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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13
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343 views

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....
6
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0answers
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, ...
5
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0answers
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 ...
5
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0answers
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 ...
4
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0answers
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 ...
4
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0answers
602 views

Is this methodology to calculate Alpha using multi-factor regression model correct?

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. $$...
4
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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 ...
3
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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 ...
3
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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 ...
3
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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 ...
3
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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 ...
3
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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(...
3
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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 ...
3
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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 ...
3
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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
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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
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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 ...
2
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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 ...
2
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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. ...
2
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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 ...
2
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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 ...
2
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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 ...
2
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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 ...
2
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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*...
2
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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 ...
2
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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 ...
2
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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 ...
2
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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. ...
2
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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, ...
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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 ...
1
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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 ...
1
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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 ...
1
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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 ...
1
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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 ...
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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.
1
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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 ...
1
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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 ...
1
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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 ...
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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 ...
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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 ...
1
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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” ...
1
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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)'...
1
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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 ...
1
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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 ...
1
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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 ...
1
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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 ...
1
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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 ...
1
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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(...
1
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0answers
25 views

Sample distribution of cross-sectional statistics of returns

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 ...
1
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0answers
28 views

Choosing observations/sample selection in behaviour credit scoring models

In retail banking the credit risk of a creditor after the credit had been granted is often modeled using behavioral credit scoring. In this setting the customer already has an account (or a few) and ...