# 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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### Proving the asymptotic distribution of Manipulation-Proof Performance Measure (MPPM) (Paper by Goetzmann et al.)

In Goetzmann et al.'s (2007) paper, the authors derive a "Manipulation-Proof Performance Measure" (MPPM), which is a performance measure that is impervious to performance manipulation by fund managers....
1k 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, ...
212 views

### Implementing Hanson`s LMSR with Limit Orderbooks

I am trying to integrate Hanson's LMSR (see (see logarithmic market scoring rule)into an order-book with traditional bid/ask-limit orders (in KDB+/Q). The following functions define the basic LMSR ...
199 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 ...
73 views

### Cointegration stationary test yields different results if the pairs are swapped

I've been backtesting on a spread mean reversion strategy on certain stock pairs. I observe the stationarity via scatterplot and plotting a histogram. Then I verify it using Augmented Dickey Fuller ...
602 views

I am trying to find out Historical Alphas of a bunch of fund returns ${F_i}$ by Using Regression Model$(stepwise)$ with regressors as its underlying exposure-returns(risk-free rate subtracted) i.e. ... 0answers 649 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 ... 2answers 83 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 ... 0answers 97 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 ... 0answers 303 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 ... 0answers 82 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 ... 0answers 171 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(... 0answers 348 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 ... 0answers 211 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 ... 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 ... 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-... 0answers 57 views ### Why does the Hurst exponent pseudo code not match the Python implementation? I am working on understanding the Hurst exponent calculation by Ernest Chan; however, the description of the algorithm does not match the Python implementation. Chan [Algorithmic Trading: Winning ... 0answers 65 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 ... 0answers 33 views ### Estimator for Conditional value at risk (average value at risk) I am following a book: Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization by Svetlozar T. Rachev, Stoyan V. Stoyanov, Frank J. Fabozzi I'm learning about average value at risk. ... 0answers 95 views ### How to determine expected returns of an options portfolio? Lets say I have a delta neutral portfolio, iron condors on spy for example. I'm short a call credit spread and a put credit credit spread of equal widths. I would like to determine the expected ... 0answers 112 views ### Does Academic Research Destroy Stock Return Predictability? McLean/Pontiff (2016) give evidence that portfolio returns are 26% lower out-of-sample and 58% lower after publishing an academic paper on variables, which are likely to predict cross-sectional ... 0answers 67 views ### Statistical methods to compare two financial series data I have two financial series data, x and x', where x' was formed form ... 0answers 66 views ### Reduced rank / matrix factorisation techniques and their uses in portfolio optimisation? I am interested in reduced rank / matrix factorisation techniques and their uses across finance and portfolio optimisation. For example, PCA might be used to reduce the number of components you are ... 0answers 120 views ### Negative constant in GARCHX model I am fitting the following ARX(1,1)-GARCHX(1,1,1): \begin{align*} y_t&=c+a_1y_{t-1}+\gamma_1x_t+\varepsilon_t\\ h_t&=\delta+\omega_1h_{t-1}+\theta_1\varepsilon_{t-1}^2+\pi_1x_{1,t} \end{align*... 0answers 48 views ### LSE GARCH Modells currently I am working with GARCH Modells. And it came to my attention that for the parameter estimation Maximum Likelihood approaches are commonly used. However I was wondering why Least Squared ... 0answers 502 views ### subadditivity of VaR It is known that the VaR (Value at risk) doesn't fulfill subadditivity, i.e. VaR(X)+VaR(Y) \le VaR(X+Y) But for elliptical distributions subadditivity is true. Questions: (1) Which ... 0answers 428 views ### Can you tell me what this RBloomberg formula means? I've been asked to re-create a spreadsheet that used RBloomberg using a different data source. But I'm having trouble figuring out exactly what one of the spreadsheet's formulas does. Can anyone tell ... 0answers 142 views ### seasonality and generalized additive model I am reading a report which talks about seasonality. There is a chart showing the average returns for each month of the year. In the chart it appears the last 3 months of the year tend to be negative. ... 0answers 306 views ### Simple EOD computations for tick data As part of End-Of-Day calculations once a particular market/exchange has closed for all the tickers traded on that market one may typically compute the following properties: OHLC Bid/Ask Price (mean, ... 0answers 43 views ### garch(1,1) Annualised Volitility with python I am trying to calculate the annualized Volatility of given returns for a stock with Garch(1,1) on python using a code I found online. The value I should be getting is around 27, but the value I am ... 0answers 53 views ### The distribution of mean reversion time from the OU process I was reading the paper Statistical Arbitrage in the US Equity Market and I couldn't understand the figure that plots the histogram of the empirical distribution of characteristic time to mean ... 0answers 81 views ### Proof of variance reduction of bagging In Lecture 4 of the following course: Advances in Financial Machine Learning: 10 Lectures by Marcos Lopez de Prado link in the proof of variance reduction for a ... 0answers 73 views ### Why doesn't the first principal component maximize the standard deviation of returns I am trying to apply PCA to portfolio of securities. My understanding is that the first principal component can be used to evaluate weights for portfolio of maximum variance and each next principal ... 1answer 88 views ### Old codes for Companies (CUSIP/ISIN/SEDOL) I found that for example ISIN have following rules: Merger and acquisition: Old ISINs for stock become inactive and are replaced by securities with a new ISIN. Bonds only need new ISINs if old ones ... 0answers 33 views ### Asset prices Boom,Bust and Recovery cycles Is there any systematic way to detect the Boom, bust and Recovery cycles in Asset Prices ? Are there any good references about the Topic ? Thanks in advance. 0answers 32 views ### Average of R squared correct/allowed/useful? I just conducted a Fama-Macbeth analysis to estimate the risk premia of Fama/French. In short, I estimated the betas on a company-individual basis first and then conducted a cross-section regression ... 0answers 41 views ### Correlation coefficient without cash flows? I'm an intern at a company and one of our tasks is to calculate the the probability of default of both participants of a Swap(a Client and a Bank), for which we first need the correlation coefficient ... 0answers 58 views ### William K. Bertram's sharpe formula checking I have some issues to verify by simulation the formulas in the paper of William K. Bertram "Analytic solutions for optimal statistical arbitrage trading". first, the reversion parameter alpha=180 in ... 0answers 28 views ### Which technique determines if var x1 leads var y? Assuming var x1 may need to be transformed Suppose I want to predict future changes in variable y (stock price over time). I notice that variable x1, inverted and delayed three months, tends to lead y. Which technique can I use to find other ... 0answers 262 views ### How to normalize stock exchange indexes I am doing an academic research in behavioral finance and I need to calculate my abnormal return based on the normalized returns of the stock exchange index being the S&P 500. In other words, I ... 0answers 67 views ### Convolution of Dependent Random Variables with Copulas Lets say I have 2 different observations which are fitted to a parametric distribution. And lets say that they are dependent and can be modeled by one of the copulas. I want to calculate “a value” ... 0answers 60 views ### statsmodels's granger causality tests return value im a developer(with no background in statistics) and i need to use granger causality test, i cant seem to understand the results of the func. one result: Granger Causality ('number of lags (no zero)'... 0answers 53 views ### Statistical distribution of MACD I was (unsuccessfully) trying to find results on what the distribution of the MACD values for a stationary time series with IID returns would be. Are there any such results or any that go in a similar ... 0answers 32 views ### Using CFNAI index for identifying sample periods I'm doing my Thesis on Asset pricing models and I would like to find out the effects of business cycles on the performance of asset pricing models for industry portfolios. My initial idea was to ... 2answers 157 views ### How to obtain annualized IR from t-monthly IC? When we checking the relation between some factors and Stock price, we could use Information Coefficient(IC) to meausre. And then I already have t-monthly IC for each factor, and I need to calculate ... 1answer 94 views ### Backtesting model results, but backtesting output sampled at different frequency than model output So, I'm trying to backtest a model that computes P&L. This model pulls sensitivities on a weekly basis and applies market shocks to these sensitivities to project quarterly P&L. I want to ... 0answers 32 views ### How to count [and report] the values of significance at 1% and 5%? I am slightly confused with this: I have calculated the Chi square for the number of funds and the methods description tells me that if the values I have calculated are greater than 3.84 (6.64) that ... 0answers 42 views ### Log likelihood function, GARCH(1,1) with asymmetric term I am modelling a GARCH(1,1) and a GARCH(1,1) with an asymmetric term.h(t)=\omega+\alpha\varepsilon(t-1)^2+\beta\sigma(t-1)^2$$and$$h(t)=\omega+\alpha u(t-1)^2+\beta\sigma(t-1)^2 + \gamma (u(...
Currently doing an application of VaR on sample of industry portfolios in the US. I have a matrix of $n$ industry portfolios with $m$ time-series observations. I calculate cross-sectionally (for each ...