)+GARCH(1,1)+Threshold order(1) equation for time series of stock prices. Now I'm going to estimate the residuals' marginal ...
3
votes
4answers
352 views

Compare two time series with different frequencies

Lets say I have two time series $X_t$ and $Y_{t,q}$. As an examples, lets say $X_t$ is a series that measures year over year changes in the level of output of a good (say number of widgets). So $X_t = ...
3
votes
1answer
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, \...
3
votes
1answer
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 ...
3
votes
1answer
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 ...
3
votes
2answers
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 ...
3
votes
0answers
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 ...
3
votes
0answers
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 ...
3
votes
1answer
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 ...
3
votes
0answers
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 ...
3
votes
0answers
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 ...
3
votes
2answers
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 ...
3
votes
0answers
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 ...
3
votes
0answers
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 ...
3
votes
0answers
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, ...
3
votes
0answers
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 ...
3
votes
0answers
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(...
3
votes
0answers
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 ...
3
votes
0answers
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 ...
3
votes
0answers
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 ...
3
votes
0answers
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-...
2
votes
2answers
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 ...
2
votes
1answer
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 ...
2
votes
1answer
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 ...
2
votes
2answers
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, ...
2
votes
2answers
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,
2
votes
1answer
568 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
2answers
1k views

main arbitrage & statistical arbitrage concepts

Can we please sumarise 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 stock ...

1 2
3
4 5
9