# 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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144 views

### Estimating realised gains given growth rate and churn

If one can estimate that the value of an investment portfolio will grow at $g$% per annum, and can estimate that approximately $c$% of that portfolio will be churned each year (sold and reinvested), ...
99 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 ...
153 views

### Why futures pricing not calculated like options?

I have read about futures and options ( from online resources ). I only have the basic understanding,not math heavy ( for eg. for Black Scholes I know only the intuitive idea from the khan academy ...
536 views

### Filling a few missing data in time series?

I'm writing a paper about Uncertainty indices like VIX, etc. I already collected all data but it seems that some of the variables got a few or a little more missing data. I have daily and monthly data ...
113 views

### Measuring correlation between random variables when they are not normally distributed?

I want to perform some analysis on portfolio that consists of hedge funds (thus fund of hedge funds) In particular, I want to know the relationship between the funds during the downmarket. The ...
597 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 ...
488 views

### beginner portfolio statistics - annualized volatility of multi-asset portfolio

Sorry for the dumb question, but I wanted to make sure my understanding of what I read and compiled was correct! I am trying to calculate the variance-covariance matrix, and annualized volatility of a ...
32 views

### Identifying primary share class of U.S. firms and deleting excess observations

I have a fairly large dataset of CRSP firms with their daily closing prices from 2006 till 2017. I need to filter the data so that I have one daily observation per unique firm. I've identified the ...
67 views

### Statistical methods to compare two financial series data

I have two financial series data, x and x', where x' was formed form ...
39 views

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 ...
61 views

### Correlation between a sector and MSCI ACWI returns

I have daily return data of 11 sectors of MSCI World Index and the MSCI ACWI index. I want to know the stationarity of correlations between the sectors and MSCI ACWI index. This is what I have done: ...
439 views

### Filtering smallest eigenvalues

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

### For a trading strategy how many trades have to occur for statistical significance [closed]

I created a strategy using a regression on a price series. I tested it with many walk-forward analyses and it has passed. I am currently live trading it with real capital (the ultimate test). My ...
37 views

### Negative abnormal stock return and permanent impact

Assume we have a day where stock price falls many standard deviations of the mean (e.g >3) . How could we test, in terms of time-series, if this negative shock is permanent or deminishes in the long ...
301 views

### Calculating implied volatility from moneyness/volatility values for date

For an option expiring at a particular date I have Moneyness 0.4,0.7,0.85,0.95,1,1.05,1.15,1.3,2.5 Vol 0.105,0.075,0.045,0.045,0.202,0.045,0.045,0.075,0.085 ...
40 views

### Trading rules: Controlling the portfolio FDR+ level

I'm trying to apply the FDR+ (False Discovery Rate +) methodology from Bajgrowicz (2011) link another_link. I have computed the p-values with the stationary bootstrap as they did, however I am not ...
40 views

### Bootstrapping to Judge the Fit of a Sampled Return Distribution

Consider the following: I have sampled yearly stock returns from a specified distribution. What I want to do is compare how well my sampled distribution fits the empirical distribution of yearly ...
91 views

### Uniqueness of data metric [closed]

Is there a metric that calculates "uniqueness of data"? For example if i have two sets of 200 observations, DataSet 1 has 70 unique values but 4 values take up the next 130 observations. DataSet 2 ...
198 views

### Would you consider yield a stationary or non-stationary process?

Doing some yield curve forecasting and unsure whether should be working with yield or change of yield.
155 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.
195 views

### Average Return Differential Calculation - Newey West t-Statistic

I am reading Table II on page 28 in Bali et al. (2007), Value at Risk and the Cross-Section of Hedge Fund Returns: Please can anyone explain the calculation of t-statistic and Newey West t-statistic ...
342 views

Is it possible to weight the bid-ask spread? I'll explain ... In the moment, for a share X, to trade I use the price, volume, \$ volume, # trades, % chg and the bid-ask spread (BAS). To make day ...
558 views

### conditional probability of default

I would like to ask the following question. I would appreciate if someone could help me out. On what argument is based that states that conditional default rates ( loans of corporate borrowers) ...
150 views

### When constructing a cointegrating series, does choosing the linear regression with the lowest ADF test statistic yield the optimal hedging ratio?

Multiple sources say that you should find the optimal hedging ratio between two stocks in a pairs trade by conducting 2 linear regressions (with each stock as the independent variable), and using ...
5k views

### How did James Simons clinch that security prices didn't look random?

Source: D. T. Max. Jim Simons, the Numbers King. December 18 & 25, 2017 Issue [...] In the late seventies, not long after he won the Veblen Prize, Simons founded a small investment firm in an ...
822 views

### log return of sp500. Stationary vs strictly stationary

By first glance of this time series; will you say it is stationary? I can easily see some "seasonality" which means that this is not strictly stationary since the distribution will not be the same; ...
556 views

### Can portfolio Value-at-Risk be calculated analytically for multivariate t-distributed returns?

It is widely known that VaR is generally not sub-additive in all but the most restrictive cases (typically when a Gaussian return distribution is assumed, which fails when it matters the most). ...
101 views

### When predicting Forex price using HMM what, typically, are the states and what are the observations?

I understand their abstract definition but having trouble applying the HMM method to Forex prices. What should the observations be? Then what should the states be (like "hot", "cold", etc.)?
65 views

### How to solve endogeneity between capital expenditure and Tobin's q without using instrumental variables?

Currently, I am analyzing capital expenditure of takeover-targets in the year prior to the takeover. The dependent variable is capital expenditure and one of the explanatory variables is Tobin's q. ...
324 views

### R Calculate future price range and plot the result

First I want to say that I've read this post (How to calculate future distribution of price using volatility?) but it doesn't help much. Here is what I'm trying to do (values are not real) Let's ...
6k views

### Principal Component Analysis of yield curve change

Following pictures are the Principal Component Analysis for the yield curve change from https://www.coursera.org/learn/interest-rate-models/lecture/ZHMM6/principal-...
411 views

### p-value of Sharpe Ratio Differences

I am trying to understand what was done in this study by Research Affiliates on the small cap anomaly. Looking at Table 1, how are the authors actually calculating the p-value? I have read that the ...
75 views

### which method is the roubust method to estimate the Hurst parameter?

I know there exist lots of method to estimate the Hurst parameter, such as R/S, V/S, GHE, DFA, DMA, Wavelet Spectral Density, Whittle and so on. Can you tell me which one is the best one. Is anyone ...
396 views

### Predict the behavior of a time series (P&L trading desk)

I work at the trading desk P&L department at a large bank. The trading desk has positions in almost all sorts of derivatives (options, futures) over a long list of stocks, currencies, commodities.....
73 views

### CAPM Beta zero-correlation performance issue

I am working on a research project that requires me to run a CAPM regression on all intra-day stock quotes in NSDAQ, NYSE and all other U.S. exchanges since 1993. The precision of the quote data is ...
60 views

### What CAPM/Financial ratios involve kurtosis?

Simple question, what universally accepted financial ratios involve kurtosis? I'm not looking for a made up one. I want something that academics may have discussed.
99 views

### Stock returns: Determining the window size

I am looking for a rigorous way to determine a suitable rolling window size for my stock data. Factors that will influence the window size are how fine my data is (minutely, daily, weekly etc.) and ...
67 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 ...
1k views

### How to build Factor model like Fama & French (2014)?

I would like to conduct a study where I build a factor model based on the characteristics/variables I have collected about firms, using a couple of countries. I have acquired two Excel data files ...
3k views

### What is the total correlation between assets in a portfolio?

Suppose I have portfolio with 10 assets, each one of them with a weight of 10% from the total portfolio (equally weighted). It's well known how to measure from historical prices->returns a variance-...
51 views

### How a chose between strict vs dynamic measurement of moving average

I am building a simple stock model with Pandas and part of that is calculating moving averages. I would like to understand what are and how to measure accuracy implications of using strict vs dynamic ...
314 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 ...
352 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 ...
322 views

### Portfolio Theory: Why is so much effort put into the reduction of estimation errors?

In MPT, very much effort by researchers is put into developing methods and techniques to handle the rather poor performance of the estimated means, variances and covariances. There are shrinkage ...
563 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 ...
123 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*...