# 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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28 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 ...
26 views

### Understanding output from Johansen Cointegration test

I have a VECM model that Im using to determine the revenues for a firm, based on factors like Interest rates, S&P 500 and company specific variables, as follows: Stage 1: $$z_t= a+ bX_t+e_t$$ ...
54 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 ...
21 views

### Performance attribution of indices to their sector weights

Is it possible to attribute performance of indices (monthly returns and risk measures - Sharpe ratio, etc.) to their sector weights (if I know them)? Example: I know the monthly performance of ...
101 views

### How to get know when CUSIP is changed

CUSIP code is not a constant, it could be changed. Does anybody know how to detect a CUSIP change? Is there any report with this info? Where can i find it? Thank you.
215 views

### Correlation between stock prices given correlation between returns

assume I have two stocks with known volatilities and a known correlation coefficient of returns - does anyone know how to determine the correlation between the prices and NOT THE RETURNS
64 views

### Determining Value at Risk of a Poisson distribution

If my discrete random variable had a poisson distribution with both moments say equal to 10, how can I find the Value at Risk for a 95 percent confidence interval? I have seen that I need to ...
11 views

### A bounded random variable is sub-Gaussian, thus financial returns are not bounded?

Bounded random variables are sub-Gaussian, yet I, intuitively, assume financial returns are bounded random variables; however, they are not sub-Gaussian. Am I wrong to assume financial returns are ...
122 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 ...
61 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 ...
151 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 ...
50 views

### How to calculate R for strategies with dynamic exit points

Calculating risk-reward ratio R is easy when trading a straight forward strategy which has its entry and exit points clear: ...
126 views

### Fama/Macbeth Regression - negative estimate for market premium

I just conducted a Fama-Macbeth regression to estimate the risk premia of Mkt-Rf, HML and SMB. As a result, I got a negative risk premium for Mkt-Rf which makes no sense in my opinion. As I couldn't ...
70 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 ...
88 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 ...
31 views

### What should basic statistical analysis of different price forecasts contain

we have set of historical data of different price forecasts and the real prices. When assessing "which forecasts are best", what parts of the analysis should one never miss out? We are at a very ...
90 views

### How to apply derived beta to daily change?

I've taken three months of price return data for two instruments and calculated a $\beta$ between the two using the formula $\beta = \frac{Cov(x,y}{Var(y)}$ with the goal of estimating what the ...
9k 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 ...
41 views

### Hurst Exponent and fractional differencing

I have a quick question. Currently I study daily OHLCVs of some stocks and find that many of them have the Hurst exponent not being equal to 0.5. I know that if it is less than 0.5 then it is a mean ...
8k 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 ...
127 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 ...
55 views

### Predicting time series based on another

This is more of a generic question, but I'm sure it has a best answer/methodology which is what I'm trying to reach. I'm trying to figure out a solid line of thought when looking at a time series X ...
36 views

### Optimal Cash Deployment in a Bear Market

Assume: You can't time the market bottom You have a finite amount of cash to buy equities There are P dip/bear periods you're gonna purchase the equity 2 Problems: You deploy too much cash early, ...
82 views

### Can someone prove (or disprove) this assertion about the normal distribution? [closed]

Let $X$ be distributed as a $Normal (\mu, \sigma^2)$. Then for a fixed $\mu$ it is always the case that: \begin{equation} \frac{90th quantile-10th quantile}{\sigma}=constant \quad \forall \sigma>0 ...
52 views

### Why combining market share behaviours brings a different conclusion

Please check the following dummy example to explain the paradox. Both areas in the company keep the same market share during the years, but at the end company lost share in the market! Math is 100% ...
19 views

### Sample conditional multivariate random variable?

There's multivariate random variable, future prices of assets, 5 years from now: $$X = [Gold, Silver, SP500]$$ There's historical prices for $X$ available for last 50 years. It's possible to fit ...
25 views

### Unbalanced Panel Data in Excel and Stata

We have unbalanced panel data (columns for date and firm identifier as well as other variables) that is heavily unbalanced involving several thousand firms. We would like to turn it into what ...
189 views

### Forecasting Volatility using GARCH in Python - Arch Package

Disclaimer: Posted this on stackoverflow, but maybe here should be the right place to ask something about GARCH I'm testing ARCH package to forecast the Variance (Standard Deviation) of two series ...
53k 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 ...
144 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.
85 views

### how to I get the statistical significance of a backtested result

If I have a simple long/short value strategy (say long stocks with high e/p and short stocks low e/p or any other parameter) rebalanced monthly, and a look back window of say 15 years. How do I ...
127 views

### Two Probability Questions from Quantitative Finance Interview Book

I posted the two questions in math stack exchange one month ago but cannot get an answer, so I post it here and appreciate your advice:) I'm reading an interview book called A Practical Guide to ...
55 views

### Why is SPY daily adjusted close negatively autocorrelated?

I took daily adjusted close prices (all history) from Yahoo Finance and ran the following code: ...
25 views

### Interpretation of $\alpha$ (confidence level) in mean CVaR optimization

How are an investors risk preferences related to $\alpha \in (0,1)$ in a mean CVaR optimization? Would a risk averse investor choose a higher value of $\alpha$, and if so why? My understanding is, ...
66 views

### Fama-Macbeth Regression: Weird Risk Premia

I just conducted a Fama-Macbeth regression where in the first step I calculated a time-series regression for each individual stock to get three betas (for mkt-rf, smb, hml) for each stock. Then I ran ...
54 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 ...
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.
57 views

### What does a regression of squared returns of stock on squared index returns and lags show?

We have a squared stock return at t regressed on 3 variables: squared index return, squared stock return at t-1, and squared index return at t-1. My two questions would be: 1. What does this test ...
28 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 ...
34 views

### Markov Switching ARMA-GARCH

I am looking for R function for modelling Markov Switching ARMA-GARCH. I found package MSGARCH but that package can not accommodate mean model. Do you have an idea for my case?
62 views

### Classical Cramer Lundberg model - Ruin Theory Simple Question

I am trying to solve the following problem: 'An insurance company has an initial surplus of 150 and premium loading factor of 15%. Assume that claims arrive according to a compound Poisson process \$(...
7k views

### How to calculate the JdK RS-Ratio

Anyone have a clue how to calculate the JdK RS-Ratio? Let's say I want to compare the Relative strength for these: EWA iShares MSCI Australia Index Fund EWC iShares MSCI Canada Index Fund EWD ...
64 views

### Why is R^2 negative on random data? [closed]

The introductory book says R^2 is between 0 and 1, but I have two randomly generated sequences and the R^2 is negative. So I read further and now understand the negative value is because R^2 ...
65 views

### 0.0006 r-squared after trying to test whether the intercepts differ significantly. Did I do it wrong?

I am trying to test if the intercepts of two linear regression (CAPM) differ significantly or not. I have 2 fund's monthly return in the same period and regress them on the same market variable (MKT = ...
9k views

### Annualzing the log of daily returns riddle

Two popular ways to measure returns are Arithmetic returns and Log returns. Let's define arithmetic (simple period) returns as: P(t) - P(t-1) / P(t-1). Let's define log return as Ln( P(t)/P(t-1) ) or ...
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 ...
54 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 ...
27k views

### Is R being replaced by Python at quant desks?

I know the title sounds a little extreme but I wonder whether R is phased out by a lot of quant desks at sell side banks as well as hedge funds in favor of Python. I get the impression that with ...