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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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2answers
44 views

Annualisation of Downside Deviation

Is it possible to annualise the downside deviation? If so, on the basis of what theory? The downside deviation (DD) of a series of daily returns is computed according to the formula: $\text{DD} = \...
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0answers
51 views

What is 'conditional variance' in a GARCH model?

How can a single observation possess variance (by definition it is 0)? For example, we read notation such as sigma(t) as the conditional variance at time t? Yet GARCH's generate conditional variances ...
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0answers
49 views

Nonlinearity in returns?

Reading academic papers on hedge funds, I find that many authors saying that hedge fund returns are often non-linear and thus many simple quantitative techniques are not suitable. It seems like they ...
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1answer
111 views

How to calculate one-year forward one-year rate? [closed]

I'm just a little lost on how to calculate forward rates. I know this is an easy question, but, if we are given a one-year and two-year zero rate (let's say, for the sake of the argument, 2% and 3% ...
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0answers
22 views

Gluing the error terms to a VAR model

I am trying to simulate a VAR model with heterokskedastic errors. I have no problem simulating a VAR model, And I have no problem simulating heteroskedastic errors. My problem is trying to do ...
1
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1answer
38 views

Cross Product Ratio Analysis

Can you please advise? I have been recently trying to sort this out for couple of days but cannot get the same numbers as previous authors: The equation is shown in Agarwal and Naik Multi-Period ...
1
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0answers
31 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
34 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(...
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1answer
100 views

How did Dickey and Fuller know something was wrong?

I am interested in testing if there is size distortion through simulations. I have recently been interested in replicating Dickey and Fuller (1979) and this source from another post helped a lot, here ...
0
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1answer
54 views

Mean Variance optimization on hourly data with gaps

I'm building a mean variance optimizer for a portfolio of FX, commodity and bond futures. The input data is hourly returns for each underlying. Given each underlying has different market opening hours,...
-1
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1answer
73 views

How to calculate number of round trips given volatility?

Suppose we know stock price volatility is normally distributed with mean = 0 and annual volatility say 20%. Let's assume markets never close and we can trade at 1 second intervals. Let's assume stock ...
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2answers
55 views

Testing which index is a better benchmark to track stock prices

Let's say a Hedge Fund is tracking a stock price. Now the fund has three columns of data, Stock price, Index 1, and Index 2. All of these have data from 2016/01/01 - 2017/01/01. If the fund is to ...
2
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2answers
91 views

Statistical estimation vs Stochastic calibration of models

I have never been able to deduce the precise differences between model building from the statistical perspective and the stochastic processes/calibration perspective. I can only infer that these are ...
1
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1answer
53 views

Kalman filter state/measurement noise

In a linear Kalman filter, we assume that the state and measurement noise are white noise N(0,Q) and N(0,R) respectively. Is it common practice to test these hypothesis? And what are the most common ...
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0answers
21 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 ...
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2answers
63 views

Sample from aggregate portfolio distribution versus individual asset distributions

Suppose I have three assets $x_1,x_2,x_3$ in a portfolio with weights $W=\begin{bmatrix} w_1 \\ w_2 \\ w_3 \end{bmatrix} $, expected returns $R=\begin{bmatrix} \mu_1 \\ \mu_2 \\ \mu_3 \end{bmatrix}$, ...
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0answers
22 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 ...
0
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1answer
67 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 ...
2
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0answers
76 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 ...
1
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1answer
73 views

selecting key performance indicators for a stock

Say, I read a financial statement of a company, and it reports, maybe 20-30 metrics, both generic, like revenue, free cash flow and specific to the company, like iphone sales etc. Is there a ...
2
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1answer
121 views

Why does computing correlation between index levels vs. percentage changes yield completely different results?

I am examining the relationship between the S&P 500 and the Industrial Production Index. Computing the correlation between these these variables yield vastly different results if expressed in ...
0
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2answers
135 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), ...
3
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0answers
88 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 ...
1
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1answer
97 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 ...
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3answers
89 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 ...
0
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2answers
101 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 ...
3
votes
1answer
474 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 ...
0
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1answer
153 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 ...
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0answers
25 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 ...
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0answers
60 views

Statistical methods to compare two financial series data

I have two financial series data, x and x', where x' was formed form ...
0
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0answers
36 views

Joint hypothesis tests

When running regressions, $$Y_t=\alpha+\beta_{9}x_{9,t-1}+\beta_2x_{2,t-1}+\beta_3x_{3,t-1}+\beta_4x_{4,t-1}+\varepsilon_t (1)$$ $$Y_t=\alpha+\beta_1x_{1,t-1}+\beta_2x_{2,t-1}+\beta_3x_{3,t-1}+\...
2
votes
1answer
31 views

Deriving the long-horizon predictive regression and hypothesis testing

I am working on the long-horizon regression, $$y_{t,K}=\mu+\beta_1x_{1,t-1}+...+\beta_nx_{n,t-1}+e_{t} $$, where $$y_{t,K}=y_{t}+y_{t+1}+...+y_{t+K-1}$$ and there can be multiple x's. So I am ...
4
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0answers
135 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 ...
1
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0answers
45 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: ...
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0answers
22 views

Informal definition of the almost complete convergence

I'm searching for the informal definition of the almost complete convergence (P. L. Hsu and H. Robbins (1947), Dugué (1955)), which means a definition without any mathematics formula. Thank you for ...
3
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2answers
253 views

Filtering smallest eigenvalues

In Risk Budgeting and Diversification Based on Optimized Uncorrelated Factors [1], which introduces minimum torsion bets, Meucci gives an example involving the computation of covariance matrices on ...
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1answer
114 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 ...
1
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0answers
32 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 ...
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2answers
88 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 ...
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0answers
36 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 ...
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0answers
33 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 ...
1
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0answers
45 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 ...
1
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1answer
75 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.
2
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0answers
85 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.
1
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1answer
93 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
298 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
266 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) ...
1
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1answer
63 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 ...
14
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3answers
3k 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
352 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; ...