# 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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72 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 ...
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 ...
303 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 ...
56 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 ...
108 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 ...
265 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.. ...
190 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 ...
2k 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 ...
37 views

### GDP and Statistical Significance

Letā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 ...
88 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. ...
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 ...
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 ...
17k 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: ...
521 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 (Ī»1) contains ...
180 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 ...
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, ...
153 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 ...
198 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 ...
288 views

110 views

### The use of $p$-value in finance after the recent statement of ASA (American Statistical Association)

The ASA (American Statistical Association) has just released a statement about the misuse of $p$-value. Will this action have much effect on the use of $p$-value in finance?
239 views

### Historical volatility from non-uniform samples

The way I compute historical volatility is that I take two parameters $dt$ and $T$, get a list of stock prices with the step of $dt$ over the window $T$ (so $T/dt+1$ samples in total), compute $T/dt$ ...
508 views

### Augmented Dickey-Fuller Questions

I've been searching in bibliography about this test applied to an AR(p) model. $$Q(L)(Y_{t})=c+\epsilon_{t}$$ Where L represent the Lag Operator and $Q=1-\phi_{1}x-.....-\phi_{p}x^{p}$ is the ...
1k views

### How to calculate confidence interval for option price?

I model option prices for European call using Monte Carlo method. What is the proper way to calculate the confidence interval? A. -> Calculate the payoffs (there will be number of zeros as some ...
72 views

### How to calculate 5 years return & STD for ETF?

I want to calculate by-myself 5 year return & STD for SPY ETF. What I did: Downloaded to Excel from yahoo finance historical data for the ETF (daily Adj. Close) from ...
454 views

### Impulse response function interpretation

I would need a quick help with Impulse response function interpretation which I have done after Vector autoregression model in stata. I need to understand how to interpret IRF graph or table values ...
708 views

### High values of skewness and kurtosis of realized protfolio returns

I am investigating some asset allocation strategies and I am wondering about the results I obtain. I am working on monthly and weekly data of the same stock indices (SP500, FTSE 100 etc). And when I ...
408 views

### Monte Carlo Convergence

Let $\{X_i\}$ be an i.i.d. sample of $X$ with $E(X) = \mu$ and $Var(X) = \sigma^2$. We know a MC estimate converges to the true value almost surely by the SLLN. That is,  \bar{X}_n \to \mu, \...
77 views

### state space for affine yield curve

i would like to reproduce in R the working paper " Affine free arbitrage class of Nelson Siegel term structure". The authors considering the equation of nelson siegel plus an adjustment term(C(t,T)) ...
54 views

### What is wrong in my non-linear estimation sample code?

I am trying to reproduce the code and plot you see here on pages 8,9 and 10 which was coded in MATLAB, but I'd like to convert it to R code. I believe I converted the MATLAB code below to R syntax ...
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 ...
151 views

### Fitting (marginal/multivariate) distributions to financial return data

I have calculated the simple arithmetic return on a number of different financial securities and am fitting both a Student-T and Generalised Pareto Distribution. My question is can I just use the ...
149 views

### Calculating unweighted performance of stocks within a period

The well known calculation of unweighted index of stocks is just calculating an arithmetic average. And then, to calculate the performance of the index, I calculate the %change of the unweighted ...
773 views

### Is variance additive only under Log-returns?

Can't seem to figure this one out by thinking it through. Let's say that the simple return $R_t=P_{t+1}/P_t -1$ is assumed to be $R_t \sim iid N(0,\sigma^2)$. Thus, a two period return would be \$(1+...
618 views

### Weights Blowing up in PCA

I'm using daily settlement data to get yield levels for a couple of products. From this data I am doing PCA on a rolling collection of the yield levels. I have been using sci-kit learn's PCA function, ...