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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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 ...
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83 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 ...
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1answer
165 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.
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1answer
147 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.
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1answer
153 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 ...
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3answers
336 views

Differentiate a good from a bad bid-ask spread

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 ...
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1answer
514 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) ...
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2answers
128 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 ...
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3answers
4k 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 ...
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3answers
697 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; ...
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1answer
485 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). ...
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1answer
100 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.)?
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1answer
62 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. ...
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1answer
292 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 ...
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2answers
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-...
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1answer
361 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 ...
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1answer
71 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 ...
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1answer
370 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.....
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67 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 ...
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1answer
59 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.
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0answers
93 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 ...
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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 ...
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1answer
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 ...
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2answers
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-...
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1answer
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 ...
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0answers
286 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 ...
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2answers
292 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 ...
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3answers
316 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 ...
3
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1answer
541 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 ...
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0answers
115 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*...
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1answer
653 views

How to calculate the hedge ratio between two securities using the Least Squares model in Java

How does one, having two lists of prices Y and X and wishing to fit the Least Squares model, perform this in Java? The fit is required to calculate the hedge ratio in a pairs trading strategy. For ...
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0answers
59 views

J-test and Empirical Model Performance of Conditional and Unconditional Estimations (as for example in Cochrane (1996))

Take for example the Consumption-based model with a power utility function estimated by Cochrane in his paper "A Cross-Sectional Test of an Investment-Based Asset Pricing Model" (1996). The following ...
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1answer
71 views

Tools to measure the randomness of database

I was working on historical data looking for anomalous patterns that we would not expect to occur at random. I'd like to create a scheme to analyze data and markets to test for statistical ...
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1answer
54 views

The weight of interest rates

Why are average interest rates often weighed by loan (and deposit) sizes? Since the size and interest rate of a loan are function of each other, I expect the resulting statistic to be hard to ...
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1answer
291 views

Calculating HIstorical VaR with short time series

Intuitively, Historical VAR is an approach which assumes that in the past data, we have observed everything that can happen, so we consider the worst case(tail). However, when your equity/instrument ...
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1answer
55 views

Probability Distribution that fits my parameters?

I'm trying to create a PDF that has the max values at its tails, and a P(x) of 0 at its mean. Essentially it would be something like two normal distributions lined up side to side. Is there any ...
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1answer
107 views

What is a good choice of threshold for Value at Risk?

As far as I know, there is usually a betwixt in choosing the right value for a threshold. A trade off between bias and variance has to be encountered. If a low threshold is chosen, the number of ...
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1answer
238 views

Error/Bug in computing the Hurst Exponent on timeseries

I tried calculating the Hurst Exponent using c#, and compared the results to a series with a known exponent. I am having the following issue in my calculations: 1- All my results are negative.. ...
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0answers
174 views

Expected shortfall of stable distribution by Stoyanov

I've been working on calculating parametric ES assuming the returns follow Paretian stable law. Given the four parameters - $\alpha, \beta,\sigma,\mu$- Stoyanov introduces closed form solution of the ...
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2answers
1k views

Test statistical significance of a trading strategy

I have created a trading strategy which operate every single day on the DAX 30, for the last 1700 trading sessions (some years). I have the daily returns of my strategy and also the daily returns of ...
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1answer
37 views

GDP and Statistical Significance

Let’s say that we are defining a U.S. recession trend as 3 consecutive quarters of GDP decline. The GDP figures below would satisfy this definition. However, these figures are statistics taken from a ...
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0answers
86 views

Transformation of GARCH Equation to multiple-day Forecast Equation

I want to understand the procedure of how to predict with the GARCH Modell. Therefore it is said that a one day ahead forecast is easy due to the fact that the GARCH equation can produce this. ...
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0answers
47 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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1answer
1k views

Implementation of the Chow test in Excel/R

Has anyone used Excel or R Studio to do a simple Chow Test (compare a set of data before and after one particular year)? I have tried to find info but there is not much, especially regarding the use ...
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3answers
15k 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: ...
4
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1answer
443 views

Interpreting Eigenvalues of Co-variance Matrix

Im working on market reaction to events and I'm using the co-variance matrix to do this. In this paper the author writes It has been known for some time that the largest eigenvalue (λ1) contains ...
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1answer
174 views

EM for conditional Gaussian model

Let $$X_1\sim N(\mu_{X_1},\sigma_{X_2}^2)$$ $$X_2\sim N(\mu_{X_2}, \sigma_{X_2}^2)$$ where $\mu_{X_2}=c+aX_1$. Also, I have data $D$ (with missing values on $X_1,X_2$). How can I update/estimate the ...
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0answers
50 views

Distribution of loans by types of interest

Im looking for some kind of report that would inculde data on the distribution of corporate loans by types of interest(fixed/floating), specifically global not just for one country(developed, ...
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0answers
152 views

logistic regression multivariable fractional ploynomials stata vs. R

I a going through Hosmer, Lemenshow and Sturdivant's (HLS) Applied Logistic Regression (2013) and trying to interpret the difference between what STATA is doing and what R is doing. Concerning the fit ...
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3answers
191 views

Extreme value theory expected value of GPD

We're using extreme value theory to model tail risks on our portfolio. After we choose the threshold, we fit generalized Pareto distribution to our data over the threshold. The expected value of GPD ...

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